2.2 Two objects are connected by a light string that passes over a frictionless pulley, as shown in the figure below. If the incline has a kinetic friction between mass m2 and the table, and if m1 = 2 kg, m2 = 7 kg, and θ = 55∘, draw free-body diagrams of both objects and (a) Derive the equation for acceleration of this motion. Calculate:- (b) the accelerations of the objects, (c) the tension in the string, (2) (d) the speed of each object 4 s after being released from rest. (2) (e) the kinetic energy of the system after 4 s. (4)
A playful Jack Russel Terrier named "Sally, the Lord of Destruction" is spending the afternoon sitting in her favorite cardboard box. Unbeknownst to her, her nemesis, the giant red ball, is preparing to strike. The 8 kg red ball begins rolling from rest at the top of an 8 meter tall hill, as shown (it rolls down the hill without frictional losses). Upon reaching the bottom of the hill, the big red ball crashes into Sally's box, sending Sally (and her box) forward towards a cliff. Sally and her box together have a mass of 15 kg, and immediately after the collision, the ball bounces backwards off the box, with a velocity of 5 m/s. As Sally is propelled forward, the box immediately begins sliding up a 1 meter tall incline (inclined at 60∘ ) with coefficient of friction of 0.3 (assume the box does not slide over horizontal ground at all, it immediately begins going up the incline). Sally and her box fly off the cliff, but land safely in a kiddie pool filled with tapioca pudding (Sally put it there, since she suspected the giant red ball might attack her). If she lands 4 meters below the spot she left the cliff, how far horizontally did she fly?
A 71.5 kg bungee jumper is standing on a tall platform (h0 = 55 m), as indicated in Figure 10.36. The bungee cord has an unstrained length of L0 = 9 m, and when stretched, behaves like an ideal spring with a spring constant of k = 62.5 N/m. The jumper falls from rest, and the only forces acting on him are his weight and, for the latter part of the descent, the elastic force of the bungee cord. (To simplify the problem slightly, assume the cord is attached at the center of mass and the center of mass drops from rest from the height of the platform. ) Figure 10.36 What is his maximum speed during the fall? m/s How high above the water is he when he reaches this speed? m How high above the water is he when he reaches the lowest point in the fall? m
A 70.4-kg bungee jumper is standing on a tall platform (h0 = 46.4 m), as indicated in the figure. The bungee cord has a natural length of L0 = 8.60 m and, when stretched, behaves like an ideal spring with a spring constant of k = 52.5 N/m. The jumper falls from rest, and it is assumed that the only forces acting on him are his weight and, for the latter part of the descent, the elastic force of the bungee cord. What is his speed when he is at the following heights above the water: (a) hA = 37.8 m, and (b) hB = 13.9 m? (a) Number Units (b) Number Units
An elastic cable is to be designed for bungee jumping from a tower 130 ft high. The specifications call for the cable to be 85 ft long when unstretched, and to stretch to a total length of 100 ft when a 725−lb weight is attached to it and dropped from the tower. Determine the required spring constant k of the cable. (You must provide an answer before moving to the next part.) The required spring constant k of the cable is lb/ft.
The diagram below shows three charges at the corners of a square of sides d = 3.90 m. Here, q1 = q2 = −q and q3 = −1.5 q where q = 7.00 nC. (a) What is the magnitude of the electric field at the center of the square due to these three charges? N/C (b) You now replace q1 in the square with another point charge q4, while leaving q2 and q3 alone. What value of q4 will produce an electric field at the center directed vertically down? nC
The drawing shows a square, each side of which has a length of L = 0.250 m. Two different positive charges q1 and q2 are fixed at the corners of the square. Find the electric potential energy of a third charge q3 = −4.00×10−9 C placed at corner A and then at corner B. EPEA = EPEB = q1 = +1.50×10−9 C q2 = +4.00×10−9 C
A man stands on the roof of a 15 m tall bullding and throws a rock with a speed of 30 m/s at an angle of 33∘ above the horizontal. A) Calculate the maximum height the rock reaches from the ground. B) What is the velocity of the rock at the highest point?
A rectangular box of mass 7 kg rests on a table. A force of 30 N is applied to the box in a direction making an angle of 33 with the horizontal as shown in the figure. a) Draw a free-body diagram showing all the forces (including friction) acting on the box. b) What is the acceleration of the box if there is no friction? c) If we have a friction force of 13.2 N acting on the box, what would the acceleration of the box be?
A long solenoid of radius a with n turns per unit length is carrying a time-dependent current I(t) = I0sin(ωt) where I0 and ω are constants. The solenoid is surrounded by a wire of resistance R that has three circular loops of radius b with b > a. Find the magnitude of current induced in the outer loops at time t = 0. (Use the following as necessary: a, b, n, I0, R, μ0, and ω.) Iouter =
Consider the mass spectrometer shown schematically in the figure below. The magnitude of the electric field between the plates of the velocity selector is 2.60×103 V/m, and the magnetic field in both the velocity selector and the deflection chamber has a magnitude of 0.0400 T. Calculate the radius of the path for a singly charged ion having a mass m = 1.82×10−26 kg. m
The angular velocity of the disk in figure 1 is ω = 4t2 + 3 rad/s, where t is in seconds. (a) (2 points) What is angular velocity and the magnitude of the (linear) velocity of point A on the disk when t = 0.5 s. (b) (3 points) Let θ be the counter-clockwise angle of point A from the horizontal x-axis. The derivative of the angle of A is the angular velocity of A, i. e. dθ dt = ω. Integrate the angular velocity to get an expression for the angle, θ. Use the condition that at t = 0, θ = 0 to solve for the integration constant. (c) (3 points) Differentiate the angular velocity with respect to time to get an expression for the angular acceleration, α(t). (d) (2 points) What is the angular acceleration and the magnitude of the (linear) acceleration of point A at t = 0.5 s. Figure 1: Problem 2
As preparation for this problem, review Conceptual Example 10. The drawing shows two planes each dropping an empty fuel tank. At the moment of release each plane has the same speed of 182 m/s, and each tank is at the same height of 3.72 km above the ground. Although the speeds are the same, the velocities are different at the instant of release, because one plane is flying at an angle of 15.0∘ above the horizontal and the other is flying at an angle of 15.0∘ below the horizontal. Find the (a) magnitude and (b) direction of the velocity with which the fuel tank hits the ground if it is from plane A. Find the (c) magnitude and (d) direction of the velocity with which the fuel tank hits the ground if it is from plane B. In each part, give the direction as a positive angle with respect to the horizontal. Plane B
A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.20 cm and 1.00×103 turns/meter (see figure below). The current in the solenoid changes as I = 3.00 sin120 t, where I is in amperes and t is in seconds. Find the induced emf (in volts) in the 15-turn coil as a function of time. ε =
A 60-g bullet is fired horizontally with a velocity v1 = 600 m/s into the 3-kg block of soft wood initially at rest on the horizontal surface. The bullet emerges from the block with the velocity v2 = 400 m/s, and the block is observed to slide a distance of 2.70 m before coming to rest. Determine the coefficient of kinetic friction μk between the block and the supporting surface.
(a) A person stands a distance d = 0.575 m from the left end of a plank as shown in the figure. The plank is supported by three ropes. Find the tension in each rope (in N ). Assume the plank is uniform, with length L = 2.00 m and mass 25.5 kg, and the weight of the person is 675 N. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) |T→1| = N |T→2| = N |T→3| = N (b) What If? The person now begins to walk to the right. If each of the ropes can support a maximum tension of 750 N, which rope fails first? rope 1 rope 2 rope 3 At what location does this occur (measured in m from the left end of the plank)? m
A golf ball is launched with the initial conditions shown in the figure. Determine the radius of curvature of the trajectory and the time rate of change of the speed of the ball (a) just after launch and (b) at apex. Neglect aerodynamic drag. Assume v = 157 mi/hr, θ = 12∘ Answers: (a) ρ = ft, v˙ = ft/sec (b) ρ = ft, v˙ = ft/sec
A long, straight wire carries a current I. A right angle bend is made in the middle of the wire. The bend forms an arc of a circle of radius r as shown in the figure. Determine the magnetic field at point P, the center of the arc.
Assume that R = 6.00 Ω, ℓ = 1.20 m, and a uniform 2.50 -T magnetic field is directed into the page. (a) Calculate the applied force required to move the bar to the right at a constant speed of 2.00 m/s. (b) At what speed should the bar be moved to produce a current of 0.500 A in the resistor? Answers: (a) 3.00 N (b) 1.00 m/s
A solenoid that is 70.8 cm long has a cross-sectional area of 19.1 cm2. There are 1370 turns of wire carrying a current of 8.54 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy in joules stored in the magnetic field there (neglect end effects). (a) Number Units (b) Number Units
A solenoid of radius r = 1.25 cm and length ℓ = 31.0 cm has 285 turns and carries 12.0 A. a b (a) Calculate the flux through the surface of a disk-shaped area of radius R = 5.00 cm that is positioned perpendicular to and centered on the axis of the solenoid as in the figure (a) μWb (b) Figure (b) above shows an enlarged end view of the same solenoid. Calculate the flux through the tan area, which is an annulus with an inner radius of a = 0.400 cm and outer radius of b = 0.800 cm. μWb
A convex mirror has a focal length of −29 cm. Find the magnification produced by the mirror when the object distance is (a) 12 cm and (b) 24 cm. (a) m1 = (b) m2 =
Building an Adjustable Electromagnet. You and your team are tasked with designing a source to provide a uniform magnetic field for an experiment. The field inside a solenoid is uniform, provided that the length of the solenoid is much longer than its diameter. One useful characteristic of an electromagnet of this type is that the field inside can be adjusted anywhere between 0 T and some maximum value by controlling the current. In addition, the direction of the field, which is always pointed along the axis, can be reversed by reversing the current. The solenoid you are designing must be 3.60 cm in diameter and 25.0 cm long, and must generate a maximum magnetic field of magnitude B = 0.150 T. You intend to wind a cylinder of the given dimensions with wire that can safely pass a maximum current of 6.50 A. (a) How many windings should the solenoid have in order that the magnetic field at the center of the solenoid is 0.150 T when the current is 6.50 A? (b) What total length of wire is required? (c) What current should you pass through the coil to generate a smaller magnetic field of magnitude 3.50×10−2 T at its center, but directed antiparallel to the field generated in part (a)? Assume the current was positive in part (a). (a) Number Units (b) Number Units (c) Number Units
A student estimates that his daily commute to college consists of 10 minutes driving at a speed of 25 mph to a divided highway, followed by 5 minutes in which he accelerates to 70 miles per hour, and 15 minutes driving at 70 mph before slowing to exit and enter the parking lot. The figure shows his velocity in terms of time. (a) What are the units of measure of height, width, and area of the region between the speed graph and the horizontal axis? height width area (b) How far does the student drive on his commute from home before exiting to the parking lot? (Round your answer to one decimal place.) mi
A particle is moving along a horizontal straight line. The graph of its position function (the distance to the right of a fixed point as a function of time) is shown. (Assume 0 ≤ t ≤ 6. ) (a) When is the particle moving toward the right and when is it moving toward the left? (Enter your answers using interval notation.) moving right moving left (b) When does the particle have positive acceleration and when does it have negative acceleration? (Enter your answers using interval notation.) positive acceleration negative acceleration
Figure 1 shows Block A having mass mA = 3 kg and is attached to a spring with stiffness k = 100 kN/m and upstretched length l0 = 0.5 m. Another Block B with mass mB = 5 kg is pressed against Block A so that the spring deforms a distance 0.2 m. The surface plane is not a smooth surface, having the coefficient of kinetic friction between the plane and the block is given as μk. = 0.3. Answer the following Q1 to Q4. Figure 1 Q1. Based on the figure, what are the force components that are acting on Block A? a. Spring force, weight, 2 normal forces, friction force, applied force b. Spring force, weight, normal force, friction force c. Spring force, weight, 2 normal forces, friction force d. Spring force, weight, normal force, friction force, applied force Q2. Draw kinetic diagram for Block A. Q3. Draw kinetic diagram for Block B. Q4. Given aA = aB = a (as block A and block B are moving together), determine the acceleration of the block, a.
The 500 kg concrete culvert with relatively small thickness and mean radius of 0.5 m, resides on a truck, as shown in Figure 2. If the truck has an initial acceleration of 3 m/s2 and is starting from rest, determine the initial culvert's angular acceleration and the minimum coefficient of friction required such that the culvert does not experience any slipping. (25 marks) Figure 2
The flux of the electric field (24 N/C)i^ + (30 N/C)j^ + (16 N/C)k^ through a 2.0 m2 portion of the yz plane is: 32 N⋅m2/C 34 N⋅m2/C 42 N⋅m2/C 48 N⋅m2/C 60 N⋅m2/C
A cylindrical wastepaper basket with a 0.15-m radius opening is in a uniform electric field of 300 N/C, perpendicular to the opening. The total flux through the sides and bottom is: 0 N⋅m2/C 4.2 N ⋅m2/C 21 N⋅m2/C 280 N⋅m2/C can't tell without knowing the areas of the sides and bottom
A 3.5-cm radius hemisphere contains a total charge of 6.6×10−7 C. The flux through the rounded portion of the surface is 9.8×104 N⋅m2/C. The flux through the flat base is: 0 N⋅m2 /C +2.3×104 N⋅m2 /C −2.3×104 N⋅m2/C −9.8×104 N⋅m2/C +9.8×104 N⋅m2/C
A particle with charge +Q is placed outside a large neutral conducting sheet. At any point in the interior of the sheet the electric field produced by charges on the surface is directed: toward the surface away from the surface toward Q away from Q none of the above
A conducting sphere of radius 0.01 m has a charge of 1.0×10−9 C deposited on it. The magnitude of the electric field just outside the surface of the sphere is: 0 N/C 450 N/C 900 N/C 4500 N/C 90,000 N/C
Positive charge Q is placed on a conducting spherical shell with inner radius R1 and outer radius R2. A point charge q is placed at the center of the cavity. The magnitude of the electric field at a point outside the shell, a distance r from the center, is: Q 4πε0(R12 − r2) (q+Q) 4πε0(R12 − r2) Q 4πε0R12 q 4πε0r2 (q+Q) 4πε0r2
A uniformly charged ball (a plasma ball) has a radius of 0.200 m. The electric field on its surface is outward and has a magnitude of 40.0 N/C. Two radial distances (two radii) have a field magnitude of 20.0 N/C. What is the larger value r2 (m)? 0.667 0.341 0.382 0.523 0.367 0.424 0.781 0.560 0.283 1.22
A uniformly charged ball (a plasma ball) has a radius of 0.300 m. The electric field on its surface is outward and has a magnitude of 60.0 N/C. Two radial distances (two radii) have a field magnitude of 30 N/C. What is the larger value r2 (m)? 0.283 1.22 0.367 0.382 0.781 0.560 0.341 0.523 0.424 0.667
A+2.50 μC point charge is at the center of a thin spherical shell of radius 0.100 m that has a uniform surface charge density. The electric field 0.200 m from the point charge has magnitude 2.93×105 N/C and points away from the point charge. What is the charge density (μC/m2) on the shell? −4.97 −18.3 1.20 −7.83 19.9 −2.39 −9.52 29.4 −6.68 −38.2
A - 9.02 nC point charge is 4.58 mm away from a large neutral conductor. Over a very small region on the conductor closest to the point charge, the electric field from the point charge is approximately constant. What is the surface charge density (μC/m2) in that area? 137 −1.97 −430 −137 −34.2 430 −56.9 56.9 34.2 1.97
A long, nonconducting, solid cylinder of radius 3.0 cm has a nonuniform volume charge density ρ that is a function of radial distance r from the cylinder axis: ρ = k/r where k is a constant. If the electric field strength is 7.23×105 N/C at r = 1.5 cm, what is the value of k (μC/m2)? 6.4 27 2.6 42 14.4 2.8 7.0 51.6 3.7 4.3
A nonconducting sphere of radius R has a volume charge density that varies with radius as ρ = kr where k is a constant. How does the magnitude of the electric field depend on r? E ∝ r2 for r < R and r > R E ∝ r−2 for r < R and r > R E ∝ r2 for r < R and E ∝ r−2 for r > R E ∝ r for r < R and r > R E ∝ r3 for r < R and E ∝ r2 for r > R E ∝ r for r < R and E∝r−2 for r > R E ∝ r2 for r < R and E ∝ r for r > R E ∝ r3 for r < R and E ∝ r for r > R E ∝ r for r < R and E ∝ r2 for r > R E ∝ r3 for r < R and E ∝ r−2 for r > R
The electric field in a certain region of Earth's atmosphere is directed vertically down. At an altitude of 342 m the field has magnitude 71.5 N/C; at an altitude of 247 m, the magnitude is 144 N/C. Find the net amount of charge contained in a cube 95 m on edge, with horizontal faces at altitudes of 247 m and 342 m. Number Units
A particle of charge q = 95 μC is placed at a corner of a Gaussian cube of edge a = 11 cm. What is the flux through (a) each cube face forming that corner and (b) each of the other cube faces? (a) Number Units (b) Number Units
A long straight wire has fixed negative charge with a linear charge density of magnitude 5.1 nC/m. The wire is to be enclosed by a coaxial, thin-walled, nonconducting cylindrical shell of radius 1.2 cm. The shell is to have positive charge on its outside surface with a surface charge density σ that makes the net external electric field is zero. Calculate σ. Number Units
Two long, charged, thin-walled, concentric cylindrical shells have radii of 3.4 and 7.7 cm. The charge per unit length is 5.9×10−6 C/m on the inner shell and −10.7×10−6 C/m on the outer shell. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 4.9 cm? What are (c) E and (d) the direction at r = 11 cm ? (a) Number Units (b) (c) Number Units (d)
A positively charged particle is held at the center of a spherical shell. The figure gives the magnitude E of the electric field versus radial distance r. The scale of the vertical axis is set by Es = 13.0×107 N/C. Approximately, what is the net charge on the shell? Assume rs = 3 cm. Number Units
Charge of uniform volume density ρ = 3.7 nC/m3 fills an infinite slab between x = −4.6 cm and x = +4.6 cm. What is the magnitude of the electric field at any point with the coordinate (a) x = 4.1 cm and (b) x = 6.8 cm ? (a) Number Units (b) Number Units
A particle with charge 5.0 μC is placed at the corner of a cube. The total electric flux through all sides of the cube is: 0 N⋅m2/C 7.1×104 N⋅m2/C 9.4×104 N⋅m2/C 1.4×105 N⋅m2/C 5.6×105 N⋅m2/C
Two large insulating parallel plates carry positive charge of equal magnitude that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest. 1, 2, 3, 4, 5 5, 4, 3, 2, 1 1 and 4 and 5 tie, then 2 and 3 tie 2 and 3 tie, then 1 and 4 tie, then 5 2 and 3 tie, then 1 and 4 and 5 tie
Suppose you throw a ball with mass 0.40 kg against a brick wall (Figure 1). It hits the wall moving horizontally to the left at 30 m/s and rebounds horizontally to the right at 20 m/s. Find the impulse of the force exerted on the ball by the wall. If the ball is in contact with the wall for 0.010 s, find the average force on the ball during the impact. Figure 1 of 2 Part A - Practice Problem: Suppose, rather than throwing a ball, you throw a lump of clay with mass 0.55 kg and initial velocity 30 m/s. When it hits the wall, the lump of clay sticks to the wall. Find the average force exerted on the wall by the lump of clay if it comes to a stop in 0.010 s. Express your answer with the appropriate units. F = Units
A ball of mass m hangs from a spring of stiffness k. A string is attached to the ball, and you are pulling the string to the right, as shown, such that the ball is in static equilibrium. In this position, the spring is stretched to length L and makes an angle θ with the vertical. The gravitational constant is g. What is the relaxed length of the spring L0? That is, what would the length of the spring be if it were detached from the ball and laid flat on a table? Express your answer with only the variables given above.
A block of mass m is released from rest and slides down a frictionless track of height h as is shown. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring of force constant k. Determine an expression for the maximum distance the spring is compressed. NOTE: Express your answer in terms of m, h, k and any other relevant physical constants.
Two joggers, Jim and Tom, are both running at a speed of 4.20 m/s (see the figure). Jim has a mass of 81.0 kg, and Tom has a mass of 55.0 kg. Find (a) the kinetic energy and (b) the momentum of the two-jogger system when Jim and Tom are both running due north as in part a of the figure. Find (c) the kinetic energy and (d) the momentum of the two-jogger system when Jim is running due north and Tom is running due south, as in part b of the figure.
Two joggers, Jim and Tom, are both running at a speed of 4.10 m/s (see the figure). Jim has a mass of 75.0 kg. and Tom has a mass of 54.0 kg. Find (a) the kinetic energy and (b) the momentum of the two-jogger system when Jim and Tom are both running due north as in part a of the figure. Find (c) the kinetic energy and (d) the momentum of the two-jogger system when Jim is running due north and Tom is running due south, as in part b of the figure.
The 100-lb block is stationary at time t = 0, and then it is subjected to the force P shown. Note that the force is zero for all times beyond t = 18 sec. Determine the velocity v of the block at time t = 18 sec. Also calculate the time tat which the block again comes to rest. Answers: At t = 18 sec, v = ft/sec Comes to rest at t = sec
A ball with weight mg = 20 N is placed on a light platform on the top of a vertical spring with a stiffness k = 200 N/m and is pushed against it. The spring is compressed to a point A, 0.4 m from its equilibrium position. Then, the ball is released from rest. How far from point A, will the ball rise? Neglect air resistance and take g = 10 m/s2.0.8 m 1 m 1.6 m 0.4 m 0.5 m
A 1.5 kg ball is released from the rest from a height 0.409 m. This 1.5 kg ball then swings downward and strikes (fully elastic) a 4.60 kg ball that is at rest. a) Using the principle of conservation of energy, find the speed of the 1.50 kg ball at the height of 0.30 m. b) Find the maximum height of the 4.6 kg ball the collision c) Find the maximum velocity of 4.6 kg ball.
An 84-kg jogger is heading due east at a speed of 1.6 m/s. A 66-kg jogger is heading 39∘ north of east at a speed of 2.4 m/s. Find (a) the magnitude and (b) the direction of the sum of the momenta of the two joggers. Describe the direction as an angle with respect to due east. (a) Number Units (b) Number Units
An 65-kg jogger is heading due east at a speed of 1.1 m/s. A 89-kg jogger is heading 66∘ north of east at a speed of 1.4 m/s. Find (a) the magnitude and (b) the direction of the sum of the momenta of the two joggers. Describe the direction as an angle with respect to due east. (a) Number Units (b) Number Units
An 88−kg jogger is heading due east at a speed of 3.3 m/s. A 77−kg jogger is heading 46∘ north of east at a speed of 2.7 m/s. Find (a) the magnitude and (b) the direction of the sum of the momenta of the two joggers. Describe the direction as an angle with respect to due east. (a) Number Units (b) Number Units
A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.8 kg and 2.4 kg, and the length of the wire is 1.40 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision. (a) v = (b) v =
The mass of block A is 50 kg. The coefficient of friction between A and B is 0.20 , and 0.15 between the string and drum C. Motion of C is impending downwards. The frictional force, fBA, is nearest to: 20 N 440 N NONE OF THE CHOICES 88 N 102 N
A person pulls a 9 kg crate from rest up a rough (μ = 0.11) 30∘ slope that is 15 m high, as shown. Assume that the crate is moving at constant speed. How much work was done by the person?
The charges q1 = 3.6×10−7 C, q2 = −5.5×10−7 C, and q3 = −1.8×10−7 C are placed at the corners of the triangle shown below. What is the force on q1 (in N)? (Assume that the +x-axis is to the right and the +y-axis is up along the page. ) F→on 1 = N
An object is in between a converging mirror and a converging lens, as shown in the figure below. Two images are produced for this object. a) For the first image, the light from the object refracts through the lens. What is q1 ? The location of this image, as measured from the converging lens? What is the magnification of this image? Sketch a ray diagram for this image. Answer: q1 = −10 cm: the image is 10 cm to the left of the lens, M1 = 2. b) For the second image, the light from the object is reflected from the mirror and then the reflected light refracts through the lens. What is q2 ? The location of this image, as measured from the converging lens? What is the magnification of the final image? Sketch a ray diagram for this image. Answer: q2 = 20 cm: the image is 20 cm to the right of the lens, M = −2.
A catapult on a cliff launches a large round rock towards a ship on the ocean below. The rock leaves the catapult from a height H of 34.0 m above sea level, directed at an angle above the horizontal with an unknown speed v0. The projectile remains in flight for 6.00 seconds and travels a horizontal distance D of 158 m. Assuming that air friction can be neglected, calculate the value of the angle (in degrees). Answer: Submit All Answers
A(n) 60.3 g ball is dropped from a height of 53.7 cm above a spring of negligible mass. The ball compresses the spring to a maximum displacement of 4.68317 cm. The acceleration of gravity is 9.8 m/s2. Calculate the spring force constant k. Answer in units of N/m.
A projectile is fired at an upward angle of 25 degrees relative to horizontal. The projectile starts at a position 85 meters above the ground and hits a wall at a point 67 meters above the ground. The projectile travels a total of 1200 meters in the X direction. What is the initial velocity of the projectile in the direction of the 25 degree angle? This problem will need algebra to solve, give it your best attempt. This problem will not be on the final.
A ball (mass 0.40 kg ) is initially moving to the left at 30 m/s. After hitting the wall, the ball is moving to the right at 20 m/s. What is the impulse of the net force on the ball during its collision with the wall? A. 20 kg⋅m/s to the right B. 20 kg⋅m/s to the left C. 4.0 kg⋅m/s to the right D. 4.0 kg⋅m/s to the left E. none of the above
An 86−kg jogger is heading due east at a speed of 3.6 m/s. A 55−kg jogger is heading 38∘ north of east at a speed of 1.1 m/s. Find (a) the magnitude and (b) the direction of the sum of the momenta of the two joggers. Describe the direction as an angle with respect to due east. (a) Number Units kg⋅m/s (b) Number Units
Four very thin rods, each 8.9 m long, are joined to form a square, as part (a) of the drawing shows. The center of mass of the square is located at the coordinate origin. The rod on the right is then removed, as shown in part (b) of the drawing. What are the x- and y- coordinates of the center of mass of the remaining three-rod system? (a) (b) x coordinate of the center of mass = Number Units y coordinate of the center of mass = Number Units
Problem 3: Ray tracing for concave mirrors An object is located 60 cm from a concave mirror with a focal length of 20 cm. Use the scaled down version shown to make your measurements. A. Draw a ray diagram to find the image. You only need to draw 2 of the special rays but draw more if you prefer. B. Use a ruler to measure, in mm, the height and location of the object and of your image in the figure, use the appropriate sign to indicate whether the image is real or virtual, upright or inverted.
A 15.0 kg stone slides down a snow-covered hill, leaving point A at a speed of 10.0 m/s. There is no friction on the hill between points A and B, but there is friction on the level ground at the bottom of the hill, between B and the wall. After entering the rough horizontal region, the stone travels 100 m and then runs into a very long, light spring with force constant 2.0 N/m. The coefficients of kinetic friction between the stone and the horizontal ground is 0.2 . A. What is the speed of the stone when it reaches point B? (3 marks) B. How far will the stone compress the spring? (6 marks)
The 100−lb block is stationary at time t = 0, and then it is subjected to the force P shown. Note that the force is zero for all times beyond t = 15 sec. Determine the velocity v of the block at time t = 15 sec. Also calculate the time t at which the block again comes to rest.
A plane mirror and a concave mirror (f = 7.30 cm) are facing each other and are separated by a distance of 18.0 cm. An object is placed between the mirrors and is 9.00 cm from each mirror. Consider the light from the object that reflects first from the plane mirror and then from the concave mirror. Find the location of the image that this light produces in the concave mirror. Specify this distance relative to the concave mirror. Number Units cm
Block A (0.40 kg) and block B (0.30 kg) are on a frictionless table (see figure). Spring 1 connects block A to a frictionless peg at O and spring 2 connects block A and block B. When the blocks are in uniform circular motion about 0, the springs have lengths of 0.60 m and 0.40 m, as shown. The springs are ideal and massless, and the linear speed of block B is 2.0 m/s. If the distance that spring 2 stretches is 0.060 m, the spring constant of spring 2 is closest to A) 18 N/m. B) 20 N/m. C) 22 N/m. D) 24 N/m. E) 26 N/m.
An object that is 37 cm in front of a convex mirror has an image located 14 cm behind the mirror. How far behind the mirror is the image located when the object is 12 cm in front of the mirror?
In the figure, an isotropic point source of light S is positioned at distance d from a viewing screen A and the light intensity IP at point P (level with S) is measured. Then a plane mirror M is placed behind S at distance 3.7 d. By how much is Ip multiplied by the presence of the mirror? Number Units
A concave mirror has a focal length of 34.0 cm. The distance between an object and its image is 49.6 cm. Find (a) the object and (b) image distances, assuming that the object lies beyond the center of curvature and (c) the object and (d) image distances, assuming that the object lies between the focal point and the mirror. (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Two charges are located on the x axis: q1 = +6.8 μC at x1 = +4.7 cm, and q2 = +6.8 μC at x2 = −4.7 cm. Two other charges are located on the y axis: q3 = +3.6 μC at y3 = +4.9 cm, and q4 = −9.2 μC at y4 = +7.0 cm. Find (a) the magnitude and (b) the direction of the net electric field at the origin. (a) Number Units
Sphere A collides with sphere B as shown in the figure. If the coefficient of restitution is e = 0.30, determine the velocity of each sphere immediately after impact. Motion is confined to the x-y plane. Answers: vA = ( i + j) m/s vB = ( i + j) m/s
A 48.0-kg boy, riding a 1.80-kg skateboard at a velocity of 5.20 m/s across a level sidewalk, jumps forward to leap over a wall. Just after leaving contact with the board, the boy's velocity relative to the sidewalk is 6.00 m/s, 8.90∘ above the horizontal. Ignore any friction between the skateboard and the sidewalk. What is the skateboard's velocity relative to the sidewalk at this instant? Be sure to include the correct algebraic sign with your answer. Number Units
A 3.0 m long vertical cylinder is placed under a stretched string as shown in the figure (not to scale). The radius of the cylinder is 2.5 cm. The string is set to vibrate at 135 Hz with a standing wave pattern as show in the diagram. [Answer in 2 significant figures] a. [9 pts] If the tension of the string is 62 N, what is the mass of the string? b. [15 pts] How much water is needed to add to the cylinder for the air column in the cylinder to resonant with the string at second resonance. The air has a temperature of 35∘C. c. [6 pts] Sketch the standing wave pattern of the air column in the cylinder. Indicate what kind of wave you use for the sketch (pressure wave or displacement wave).
A 10 kg steel wheel in Figure 9, has a radius of 100 mm and rest on an inclined plans made of wood. If θ is increased so that the wheel begins to roll down the incline with constant velocity when θ = 1.2∘, determine the coefficient of rolling resistance, a) (Ans : 2.09 mm ) Figure Q9
The bob of mass m of a conical pendulum of length l = 2 m rotates in a circle while the string makes an angle of 25∘ with the vertical. a. Draw the free body diagram for the mass m. b. Determine period of the pendulum. a. 8.1 s b. 0.56 s c. 1.03 s d. 2.7 s e. 0.81 s
A pendulum bob of mass m is attached to a light string of length L and is also attached to a spring of force constant k. With the pendulum in the position shown in Figure, the spring is at its unstressed length. If the bob is now pulled aside so that the string makes a small angle ϑ with the vertical and released, what is the speed of the bob as it passes through the equilibrium position? Hint: Recall the small-angle approximations: if ϑ is expressed in radians, and if ϑ < 1, then sinϑ ≈ tanϑ ≈ ϑ and cosϑ ≈ 1 − 1/ θ2.
The natural frequency of a spring-mass system is originally 1 rad/s. The spring-mass system is connected to an inverted pendulum, with the spring attached to the midpoint of the pendulum, which has a length of 2l. Determine the mass ratio r(r = M/m) that restricts the natural frequency of the assembled system to less or equal to 2 rad/s. (Neglect the gravity, sinθ ≈ θ, cosθ ≈ 1)
A mass of 0.5 kg stretches a spring 0.09 m. The mass is in a medium that exerts a viscous resistance of 38 N when the mass has a velocity of 4 ms. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.08 m and released. Find an function to express the object's displacement from the spring's natural position, in m after t seconds. Let positive displacements indicate a stretched spring, and use 9.8 ms2 as the acceleration due to gravity. u(t) =
A block, whose mass is 0.620 kg, is attached to a spring with a force constant of 128 N/m. The block rests upon a frictionless, horizontal surface (shown in the figure below). The block is pulled to the right a distance A = 0.120 m from its equilibrium position (the vertical dashed line) and held motionless. The block is then released from rest. (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the block? N (b) At that very instant, what is the magnitude of the block's acceleration (in m/s2 )? m/s2 (c) In what direction does the acceleration vector point at the instant of release? Away from the equilibrium position (i. e. , to the right in the figure). The direction is not defined (i.e., the acceleration is zero). Toward the equilibrium position (i.e., to the left in the figure). You cannot tell without more information.
A 3.00 kg object rests upon a frictionless, horizontal floor. The object is attached to a horizontal spring (of force constant k = 575 N/m) whose other end is anchored to a nearby wall. The object is pulled until it lies a distance xi = 5.30 cm from its equilibrium position (x = 0). The object is then released and undergoes simple harmonic motion. (a) Calculate how much work must be done (in J) to stretch the spring from equilibrium (x = 0) to the pre-release position (xi). J (b) With what speed (in m/s) does the object pass through the equilibrium position once it has been released from xi? m/s
Figure 1 shows a special triple-star system consists of two stars, each of mass m, revolving in the same circular orbit radius r around a central star of mass M. The two orbiting stars are always at the opposite ends of a diameter of the orbit. Derive an expression for the period of revolution of the stars. Figure 1
As shown below, a 5.4 g bullet is moving horizontally at 967 m/s when it embeds itself in a 0.704 kg block that is attached to a 510 N/m spring. The block is on a frictionless surface and prior to being struck it was in static equilibrium. As a result of the collision, the system starts exhibiting SHM. Determine the following quantities ω = f = T = vmax = amax = A = amount of TE generated during collision =
A block-spring system has a kinetic energy of 3 J and the spring has an elastic potential energy of 2 J when the block is at x = +2 cm. (a) What is the kinetic energy when the block is at x = 0? (b) What is the elastic potential energy when the block is at x = −2.0 cm and x = −xm?
Block A has a mass of 5 kg; block B's mass is 8 kg. They are pushed with a force of magnitude 20 N. What can you say about two forces: force with which A pushes on B force with which B pushes on A A on B is the same as B on A A on B is less than B on A because B is heavier than A A on B is greater than B on A because both move to the right
Consider the system of blocks shown in the diagram below. If the weight of block B is 711 N, the coefficient of static friction between block and table is 0.25, and the angle θ is 30∘, find the maximum weight of block A for which the system will be stationary.
Charge of uniform volume density ρ = 4.4 nC/m3 fills an infinite slab between x = −4.5 cm and x = +4.5 cm. What is the magnitude of the electric field at any point with the coordinate (a) x = 4.1 cm and (b) x = 8.3 cm ? (a) Number Units N/C (b) Number Units
Charge of uniform volume density ρ = 1.7 nC/m3 fills an infinite slab between x = −4.7 cm and x = +4.7 cm. What is the magnitude of the electric field at any point with the coordinate (a) x = 3.7 cm and (b) x = 8.4 cm? (a) Number Units (b) Number Units
A very large, flat slab has uniform volume charge density ρ and thickness 2t. A side view of the cross section is shown in the figure below. (a) Find an expression for the magnitude of the electric field inside the slab at a distance x from the center. (Use any variable or symbol stated above along with the following as necessary: ε0.) E = (b) If ρ = 7.20 μC/m3 and 2 t = 8.00 cm, calculate the magnitude of the electric field at x = 2.00 cm. N/C
In the figure below, a nonconducting thin rod of length L has a linear charge density −λ uniformly distributed along its length. (a) What is the electric potential at the location of point P, a distance a from the rod? (b) What are the magnitude and direction of the electric field produced at point P, a distance a from the rod?
A particle of charge q = 4.4×10−6 C and mass m = 2.1×10−6 kg moving at some initial velocity v→0 enters a region in which a uniform magnetic field B→ = 0.44 Tj is suddenly switched on. The particle then moves in a helix of radius r = 17 cm and pitch p = 10.7 cm about the y-axis, as shown in the figure. Assuming that the position of the particle when the magnetic field is switched on is (17 cm, 0 cm, 0 cm), express the initial velocity vector using ijk unit vector notation. v→0 = m/s
A disk of radius 2.2 cm has a surface charge density of 6.6 μC/m2 on its upper face. What is the magnitude of the electric field produced by the disk at a point on its central axis at distance z = 11 cm from the disk? Number Units
A non-conductive rod has a uniform positive charge density +λ, a total charge Q along its right half, a uniform negative charge density −λ, and a total charge −Q along its left half, see Fig. below. (a) What is the electric potential at point A? (b) What is the electric potential at point B?
The magnitude of the net electric field at a distance x from the center and on the axis of a uniformly charged ring of radius r and total charge q is given by Enet = kqx (x2 + r2)3/2. Consider two identical rings of radius 12.0 cm each, located as shown in the diagram below. The charge per unit length on each ring is +4.65 nC/cm and d = 22.0 cm. What is the magnitude of the net electric field at the center of ring B? N/C
A disk with surface charge density σ has a hollow center. The inner radius r1 = 0.13 m and the outer radius r2 = 0.24 m. The charge density σ = 1.1×10−6 C/m2. Point P is located along the central axis of symmetry at distance a from the plane of the disk. What is the magnitude of the electric field at point P if a = 0.47 m? E→ = N/C
A ring of charge is centered at the origin in the vertical direction. The ring has a charge density of λ = 4.48×10−6 C/m and a radius of R = 2.01 cm. Find the total electric field, E, of the ring at the point P = (1.10 m, 0.00 m). The Coulomb force constant is k = 1 /(4πϵ0) = 8.99×109 N⋅m2/C2. E = N/C Find the expression for the electric field, E∞, of the ring as the point P becomes very far from the ring (x ≫ R) in terms of the radius R, the distance x, the total charge on the ring q, and the constant k = 1/(4πϵ0).
A volumetric charge density exists between two spherical shells defined by radii a [m] and b [m], respectively. If b > a and no charge exists anywhere else, determine the total charge Q enclosed between the shells. The charge density is given as ρv = ρ0R/a [C/m3], where ρ0 is a constant and R is the radial coordinate.
Potential in a charge distribution 3 points We have a sphere with diameter d = 7 m and charge density profile ρc(r) = Ar2ω where A = 6×10−8. The change in potential energy of a charge q = 5 mC moved from a radius of r = 2.3 m inside the sphere to the very edge of the sphere was found to be −25 J. Find the value of the constant ω. (Next three questions) We have a spherical ball in a vacuum with three layers: the center and outer layers have constant charge density ρ = 0.7 μC/m3 and the middle layer is a perfect conductor. We'll define zero potential, V = 0, at an infinite distance away from the sphere. The radii are a = 0.3 m, b = 0.7 m, and c = 1 m. Figure 3: Figure for Problems 9-11 Potential at purple dashed line 1 point (a) What is the potential at r = 0.4 m away from the center of the sphere (purple dashed line)? (number 10) Potential at yellow dashed line 1 point What is the potential at r = 0.85 m away from the center of the sphere (yellow dashed line)? (number 11) Potential at green dashed line 1 point What is the potential at r = 1.2 m away from the center of the sphere (green dashed line)?
Suppose that the charge density of the spherical charge distribution shown in the figures below is ρ(r) = ρ0r/R for r ≤ R and zero for r > R. Obtain expressions for the electric field both inside and outside the distribution. (Use any variable or symbol stated above along with the following as necessary: ε0.) (a) (b) inside E→ = r^ outside E→ = r^
A sphere with a uniform charge density ρ and radius R has a cavity of radius R/2 as shown in the figure below. Find the electric field at a point (x, y, z) outside the sphere. The center of the sphere is at (0, 0, 0), and the center of the cavity is at (R/2, 0, 0). (x, y, z)
The figure shows a thin rod with a uniform charge density of 3.00 μC/m. Evaluate the electric potential at point P if d = D = L/4.00. Number Units
A point charge q is located at the center of a uniform ring having linear charge density λ and radius a, as shown in the figure below. Determine the total electric flux through a sphere centered at the point charge and having radius R, where R < a. (Use the following as necessary: q and ε0.) (i) Φ = If q = 2×10−6 C, R = 3 m and a = 5 m, calculate the total electric flux. N⋅m2/C
A finite line of charge with linear charge density λ = 2.00×10−6 C/m and length L = 0.720 m is located along the x-axis (from x = 0 to x = L). A point charge of q = −6.00×10−7 C is located at the point x0 = 1.00 m, y0 = 4.75 m. Find the electric field magnitude E and direction θ (measured counterclockwise from the +x axis) at the point P, which is located along the x-axis at xP = 10.70 m. The Coulomb force constant is k = 1/(4πϵ0) = 8.99×109 (N⋅m2)/C2. E = N/C θ =
Electric charge is distributed over the triangular region D shown below so that the charge density at (x, y) is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m2). Find the total charge on D. Round your answer to four decimal places. coulumbs
Let E be the solid below z = 18 − x2 − y2 and above the square [−3, 3]×[−3, 3] Given the solid has a constant density of 3, find the moment of inertia of E about the z-axis. Round your answer to the nearest whole number.
Two point charges are fixed on the y axis: a negative point charge q1 = −28 μC at y1 = +0.21 m and a positive point charge q2 at y2 = +0.32 m. A third point charge q = +8.4 μC is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 27 N and points in the +y direction. Determine the magnitude of q2.
Two particles are in a uniform electric field whose value is +2500 N/C. The mass and charge of particle 1 are m1 = 1.93×10−5 kg and q1 = −7.51 μC, while the corresponding values for particle 2 are m2 = 2.98×10−5 kg and q2 = +15.9 μC. Initially the particles are at rest. The particles are both located on the same electric field line but are separated from each other by a distance d. When released, they accelerate, but always remain at this same distance from each other. Find d.
P55. A fish swimming in a horizontal plane has velocity vi = 2 i+6 j/s at a point in the ocean where the position relative to a certain rock is ri = −6i + 4j m. After the fish swims with constant acceleration for 13 s, its velocity is v = −2i + 2j m/s. If the fish maintains constant acceleration, what is its horizontal position at t = 33 s? (-107.53846153846 m)
Two bodies of mass m1 = 1 kg and m2 = 3 kg are connected to each other by a rope as in the figure; m1 is also attached to a spring with spring constant k = 100 N/m and rest length d = 1 m. At the instant t = 0, with the spring at rest and with zero initial velocity, the system is left free to move. In the absence of friction, determine: a) the equations of motion for the system of the bodies x(t); b) the maximum value of the tension in the rope.
Problem #1. A surface that is 3 m long contains two springs at opposite ends with a patch of friction μk = 0.2 between x = 1 m and x = 2 m. The spring constant k1 for the spring on the left is 680 N/m and the equilibrium length is 0.6 m. The spring constant k2 for the spring on the right is 700 N/m and the equilibrium length is 0.5 m. At the start of the experiment, a block of mass 8 kg is pushed against the spring on the left so that the spring is compressed to x = 0.1 m. The block is then released from rest. A. Determine the displacement of spring 2 the first time block compresses it. B. Determine the displacement of spring 2 the second time the block compresses it. C. At what position (x) along the surface does the block come to rest?
You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 31∘ from the edge of the building with an initial velocity of 21 m/s and lands 63 meters away from the wall. How tall, in meters, is the building that the child is standing on? m
You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 41∘ from the edge of the building with an initial velocity of 17 m/s and lands 65 meters away from the wall. How tall is the building that the child is standing on? m
A flexible rope of length 1.0 m slides from a frictionless table top as shown in the Figure below. The rope is initially released from rest with 25 cm hanging over the edge of the table. Find the time at which the left end of the rope reaches the edge of the table. [32] A particle of mass m1, and velocity u1, collides with a particle of mass m2 at rest. The two particles stick together. What fraction of the original kinetic energy is lost in the collision? [18]
Car A rounds a curve of 127−m radius at a constant speed of 39 km/h. At the instant represented, car B is moving at 99 km/h but is slowing down at the rate of 3.0 m/s2. Determine the velocity and acceleration of car A as observed from car B. Answer: vA/B = ( i + j) m/s aA/B = ( i + j) m/s2
The velocity-time graph of a car moving along a straight road is shown in Figure 3 below. [Assumption: The car is travelling in a straight line. ] Figure 3 (Not drawn to scale) a) Determine the velocity of the car at time t = 1 s. b) Determine the acceleration of the car at time t = 5 s. c) Determine the rate of change of velocity of the car at time t = 7 s. d) Determine the displacement of the car from time t = 4 s to t = 6 s. e) Determine the average velocity of the car from time t = 0 s to t = hs, leave your answer in terms of h. f) When the car starts moving from rest at time t = 0 s, a lorry travelling with a uniform constant velocity of vm/s passes by the car. At t = 4 s, the car and lorry have the same displacement. Determine the value of v. g) When the car starts moving from rest at time t = 0 s, a motorcycle travelling with a uniform constant velocity of 16 m/s passes by the car. The motorcycle maintains this uniform velocity for 2 s before decelerating uniformly to rest at t = 10 s. The car overtakes the motorcycle at time t = ws, where 4 < w < 6. Determine the value of w.
A 50-lb uniform thin panel is placed in a truck with end A resting on a rough horizontal surface and end B supported by a smooth vertical surface. The deceleration of the truck is 13 ft/s2. Determine the minimum required coefficient of static friction at end A. μ =
Figure 3 [a] shows a lorry on a incline road. The coefficient of static friction between the tires of the 8000−kg lorry and the road is μs = 0.6. Draw the free body diagram. Figure 3[a] (ii) If the lorry is stationary on the incline road and α = 15∘, determine the magnitude of the total friction force exerted on the tires by the road. (iii) Determine the largest value of α for which the truck will not slip? (50 marks)
The uniform 14.0-ft pole is hinged to the truck bed and released from the vertical position as the truck starts from rest with an acceleration of 2.3 ft/sec2. If the acceleration remains constant during the motion of the pole, calculate the angular velocity ω of the pole as it reaches the horizontal position. Answer: ω = rad/sec
A farm truck moves due east with a constant velocity of 7.00 m/s on a limitless, horizontal stretch of road. A boy riding on the back of the truck throws a can of soda upward (see figure below) and catches the projectile at the same location on the truck bed, but 14.0 m farther down the road. (i) (a) In the frame of reference of the truck, at what angle to the vertical does the boy throw the can? (b) What is the initial speed of the can relative to the truck? m/s (c) What is the shape of the can's trajectory as seen by the boy? a straight line segment upward and then downward a symmetric section of a parabola opening downward An observer on the ground watches the boy throw the can and catch it. (d) In this observer's frame of reference, describe the shape of the can's path. a straight line segment upward and then downward a symmetric section of a parabola opening downward (e) In this observer's frame of reference, determine the initial velocity of the can. magnitude m/s direction above the horizontal eastward line
In the figure, a runaway truck with failed brakes is moving downgrade at 127 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of θ = 20∘. The truck's mass is 1.5×104 kg. (a) What minimum length L must the ramp have if the truck is to stop (momentarily) along it? (Assume the truck is a particle, and justify that assumption. ) Does the minimum length L increase, decrease, or remain the same if (b) the truck's mass is decreased and (c) its speed is decreased? (a) Number Units (b) (c)
The figure shows a copper bar moving with a speed v parallel to a long straight wire carrying a current I. What is the induced emf in the bar? Assume v = 5 m/s, I = 100 A, a = 0.01 m y b = 0.02 m.
A certain aircraft has a liftoff speed of 128 km/h. (a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 234 m? m/s2 (b) How long does it take the aircraft to become airborne? s
How far does the runner whose velocity-time graph is shown in the figure travel in 16 s? The figure's vertical scaling is set by vs = 9.00 m/s. Number Units
4-61. The drum has a weight of 500 N and rests on the floor for which the coefficient of static friction is μs = 0.5. If a = 0.9 m and b = 1.2 m, determine the smallest magnitude of the force P that will cause impending motion of the drum. Probs. 4-60/61
If a = 2 ft and b = 4 ft, determine the minimum force P necessary to move the 100 lb drum. Consider both slip and tip. Take friction to be equal to 0.5 at the ground. 50.0 44.8 41.8 53.0
A car is climbing the hill of slope θ1 = 20∘ at a constant speed v = 50 km/h. If the slope decreases abruptly to θ2 = 13∘ at point A, determine the acceleration a of the car just after passing point A if the driver does not change the throttle setting or shift into a different gear. Answer: a = m/s2
The speed of a car increases uniformly with time from 51 km/h at A to 103 km/h at B during 16 seconds. The radius of curvature of the hump at A is 36 m. If the magnitude of the total acceleration of the mass center of the car is the same at B as at A, compute the radius of curvature ρB of the dip in the road at B. The mass center of the car is 0.73 m from the road. Assume ρA = 36 m, h = 0.73 m. Answer: ρB = m
QUESTION 2 A system consists of three identical point particles arranged in a line as shown in the figure. The mass of each point particle is 3 kg and the distance d = 0.2 m. What is the magnitude of the net gravitational force (in nN) acting on point particle B? QUESTION 3 Two identical point particles, each with a mass of 4 kg, are separated by a distance of 0.2 m. What is the magnitude of the gravitational force (in nN) exerted by one point particle on the other?
Charge Q1 = 16.41 mC is placed R = 33.15 cm to the left of charge Q2 = 87.23 mC, as shown in the figure. Both charges are held stationary. Point A is located R3 = 9.945 cm to the right of Q1. A particle with a charge of q = −2.551 μC and a mass of 25.81 g is placed at rest at a distance R2 = 29.84 cm above Q2. If the particle were to be released from rest, calculating its exact path would be a challenging problem. However, it is possible to make some definite predictions about the future motion of the particle If the path of the particle were to pass through point A, what would be its speed vA at that point?
In the figure particles 1 and 2 are fixed in place, but particle 3 is free to move If the net electrostatic force on particle 3 due to particles 1 and 2 is zero and L23 = 2.35L12. what is the ratio q1/q2? Number Units
Two equally charged particles, held 4.4×10−3 m apart, are released from rest. The initial acceleration of the first particle is observed to be 5.7 m/s2 and that of the second to be 7.5 m/s2. If the mass of the first particle is 5.4×10−7 kg, what are (a) the mass of the second particle and (b) the magnitude of the charge of each particle? (a) Number Units (b) Number Units
The position of a particle is given by s = 0.32t3 − 0.62t2 − 2.21t + 5.11, where s is in feet and the time t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 7 seconds of motion. After you have the plots, answer the questions as a check on your work. Questions: When t = 1.0 sec, v = ft/sec, a = ft/sec2 When t = 5.6 sec, v = ft/sec, a = ft/sec2 The positive time at which the particle changes direction is sec.
The speed of a car increases uniformly with time from 36 km/h at A to 90 km/h at B during 17 seconds. The radius of curvature of the hump at A is 43 m. If the magnitude of the total acceleration of the mass center of the car is the same at B as at A, compute the radius of curvature ρB of the dip in the road at B. The mass center of the car is 0.64 m from the road. Assume ρA = 43 m, h = 0.64 m.
The 500 kg concrete culvert with relatively small thickness and mean radius of 0.5 m, resides on a truck, as shown in Figure 2. If the truck has an initial acceleration of 3 m/s2 and is starting from rest, determine the initial culvert's angular acceleration and the minimum coefficient of friction required such that the culvert does not experience any slipping. (25 marks) Figure 2