A crate with mass 28.5 kg initially at rest on a warehouse floor is acted on by a net horizontal force of 12.0 N. Part A What is the magnitude of acceleration? Express your answer in meters per second squared. Part B How far does the crate travel in 13.5 s? Express your answer in meters. Submit Request Answer Part C What is its speed at the end of 13.5 s? Express your answer in meters per second.
At the surface of Jupiter's moon lo, the acceleration due to gravity is 1.81 m/s2. A watermelon has a weight of 49.0 N at the surface of the earth. In this problem, use 9.80 m/s2 for the acceleration due to gravity on earth. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Mass and weight. Part A What is its mass on the earth's surface? Express your answer in kilograms. Part B What is its mass on the surface of lo? Express your answer in kilograms. Submit Request Answer Part C What is its weight on the surface of lo? Express your answer in newtons.
A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of 20.0∘, and the man pulls upward with a force F→ whose direction makes an angle of 30.0∘ with the ramp in (Figure 1). Part A How large a force F→ is necessary for the component Fx parallel to the ramp to be 90.0 N ? Express your answer with the appropriate units. F = Submit Request Answer Part B How large will the component Fy perpendicular to the ramp then be? Express your answer with the appropriate units. Figure 1 of 1 Fy = Submit Request Answer
A 88.5 kg skater moving initially at 2.40 m/s on rough horizontal ice comes to rest uniformly in 3.52 s due to friction from the ice. Part A What force does friction exert on the skater? Express your answer with the appropriate units. Enter positive value if the direction of the force is the same as that of the initial velocity of the skater and negative value if the direction of the force is opposite.
For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Mass and weight. Part A Superman throws a 2400 N boulder at an adversary. What horizontal force must Superman apply to the boulder to give it a horizontal acceleration of 15.0 m/s2 ? Express your answer with the appropriate units.
A student with mass 55 kg jumps off a high diving board. Part A Using 6.0×1024 kg for the mass of the earth, what is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of 9.8 m/s2 ? Assume that the net force on the earth is the force of gravity she exerts on it. Express your answer in meters per second squared. |a| = m/s2
A .22 caliber rifle bullet traveling at 350 m/s, strikes a large tree and penetrates it to a depth of 0.130 m. The mass of the bullet is 1.80 g. Assume a constant retarding force. Part A How much time is required for the bullet to stop? Express your answer with the appropriate units. Submit Request Answer Part B What force, in newtons, does the tree exert on the bullet? Express your answer in newtons.
A chair of mass 14.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 40.0 N that is directed at an angle of 39.0∘ below the horizontal and the chair slides along the floor. Part A Use Newton's laws to calculate the normal force that the floor exerts on the chair. Express your answer in newtons. n = N
A 5.20 kg bucket of water is accelerated upward by a cord of negligible mass whose breaking strength is 85.0 N. Part A If the bucket starts from rest, what is the minimum time required to raise the bucket a vertical distance of 15.0 m without breaking the cord? Express your answer with the appropriate units. tmin = Value Units
Boxes A and B are connected to each end of a light vertical rope, as shown in the following figure. A constant upward force 90.0 N is applied to box A. Starting from rest, box B descends 12.0 m in 3.50 s. The tension in the rope connecting the two boxes is 34.0 N (Figure 1). Part A What is the mass of box B ? Express your answer with the appropriate units. Submit Request Answer Part B What is the mass of box A ? Express your answer with the appropriate units. Submit Request Answer
A parallel-plate capacitor with circular plates and a capacitance of 11.7 μF is connected to a battery which provides a voltage of 12.2 V. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Properties of a parallel-plate capacitor. Part A What is the charge on each plate? Express your answer with the appropriate units. Q = Part B How much charge would be on the plates if their separation were doubled while the capacitor remained connected to the battery? Express your answer with the appropriate units. Q = Value Units Submit Request Answer Part C How much charge would be on the plates if the capacitor were connected to the battery after the radius of each plate was doubled without changing their separation? Express your answer with the appropriate units.
The Figure (Figure 1) below shows a system of four capacitors, where the potential difference across ab is 50.0 V. Figure 1 of 1 Part A Find the equivalent capacitance of this system between a and b. Submit Request Answer Part B How much charge is stored by this combination of capacitors? Submit Request Answer Part C How much charge is stored in the 10.0−μF capacitor? Submit Request Answer Part D How much charge is stored in the 9.0−μF capacitor?
We have a soap bubble on the end of a thin glass pipe, as shown (Figure 1). The bubble has a radius r and carries a charge q. Air is free to enter or leave the bubble through the pipe. Figure 1 of 1 Part A Find the electrostatic potential energy Uelec of the bubble. (Ignore any effect from the glass tube. ) Write your answer in terms of q, r and ϵ0. Part B Find the radius r at which the total potential energy is a minimum. Write your answer in terms of q, τ and ϵ0.
Part A A budding electronics hobbyist wants to make a simple 1.4 nF capacitor for tuning her crystal radio, using two sheets of aluminum foil as plates, with a few sheets of paper between them as a dielectric. The paper has a dielectric constant of 4.7, and the thickness of one sheet of it is 0.15 mm. If the sheets of paper measure 30 cm × 39 cm and she cuts the aluminum foil to the same dimensions, how many sheets of paper should she use between her plates to get the proper capacitance? Express your answer as a whole number. Part B Suppose for convenience she wants to use a single sheet of posterboard, with the same dielectric constant but a thickness of 10.0 mm, instead of the paper. What area of aluminum foil will she need for her plates to get her 1.4 nF of capacitance? Express your answer using two significant figures. A = m2 Submit Request Answer Part C Suppose she goes high-tech and finds a sheet of Teflon of the same thickness as the posterboard to use as a dielectric. Will she need a larger or smaller area of Teflon than of posterboard? She will need a larger area of Teflon than of posterboard. She will need a smaller area of Teflon than of posterboard.
Part A Suppose that a conducting sphere of radius R carries a charge q. Find the electric potential V on the surface of the sphere. (Assume that infinitely far away from the sphere the potential is 0. ) Write your answer in terms of q, R and ϵ0. Submit Request Answer Part B Find the potential energy U of the charged sphere. Write your answer in terms of q, R and ϵ0. U = Part C Now suppose there are two conducting spheres with radii R1 and R2. We have a total charge Q to place on these two spheres, so we put q on sphere 1 and Q−q on sphere 2. Find the total potential energy U of both spheres. (Assume the spheres are far enough apart that they don't interact with each other. Thus the total energy is U = U1+U2, with U1 and U2 as in Part B. ) Write your answer in terms of q, Q, R1, R2 and ϵ0. Submit Request Answer Part D If we connect the two spheres with a thin wire, charge will flow from one to the other until the total potential energy is a minimum. What value of q makes the potential energy U as small as possible? Write your answer in terms of Q, R1, R2 and ϵ0. Part E After we connect the wire and allow the charge to redistribute itself, what is the potential V1 on the surface of sphere 1 ? Write your answer in terms of Q, R1, R2 and ϵ0. Submit Request Answer Part F After we connect the wire and allow the charge to redistribute itself, what is the potential V2 on the surface of sphere 2? Write your answer in terms of Q, R1, R2 and ϵ0.
The capacitors in the Figure (Figure 1) are initially uncharged and are connected, as in the diagram, with switch S open. The applied potential difference is Vab = + 210 V. Figure 1 of 1 Part A What is the potential difference Vcd ? Express your answer using two significant figures. Submit Request Answer Part B What is the potential difference Vad after switch S is closed? Submit Request Answer Part C What is the potential difference Vdb after switch S is closed? Vdb = V Submit Request Answer Part D What is the potential difference Vac after switch S is closed? Vac = V Part E What is the potential difference Vcb after switch S is closed? Submit Request Answer Part F How much charge flowed through the switch when it was closed?
The dielectric to be used in a parallel-plate capacitor has a dielectric constant of 4.10 and a dielectric strength of 1.50×107 V/m. The capacitor is to have a capacitance of 1.50×10−9 F and must be able to withstand a maximum potential difference of 5.90×103 V. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Energy density, both before and after the. Part A What is the minimum area the plates of the capacitor may have? Express your answer in meters squared.
Electronic flash units for cameras contain a capacitor for storing the energy used to produce the flash. In one such unit, the flash lasts for a time interval of 1.46×10−3 s with an average light power output of 3.50×105 W Part A If the conversion of electrical energy to light has an efficiency of 92.0% (the rest of the energy goes to thermal energy), how much energy must be stored in the capacitor for one flash? Express your answer in joules. Submit Request Answer Part B The capacitor has a potential difference between its plates of 105 V when the stored energy equals the value calculated in part A. What is the capacitance? Express your answer in farads.
For the capacitor network shown in (Figure 1), the potential difference across ab is 12.0 V. Part A Find the total energy stored in this network. Express your answer with the appropriate units. Submit Request Answer Part B Find the energy stored in the 4.80 μF capacitor. Express your answer with the appropriate units. U4.80 μF = Figure 1 of 1
Two capacitors are connected parallel to each other and connected to the battery with voltage V. Let C1 and C2 be their capacitances. Part A How much energy is stored in the capacitors? Express your answer in terms of C1, C2 and V. U = Submit Request Answer Part B Suppose the charged capacitors are disconnected from the battery and from each other, and then reconnected to each other with plates of opposite sign together. How much energy is stored in the capacitors now? Express your answer in terms of C1, C2 and V. U =
A 50.0 kg wrecking ball hangs from a uniform, heavy-duty chain of mass of 22.0 kg. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of One-dimensional equilibrium: tension in a rope with mass Part A Find the maximum tension in the chain. Express your answer with the appropriate units. Part B Find the minimum tension in the chain. Express your answer with the appropriate units. Submit Request Answer Part C What is the tension at a point three-fourths of the way up from the bottom of the chain? Express your answer with the appropriate units.
A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh.
A 33.0 kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds 313 N. Then you must reduce your push to 208 N. to keep it moving at a steady 25.0 cm/s. Part A What are the coefficient of static and kinetic friction between the crate and the floor? Enter your answers numerically separated by a comma. Submit Request Answer Part B What push must you exert to give it an acceleration of 1.10 m/s2 ? Express your answer with the appropriate units. Part C Suppose you were performing the same experiment on this crate but were doing it on the moon instead, where the acceleration due to gravity is 1.62 m/s2. What magnitude push would cause it to move? Express your answer with the appropriate units. Submit Request Answer Part D What would its acceleration be if you maintained the push in part B ? Express your answer with the appropriate units.
A baseball is thrown straight up. The drag force is proportional to v2. The positive y direction is upward. Part A In terms of g, what is the y-component of the ball's acceleration when its speed is half its terminal speed value and it is moving up? Express your answer as a multiple of acceleration due to gravity. View Available Hint(s) ay = g Part B In terms of g, what is the y-component of the ball's acceleration when its speed is half its terminal speed and it is moving back down? Express your answer as a multiple of acceleration due to gravity. View Available Hint(s) ay = g
A small remote-control car with a mass of 1.61 kg moves at a constant speed of v = 12.0 m/s in a vertical circle inside a hollow metal cylinder that has a radius of 5.00 m. (Figure 1) For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Uniform circular motion in a vertical circle. Figure 1 of 1 Part A What is the magnitude of the normal force exerted on the car by the walls of the cylinder at point A (at the bottom of the vertical circle)? Express your answer in newtons. Submit Request Answer Part B What is the magnitude of the normal force exerted on the car by the walls of the cylinder at point B (at the top of the vertical circle)? Express your answer in newtons.
Two 16.0 N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling. Part A What is the tension in the rope? Express your answer with the appropriate units. Submit Request Answer Part B What is the tension in the chain? Express your answer with the appropriate units. Value
In the figure (Figure 1) the weight w is 65.4 N. Figure 1 of 1 Part A What is the tension in the diagonal string? Express your answer in newtons. Submit Request Answer Part B Find the magnitudes of the horizontal forces F→1 and F→2 that must be applied to hold the system in the position shown. Express your answers in newtons separated by a comma. Submit Request Answer
Two crates connected by a rope lie on a horizontal surface (Figure 1). Crate A has mass mA and crate B has mass mB. The coefficient of kinetic friction between each crate and the surface is μk. The crates are pulled to the right at constant velocity by a horizontal force F→. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Friction in horizontal motion. Figure 1 of 1 Part A In terms of mA, mB, and μk, calculate the magnitude of the force F→. Express your answer in terms of some or all of the variables mA, mB, μk, and acceleration due to gravity g. Submit Request Answer Part B In terms of mA, mB, and μk, calculate the tension in the rope connecting the blocks. Include the free-body diagram or diagrams you used to determine each answer. Express your answer in terms of some or all of the variables mA, mB, μk, and acceleration due to gravity g.
Two blocks connected by a cord passing over a small, frictionless pulley rest on frictionless planes (the figure ( Figure 1)). Figure 1 of 1 Part A Which way will the system move when the blocks are released from rest the blocks will slide to the left the blocks will slide to the right Submit Request Answer Part B What is the acceleration of the blocks? Express your answer in meters per second squared. a = m/s2 ? Submit Request Answer Part C What is the tension in the cord? Express your answer in newtons.
A racetrack curve has radius 120.0 m and is banked at an angle of 18⋅0∘. The coefficient of static friction between the tires and the roadway is 0.300 . A race car with mass 900 kg rounds the curve with the minimum speed needed to not slide down the banking. Part A As the car rounds the curve, what is the normal force exerted on it by the road? Express your answer with the appropriate units. n = Part B What is the car's speed? Express your answer with the appropriate units. v =
Calculate the actual force of friction upon block A of the system in Figure. The coefficient of friction for the surfaces is 0.5.
Determine the magnitude of the friction force of the block when P = 110 N and W = 460 N. (Round the final answer to one decimal place. ) The magnitude of the friction force is N
Friction: A 4.00−kg block rests between the floor and a 3.00−kg block as shown in the figure. The 3.00−kg block is tied to a wall by a horizontal rope. If the coefficient of static friction is 0.800 between each pair of surfaces in contact, what horizontal force F must be applied to the 4.00−kg block to make it move? ( 78.4 N)
In the figure below, the mass of block A is 6.5 kg. The coefficient of static friction between the block and the surface on which it rests is 0.30 . The mass of w is 1.2 kg, and the system is in equilibrium. Find the friction force exerted on block A. a. 19.5 N b. 63.7 N c. 11.8 N d. 7.7 N
A block is placed on an incline. The coefficient of static friction between the block and the plane is 0.59 . What is the maximum value for θ, such that the block remains in equilibrium? A) 2.70∘ B) 30.5∘ C) 59.5∘ D) 45.0∘ E) 67.2∘
mB is massive enough such that it is moving downwards pulling mA up the incline. The coefficient of kinetic friction between mA and the incline is μk. The pulley is massless and frictionless. For this system: The speed is constant. The speed is increasing. The speed is decreasing. The speed is constant or is increasing. The speed is constant or is decreasing.
The uniform crate has a mass of 160 kg. The coefficient of static friction between the crate and the floor is μs = 0.2. The coefficient of static friction between the man's shoes and the fioor is μs′ = 0.45. Assume the man exerts only a horizontal force on the crate. (Figure 1 ) Figure 1 of 1 Part A Determine the smallest mass of the man so he can move the crate. Express your answer to three significant figures and include the appropriate units. m = Value Units Submit Request Answer
The coefficient of static friction between the rope and the fixed cylinder below is 0.12. If the rope is wrapped 2.5 turns around the cylinder, what is the smallest weight W that will prevent the 1000−lb block from dropping?
Block B in the figure weighs 700 N. The coefficient of static friction between block and table is 0.267; angle θ is 33.1∘; assume that the cord between B and the knot is horizontal. Find the maximum weight of block A for which the system will be stationary. Number Units
To measure the static friction coefficient between a 3.39−kg block and a vertical wall, the setup shown in the drawing is used. A spring (spring constant = 537 N/m ) is attached to the block. Someone pushes on the end of the spring in a direction perpendicular to the wall until the block does not slip downward. If the spring in such a setup is compressed by 0.0600 m, what is the coefficient of static friction? Number Units
23. E. A block of mass M = 1.0 kg is originally at rest slides without friction on the track seen below. It collides elastically with a smaller block of mass m = 12 M which is originally at rest. If the bigger block at height, h1 = 1.0 m, then predict the final height h′ to which the smaller block will rise. Assume no friction until after the collision and that the ramp on the right is inclined at θ = 40∘ with μk = 0.60 HELP: Apply conservation of total energy on the ramp to the right: ΔEmech = Wfriction between initial and final points P and Q
Three objects are connected as shown in the figure. The strings and frictionless pulleys have negligible masses, and the coefficient of kinetic friction between the 2.0−kg block and the table is 0.36 . What is the acceleration of the 2.0−kg block?
For the figure below, if the box is moved 2 m to the left, how much actual work is done (in J )? Assume that there is no friction between the box and surface.
Two blocks are connected by a cord that is passing over a small, frictionless pulley as shown in the picture. There is no friction between the blocks and the planes. The cord has negligible mass. Assume that the mass of the pulley is negligible. M = 100 kg m = 50.0 kg θ1 = 30.0∘ θ2 = 53.1∘ a. Which direction will the system move when the blocks are released from rest? Explain/justify your answer. b. Find an algebra expression for the acceleration of the blocks as a function of given variables and standard constants such as g. c. Calculate the acceleration and the tension in the cord. d. Now assume that pulley is a solid cylinder mass mc = 4.00 kg and radius r = 10.0 cm. Calculate the acceleration of the blocks.
Consider the Atwood machine in Fig. 1, where two blocks, one resting on top of the other. The blocks are tied to an ideal pulley (massless) through the rope and the rope can slip through the pulley without friction. The coefficients of static and kinetic frictions between the blocks are μ, and there is no friction between the block and the ground. Someone pulled the pulley with a force F. a. What will the maximum acceleration of the system be if the top block does not slip? ( 3 points) b. Now, assume that slipping does occur between the blocks. Draw the free-body diagrams of two blocks and the pulley w. (4 points) c. Express the acceleration of each block in terms of F, m1, m2, μ, and g when there is slipping. (Hint: pulley is massless, so the sum of the tensions in the rope equals to F ) (3 points)
The 24-m-long gate (see the Figure) is a quarter circle hinged at H. Determine the horizontal force, P. required to hold the gate in place. Neglect friction at the hinge and the weight of the gate. Give your results in SI units
One end of a uniform 3.80-m-long rod of weight Fg is supported by a cable at an angle of θ = 37º with the rod. The other end rests against the wall, where it is held by friction as shown in the figure below. The coefficient of static friction between the wall and the rod μs = 0.450. Determine the minimum distance x from point A at which an additional object, also with the same weight Fg, can be hung without causing the rod to slip at point A.
A mass m = 0.330 kg is attached to a spring with spring constant k = 1400 N/m and is free to oscillate in a horizontal direction (as in the figure). The mass is pulled, stretching the spring. When the mass is released, the system oscillates. Assume that friction and air resistance can be ignored. What is the angular frequency of this oscillation? ω = rad/s What is the simple frequency of this oscillation? f = Hz What is the period of the oscillation? T = s How many cycles will the system have undergone in a total time of 50 seconds? N =
You want to produce three 1.00-mm-diameter cylindrical wires, each with a resistance of 2.00 Ω at room temperature. One wire is gold ( ρg = 2.44×10−8 Ω⋅m ), one is copper ( ρc = 1.72×10−8 Ω⋅m ), and one is aluminum (ρa = 2.75×10−8 Ω⋅m). Part A What will be the length of the gold wire? Express your answer with the appropriate units. Submit Request Answer Part B What will be the length of the copper wire? Express your answer with the appropriate units. Part C What will be the length of the aluminum wire? Express your answer with the appropriate units. Submit Request Answer Part D Gold has a density of 1.93×104 kg/m3. What will be the mass of the gold wire? Express your answer with the appropriate units. Part E If gold is currently worth $40.0 per gram, what is the cost of the gold wire? Express your answer in dollars.
The power rating of a light bulb (such as a 100 W bulb) is the power it dissipates when connected across a 120 V potential difference. Part A What is the resistance of a 150 W bulb? Express your answer to three significant figures and include the appropriate units. Submit Request Answer Part B How much current does the 150 W bulb draw in normal use? Express your answer to three significant figures and include the appropriate units. Part C What is the resistance of a 50 W bulb? Express your answer to two significant figures and include the appropriate units. Submit Request Answer Part D How much current does the 50 W bulb draw in normal use? Express your answer to two significant figures and include the appropriate units.
The circuit shown in (Figure 1) contains two batteries, each with an emf and an internal resistance, and two resistors. Figure 1 of 1 Part A Find the magnitude of the current in the circuit. Express your answer with the appropriate units. Submit Request Answer Part B Find the direction of the current in the circuit. counterclockwise clockwise Submit Request Answer Part C Find the terminal voltage Vab of the 16.0 V battery. Express your answer with the appropriate units. Submit Request Answer Part D Find the potential difference Vac of point a with respect to point c. Express your answer with the appropriate units. Vac = Value Units
When switch S in (Figure 1) is open, the voltmeter V of the battery reads 3.15 V. When the switch is closed, the voltmeter reading drops to 2.91 V, and the ammeter A reads 1.63 A. Assume that the two meters are ideal, so they don't affect the circuit. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of A source with a short circuit. Figure 1 of 1 Part A Find the emf. Express your answer in volts. Submit Request Answer Part B Find the internal resistance r of the battery. Express your answer in ohms. Submit Request Answer Part C Find the resistance R. Express your answer in ohms. R =
A person with body resistance between his hands of 13 kΩ accidentally grasps the terminals of a 16 kV power supply. Part A If the internal resistance of the power supply is 2200 Ω, what is the current through the person's body? Express your answer with the appropriate units. I = Value Units Part B What is the power dissipated in his body? Express your answer with the appropriate units. Submit Request Answer Part C If the power supply is to be made safe by increasing its internal resistance, what should the internal resistance be for the maximum current in the above situation to be Imax = 1.0 mA or less? Express your answer with the appropriate units. rint = Value
A 14 gauge copper wire of diameter 1.628 mm carries a current of 12.5 mA. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Electric field, potential difference, and resistance in a wire Part A What is the potential difference across a 2.00 m length of the wire (for copper ρ = 1.72×10−8 Ω⋅m) ? Express your answer with the appropriate units. Submit Request Answer Part B What would the potential difference in part A be if the wire were silver instead of copper, but all else was the same (for silver ρ = 1.47×10−8 Ω⋅m )? Express your answer with the appropriate units.
A ductile metal wire has resistance R. Part A What will be the resistance of this wire in terms of R if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched. (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area. ) Express your answer in terms of R.R′ = R
An experimenter wants to make a layer of silver 40.0 Angstroms thick by evaporating silver onto a clean glass surface in vacuum. ( 1 Angstrom = 10−10 m. ) He first lays down by evaporation a fairly thick layer, with a central strip masked so that it remains bare (the shaded semicircles shown below). Then, using another mask in the manner of a stencil, he evaporates onto the glass a strip of the same width running across he gap (the shaded vertical rectangle), meanwhile using the heavy patches as terminals for measurement of resistance. (Figure 1) Part A At what value of the resistance should he stop the evaporation? (The resistivity of silver at room temperature is 1.47×10−8 Ωm. ) Submit Request Answer Figure 1 of 1
A battery has an EMF of V and internal resistance r. We want to use this battery to power a heating element, which is basically just an external resistor with resistance R. By varying R we can vary the amount of power dissipated in the heating element. Part A Find the maximum possible power that the battery can deliver to an external resistor. Express your answer in terms of V and r. Pmax =
An artist creates a solid sculpture made from 8.00 kg of aluminum. She wishes to create an identical sculpture, using the same mold used to make the original, out of solid silver. What is the mass (in kg ) of the silver sculpture? (The density of aluminum is 2.70×103 kg/m3, and that of silver is 10.50×103 kg/m3.) kg
A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure a. The atoms reside at the corners of cubes of side L = 0.250 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal, as shown in Figure b. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves. nm
The figure below shows a frustum of a cone. Match each of the expressions with the quantity it describes. (a) π(r1 + r2)[h2 + (r1 − r2)2]1 /2 the total circumference of the flat circular faces the volume the area of the curved surface (b) 2π(r1 + r2) the total circumference of the flat circular faces the volume the area of the curved surface (c) πh(r12 + r1r2 + r22)/3 the total circumference of the flat circular faces the volume the area of the curved surface
An Egyptian pyramid contains approximately 2.10 million stone blocks. The average weight of each block is 2.10 tons. What is the weight of the pyramid in pounds? Ibs
How many ping pong balls would fit into a room 3 m wide by 4 m long by 4 m tall (without being crushed)? Estimate the order of magnitude. ∼103 ∼106 ∼1012
A doctor prescribes medicine to a patient to treat a high cholesterol level. The patient is required to take one pill per day. The pharmacy issues a container of pills to the patient that will last for three and one-half months. How many containers of pills constitute a year's supply for the patient? (Enter a whole number of containers. ) containers/year
A high fountain of water is located at the center of a circular pool as shown in the figure below. A student walks around the pool and measures its circumference to be 39.0 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation of the top of the fountain to be ϕ = 50.0∘. How high is the fountain? m (i)
Water is poured into a bowl at a constant rate of 15.0 cm3/s. The bowl has a circular cross section, but does not have a uniform diameter. (That is, different horizontal cross sections taken at different heights of the bowl have different diameters. ) (a) As the water fills the bowl, the water level reaches a point where the diameter of the bowl is d1 = 1.45 cm. What is the rate (in cm/s ) at which the water level rises at this diameter? ◻ cm/s (b) As the water continues to fill the bowl, the water level reaches a point where the diameter of the bowl is d2 = 5.00 cm. What is the rate (in cm/s ) at which the water level rises at this diameter? cm/s
A rectangular reflecting pool is 66.5 ft wide and 126 ft long. What is the area of the pool in square meters? m2
Earth presently has 1.4 billion hectares of arable land, and each hectare produces between 1 and 2 tons of grain annually. What is the amount of grain (in tons/yr) produced annually? tons/yr If every human being became vegetarian (as feeding livestock and consuming the products of livestock is far less efficient), then 200 kg of grain would be sufficient to feed each human being on the planet. Based on this data, what is the number of people Earth can support? (Use your value for the amount of grain produced annually. ) people
The polar coordinates of a point are r = 5.40 m and θ = 250∘. What are the Cartesian coordinates of this point? x = m y = m
A plane takes off from an airport and flies to town A, located d1 = 320 km from the airport in the direction 20.0∘ north of east. The plane then flies to town B, located d2 = 255 km at 30.0∘ west of north from town A. Use graphical methods to determine the distance and direction from town B to the airport. (Enter the distance in km and the direction in degrees south of west. ) distance km direction ∘ south of west
The displacement vectors A→ and B→ shown in the figure below both have magnitudes of 3.25 m. The direction of vector A→ is θ = 36.5∘. (a) Find A→+B→ graphically. magnitude m direction ∘ counterclockwise from the +x axis (b) Find A→−B→ graphically. magnitude m direction ∘ counterclockwise from the +x axis (c) Find B→−A→ graphically. magnitude m direction . counterclockwise from the +x axis (d) Find A→−2 B→ graphically. magnitude m direction ∘ counterclockwise from the +x axis
A vector has an x component of -24.0 units and a y component of 36.0 units. Find the magnitude and direction of this vector. magnitude unit(s) direction ° counterclockwise from the +x axis
A spider is hanging from silk strands, as shown in the figure. The force of gravity on the spider is 0.160 N and is directed downward, and the two tension forces are directed as shown, so that the resultant force on the intersection point of the three strands is zero. The angle between the strands with tensions Tx and Ty is 90∘, and Tx = 0.143 N. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign. ) (i) (a) What is Ty (in N) ? N (b) What is the angle between the x-axis in the figure and the horizontal? (Enter the smallest positive angle in degrees. ) (c) What is the angle between the y-axis in the figure and the horizontal? (Enter the smallest positive angle in degrees. )
A ferry transports tourists among three islands. It sails from the first island to the second island, 5.63 km away, in a direction 37.0∘ north of east. It then sails from the second island to the third island in a direction 80.5∘ west of north. Finally, it returns to the first island, sailing in a direction 28.0∘ east of south. (a) Calculate the distance between the second and third islands. km (b) Calculate the distance between the first and third islands. km
Mariana finds a cave to explore. Starting at the cave entrance, Mariana first follows a passage 75.0 m north, then turns and moves 250 m east, then goes 123 m at an angle 30.0∘ north of east, and finally moves 168 m south. Find the resultant displacement from the cave entrance. Shown is a sketch of the situation not drawn to scale. (Give the magnitude of the displacement in m and the direction in degrees south of east. ) What is the resultant displacement from the entrance? magnitude m direction ∘ south of east
If the polar coordinates of the point (x, y) are (r, θ), determine the polar coordinates for the following points. (Use the following as necessary: r and θ. Assume θ is in degrees. ) (a) (−x, y) (−x, y) = (, ) (b) (−2 x, −2 y) (−2 x, −2 y) = (, ) (c) (3 x, −3 y) (3 x, −3 y) = (, )
Two points in a plane have polar coordinates (2.40 m, 40.0∘) and (3.90 m, 110.0∘). (a) Determine the Cartesian coordinates of these points. (2.40 m, 40.0∘)x = m y = m (3.90 m, 110.0∘)x = m y = m (b) Determine the distance between them. m
Why is the following situation impossible? A skater glides along a circular path. She defines a certain point on the circle as her origin. Later on, she passes through a point at which the distance she has traveled along the path from the origin is smaller than the magnitude of her displacement vector from the origin.
A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the average velocity in the following time intervals. (a) 0 to 2.00 s m/s (b) 0 to 4.00 s m/s (c) 2.00 s to 4.00 s m/s (d) 4.00 s to 7.00 s m/s (e) 0 to 8.00 s m/s
A block is moving along the x-axis and its position varies in time according to the expression x = (3.00 m/s2)t2, where x is in meters and t is in seconds. (a) Determine its position (in m ) at t = 3.90 s. m (b) Determine its position (in m) at t = (3.90 s)+Δt. (Use the following as necessary: Δt. Do not include units in your answer. ) xf = m (c) Evaluate the limit of ΔxΔtasΔt approaches zero to find the velocity (in m/s ) at t = 3.90 s. m/s
A horse and a squirrel participate in a race over a 1.10 km long course. The horse travels at a speed of 16.0 m/s and the squirrel can do 3.30 m/s. The horse runs for 0.880 km and then stops to tease the slow-moving squirrel, which eventually passes by. The horse waits for a while after the squirrel passes and then runs toward the finish line. Both animals cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds. (a) How far (in m ) is the squirrel from the finish line when the horse resumes the race? m (b) For how long in time (in s) was the horse stationary? s
A person takes a trip, driving with a constant speed of 97.5 km/h, except for a 30.0−min rest stop. The person's average speed is 66.2 km/h. (a) How much time is spent on the trip? h (b) How far does the person travel? km
A box proceeds along the x-axis and the figure below shows a record of its velocity as a function of time. Every gridline along the vertical axis corresponds to 2.50 m/s and each gridline along the horizontal axis corresponds to 4.50 s. (Enter your answers in m/s2. Indicate the direction with the signs of your answers. Note that t = 0 at the intersection of the axes. ) (a) Determine the average acceleration of the box in the time interval t = 0 to t = 22.5 s. m/s2 (b) Determine the average acceleration of the box in the time interval t = 22.5 s to t = 67.5 s. m/s2 (c) Determine the average acceleration of the box in the time interval t = 0 to t = 90.0 s. m/s2
A pickup truck traveling at a speed of 40.0 mi/h needs a minimum of 47.0 ft to stop. If the same truck is traveling 70.0 mi/h, determine its minimum stopping distance (in ft ), assuming the same rate of acceleration. ft
A member of the basketball team jumps straight up and their center of mass has a speed of 3.42 m/s as they leave the court. How high above this point is their center of mass at the following times? (Enter your answers in m. Ignore the effects of air resistance, and assume the initial height of their center of mass is at y = 0.)
A foreign automobile manufacturer claims that its sports car will accelerate from rest to a speed of 42.5 m/s in 7.65 s. (a) Determine the magnitude of the average acceleration of the car (in m/s2 ). m/s2 (b) Assume that the car moves with constant acceleration. Find the distance (in m) the car travels in the first 7.65 s. m (c) What is the speed of the car (in m/s ) 10.0 s after it begins its motion if it continues to move with the same acceleration? m/s
A student drives a moped along a straight road as described by the velocity versus time graph in the figure. (a) Sketch a graph of the position versus time, aligning the time coordinates of the two graphs. (b) Sketch a graph of the acceleration versus time directly below the velocity-time graph, again aligning the time coordinates. (c) What is the acceleration (in m/s2) at t = 7.0 s ? m/s2 (d) Find the position relative to the starting point (in m) at t = 7.0 s. m (e) What is the moped's final position (in m) at t = 9.0 s ? m
Make a velocity-time graph for the car in the figure below. Position of the car at various times The speed limit posted on the road sign is 30 km/h. Does the car exceed the speed limit at some time within the interval? Yes No
A chauffeur heads south with a steady speed of v1 = 24.0 m/s for t1 = 3.00 min, then makes a right turn and travels at v2 = 25.0 m/s for t2 = 3.00 min, and then drives northwest at v3 = 30.0 m/s for t3 = 1.00 min. For this 7.00−min trip, calculate the following. Assume +x is in the eastward direction. (a) total vector displacement (Enter the magnitude in m and the direction in degrees south of west. ) magnitude m direction ∘ south of west (b) average speed (in m/s) m/s (c) average velocity (Enter the magnitude in m/s and the direction in degrees south of west. ) magnitude m/s direction ∘ south of west
Suppose the position vector for a particle is given as a function of time by r→(t) = x(t)i^ + y(t)j^, with x(t) = at + b and y(t) = ct2 + d, where a = 1.80 m/s, b = 1.40 m, c = 0.131 m/s2, and d = 1.14 m. (a) Calculate the average velocity during the time interval from t = 2.25 s to t = 3.80 s. (b) Determine the velocity at t = 2.25 s. Determine the speed at t = 2.25 s. m/s
A human expedition lands on an alien planet. One of the explorers is able to jump a maximum distance of 16.0 m with an initial speed of 3.40 m/s. Find the gravitational acceleration on the surface of the alien planet. Assume the planet has a negligible atmosphere. (Enter the magnitude in m/s2. ) m/s2
To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 310 m/s at 54.0∘ above the horizontal. It explodes on the mountainside 35.0 s after firing. What are the x and y coordinates of the shell where it explodes, relative to its firing point? x = m y = m
A particle initially located at the origin has an acceleration of a→ = 1.00ȷ^m/s2 and an initial velocity of v→i = 9.00 i^m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). ( ti^+ t2 j^)m (b) Find the velocity of the particle at any time t. i^+ tj^)m/s (c) Find the coordinates of the particle at t = 3.00 s. x = m y = m (d) Find the speed of the particle at t = 3.00 s. m/s
A snowmobile is originally at the point with position vector 26.3 m at 95.0∘ counterclockwise from the x axis, moving with velocity 4.93 m/s at 40.0∘. It moves with constant acceleration 2.05 m/s2 at 200∘. After 5.00 s have elapsed, find the following. (a) its velocity vector v→ = m/s (b) its position vector r→ = m
NASA's Ames Research Center in Mountain View, California, houses a 20 g centrifuge used to conduct research and training to solve real world problems related to the effects of acceleration on systems. It consists of a horizontal rail system with a 58-foot diameter mounted on a central axis, as shown in the figure below. An astronaut is using the centrifuge for training on high accelerations during spaceflight. The astronaut is seated 29.0 ft from the axis of rotation. At what rotation rate, in revolutions per second, will the astronaut experience a centripetal acceleration of 15.1g? (i) rev/s
An astronaut orbiting the Earth is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 600 km above the Earth's surface, where the free-fall acceleration is 8.17 m/s2. Take the radius of the Earth as 6400 km. Determine the speed of the satellite. m/s Determine the time interval required to complete one orbit around the Earth, which is the period of the satellite. min
This figure (|a→| = 13.5 m/s2) represents the total acceleration of a particle moving clockwise in a circle of radius r = 3.70 m at a certain instant of time. (a) For that instant, find the radial acceleration of the particle. m/s2 (toward the center) (b) For that instant, find the speed of the particle. m/s (c) For that instant, find its tangential acceleration. m/s2 (in the direction of the motion)
A ball swings counterclockwise in a vertical circle at the end of a rope 1.23 m long. When the ball is 35.6∘ past the lowest point on its way up, its total acceleration is (−17.4 i^ + 24.3 j^) m/s2. For that instant, do the following. (a) Sketch a vector diagram showing the components of its acceleration. Choose File No file chosen This answer has not been graded yet. (b) Determine the magnitude of its radial acceleration. m/s2 (c) Determine the velocity of the ball. magnitude m/s direction
A plane is flying to a city 806 km directly north of its initial location. The plane maintains a speed of 193 km/h relative to the air during its flight. (a) If the plane flies through a constant headwind blowing south at 53.5 km/h, how much time (in h) will it take to reach the city? h (b) If instead the plane flies through a constant tailwind blowing at 53.5 km/h, how much time (in h) will it take to reach the city? h (c) If instead the plane flies through a constant crosswind blowing east at 53.5 km/h, how much time (in h) will it take to reach the city? h
A bolt drops from the ceiling of a train car that is accelerating northward at a rate of 3.10 m/s2. (a) What is the acceleration of the bolt relative to the train car? m/s2 at o to the from the vertical (b) What is the acceleration of the bolt relative to the Earth? m/s2
A certain orthodontist uses a wire brace to align a patient's crooked tooth as in the figure below. The tension in the wire is adjusted to have a magnitude of 17.7 N. Find the magnitude of the net force exerted by the wire on the crooked tooth. N
One or more external forces, large enough to be easily measured, are exerted on each object enclosed in a dashed box shown in the figures below. Identify the reaction to each of these forces. (Select all that apply. ) (a) Contact forces force exerted by spring on wall, to the right force exerted by spring on hand, to the left force exerted by spring on wall, to the left force exerted by spring on hand, to the right (b) force exerted by wagon on handle, upward to the left force exerted by wagon on ground, downward force exerted by wagon on planet, upward force exerted by wagon on ground, upward force exerted by wagon on planet, downward force exerted by wagon on handle, downward to the left (c) C (i) force exerted by football on planet, downward force exerted by football on player, downward to the left force exerted by football on player, downward to the right force exerted by football on planet, upward (d) Field forces d force exerted by small-mass object on large-mass object, to the right force exerted by small-mass object on large-mass object, upward force exerted by small-mass object on large-mass object, to the left (e) (i) force exerted by negative charge on positive charge, to the downward force exerted by negative charge on positive charge, to the left force exerted by negative charge on positive charge, to the right (f) (i) force exerted by iron on magnet, upward force exerted by iron on magnet, to the right force exerted by iron on magnet, to the left
You are working for a rocket-launching company that is preparing to launch human space travelers into low-Earth orbit. In test flights, the company is having difficulty with a particular piece of electronic equipment, which is repeatedly damaged by the vibrations of the spacecraft as it launches. In previous launches, the equipment has been kept in a storage locker on the spacecraft, and apparently the vibrations from the walls of the locker have damaged the equipment. Your director has an idea for which he would like you to submit a design. He wants to hang the equipment on a single wire from the forward bulkhead of the spacecraft, surrounded by soft foam. When the spacecraft sits on the launcher nose-up, the equipment will hang downward from its attachment point and maintain this orientation as the spacecraft accelerates straight upward. The equipment and wrapping material have a mass of 19.0 kg. Beginning from rest, the rocket will reach a height of 45.0 km from the surface of the Earth in a time interval of 30.0 s. You need to determine the tension that the wire must be able to withstand in order that it not break during launch. (Give the tension in N.) N
A 4.00-kg object undergoes an acceleration given by a→ = (3.00 i^ + 9.00 j^) m/s2. (a) Find the resultant force acting on the object. ∑F→ = (i^ + j^)N (b) Find the magnitude of the resultant force. |F→| = N
A woman has a weight of 129 lb. Calculate the following. (a) her weight in newtons N (b) her mass in kilograms kg
The gravitational force exerted on a baseball is 2.23 N down. A pitcher throws the ball horizontally with velocity 14.5 m/s by uniformly accelerating it along a straight horizontal line for a time interval of 155 ms. The ball starts from rest. (a) Through what distance does it move before its release? m (b) What are the magnitude and direction of the force the pitcher exerts on the ball? (Enter your magnitude to at least one decimal place. ) magnitude N direction above the horizontal
A 14.0 lb box is placed on the ground. (a) What force (in lb) does the ground exert on the box? magnitude lb direction (b) A cord is attached to the box and run through a pulley directly above the box, so that the cord is vertical. The free end of the cord is then connected to a hanging weight. Calculate the force exerted by the ground on the box (in lb), if the hanging weight is 11.5 lb. magnitude lb direction (c) A 39.5 lb weight is substituted for the 11.5 lb weight. Calculate the new force (in lb) exerted by the floor on the box. magnitude Ib direction
A brick of mass M has been placed on a rubber cushion of mass m. Together they are sliding to the right at constant velocity on an ice-covered parking lot. (a) Draw a free-body diagram of the brick and identify each force acting on it. (b) Draw a free-body diagram of the cushion and identify each force acting on it. (c) Identify all the action–reaction pairs of forces in the brick–cushion–planet system.
A sailboat is moving at a constant velocity due north, as depicted in the figure. The water exerts a drag force on the boat, where the magnitude of F→ is 325 N and θ = 33.0∘. (a) If +x is east and +y is north, find the magnitudes of n→ and p→. (Give your answers in N. ) n = N p = N (b) If +x is θ = 33.0∘ north of east and +y is θ = 33.0∘ west of north, find the magnitudes of n→ and p→. (Give your answers in N. ) n = N p = N (c) Do your answers to parts (a) and (b) agree? Yes No
A 2.70-kg object is moving in a plane, with its x and y coordinates given by x = 4t2 − 4 and y = 2t3 + 1, where x and y are in meters and t is in seconds. Find the magnitude of the net force acting on this object at t = 1.50 s. N
A 12.5 g bullet is moving to the right with speed 220 m/s when it hits a target and travels an additional 21.8 cm into the target. What are the magnitude (in N) and direction of the stopping force acting on the bullet? Assume the stopping force is constant. magnitude N direction
A rubber gasket is at rest on an inclined plane. When the angle of inclination of the plane is increased to 35.7∘, the gasket begins to slide down the incline. Then, when the angle is decreased to 30.8∘, the speed of the gasket is constant. What are the coefficients of static and kinetic friction between the gasket and the incline? static kinetic
A small glider is placed against a compressed spring at the bottom of an air track that slopes upward at an angle of 48.0∘ above the horizontal. The glider has mass 9.00×10−2 kg. The spring has 680 N/m and negligible mass. When the spring is released, the glider travels a maximum distance of 1.50 m along the air track before sliding back down. Before reaching this maximum distance, the glider loses contact with the spring. Part A What distance was the spring originally compressed? Express your answer in meters. Part B When the glider has traveled along the air track 0.500 m from its initial position against the compressed spring, is it still in contact with the spring? Yes No Submit Request Answer Part C What is the kinetic energy of the glider at this point? Express your answer in joules. K = J
A small model car with mass m travels at constant speed on the inside of a track that is a vertical circle with radius r = 3.00 m (Figure 1). The normal force exerted by the track on the car when it is at the bottom of the track (point A ) is equal to 2.50 mg. Figure 1 of 1 Part A How much time does it take the car to complete one revolution around the track. t =
A small rock with mass 0.26 kg is released from rest at point A, which is at the top edge of a large, hemispherical bowl with radius R = 0.48 m (Figure 1). Assume that the size of the rock is small compared to R, so that the rock can be treated as a particle, and assume that the rock slides rather than rolls. The work done by friction on the rock when it moves from point A to point B at the bottom of the bowl has magnitude 0.22 J. Figure 1 of 1 Part A Between points A and B, how much work is done on the rock by the normal force? Express your answer in joules. Submit Request Answer Part B Between points A and B, how much work is done on the rock by gravity? Express your answer in joules. Submit Request Answer Part C What is the speed of the rock as it reaches point B ? Express your answer in meters per second. Submit Request Answer Part D Of the three forces acting on the rock as it slides down the bowl, which (if any) are constant? Check all that apply. None of the forces. Frictional force. Force due to gravity. Normal force. Part E Just as the rock reaches point B, what is the normal force on it due to the bottom of the bowl? Express your answer in newtons.
On a farm, you are pushing on a stubborn pig with a constant horizontal force with magnitude 24.7 N and direction 37.0∘ counterclockwise from the +x-axis. Part A How much work does this force do during a displacement of the pig that is s→ = (5.00 m)ı^? Express your answer with the appropriate units. W = Value Units Part B How much work does this force do during a displacement of the pig that is s→ = −(6.00 m)j^? Express your answer with the appropriate units. Submit Request Answer Part C How much work does this force do during a displacement of the pig that is s→ = −(2.00 m)ı^ + (4.00 m)j^? Express your answer with the appropriate units. W = Value Units
You have just landed on Planet X. You release a 100 g ball from rest from a height of 16.0 m and measure that it takes 2.60 s to reach the ground. Ignore any force on the ball from the atmosphere of the planet. Part A How much does the 100 g ball weigh on the surface of Planet X ? Express your answer with the appropriate units.
A sled with mass 12.00 kg moves in a straight line on a frictionless horizontal surface. At one point in its path, its speed is 3.00 m/s; after it has traveled a distance 4.00 m beyond this point, its speed is 5.00 m/s. Part A Use the work-energy theorem to find the force acting on the sled, assuming that this force is constant and that it acts in the direction of the sled's motion. Express your answer with the appropriate units.
In one day, a 90 kg mountain climber ascends from the 1500 m level on a vertical cliff to the top at 2400 m. The next day, she descends from the top to the base of the cliff, which is at an elevation of 1270 m. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Height of a baseball from energy conservation. Part A What is her change in gravitational potential energy on the first day? Express your answer in joules. Submit Request Answer Part B What is her change in gravitational potential energy on the second day? Express your answer in joules.
A baseball is thrown from the roof of h = 23.4-m-tall building with an initial velocity of magnitude 11.3 m/s and directed at an angle of 53.1∘ above the horizontal. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Energy in projectile motion. Part A What is the speed of the ball just before it strikes the ground? Use energy methods and ignore air resistance. Express your answer in meters per second. Part B What is the answer for part (A) if the initial velocity is at an angle of 53.1∘ below the horizontal Express your answer in meters per second. v2 = m/s Submit Request Answer Part C If the effects of air resistance are included, will part (A) or (B) give the higher speed? The part (A) will give the higher speed. The part (B) will give the higher speed.
In a truck-loading station at a post office, a small 0.200 kg package is released from rest at point A on a track that is one-quarter of a circle with radius 1.60 m (Figure 1). The size of the package is much less than 1.60 m, so the package can be treated as a particle. It slides down the track and reaches point B with a speed of 5.40 m/s. From point B, it slides on a level surface a distance of 3.00 m to point C, where it comes to rest. Figure 1 of 1 m = 0.200 kg Part A What is the coefficient of kinetic friction on the horizontal surface? Submit Request Answer Part B How much work is done on the package by friction as it slides down the circular arc from A to B ? Express your answer in joules. Submit Request Answer
A small block with mass 0.0425 kg slides in a vertical circle of radius 0.500 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the magnitude of the normal force exerted on the block by the track has magnitude 4.05 N. In this same revolution, when the block reaches the top of its path, point B, the magnitude of the normal force exerted on the block has magnitude 0.675 N. Part A How much work was done on the block by friction during the motion of the block from point A to point B ? Express your answer with the appropriate units. Wfriction =
Part A A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45∘ with the vertical. Air resistance is negligible. What is the speed of the rock when the string passes through the vertical position? Express your answer in meters per second. v = m/s Part B What is the tension in the string when it makes an angle of 45∘ with the vertical? Express your answer in newtons. T45 = N Submit Request Answer Part C What is the tension in the string as it passes through the vertical? Express your answer in newtons. Tvert = N