In (Figure 1), R1 = 3.00 Ω, R2 = 6.00 Ω, and R3 = 3.00 Ω. The battery has negligible internal resistance. The current I2 through R2 is 3.00 A. Part A What is the current I1 through R1 ? Express your answer with the appropriate units. Submit Request Answer Part B What is the current I3 through R3 ? Express your answer with the appropriate units. I3 = Value Units Submit Request Answer Part C What is the emf of the battery? Express your answer with the appropriate units.
The batteries shown in the circuit in the figure (Figure 1) have negligibly small internal resistances. Figure 1 of 1 Part A Find the current through the 30.0 Ω resistor. Express your answer with the appropriate units. Submit Request Answer Part B Find the current through the 20.0 Ω resistor. Express your answer with the appropriate units. Submit Request Answer Part C Find the current through the 10.0 V battery. Express your answer with the appropriate units.
Part A In the circuit shown in (Figure 1), find the magnitude of current in the upper branch. Express your answer in amperes. Submit Request Answer Part B Find the magnitude of current in the middle branch. Express your answer in amperes. I = A Part C Find the magnitude of current in the lower branch. Express your answer in amperes. I = A Submit Request Answer Part D What is the potential difference Vab of point a relative to point b ? Express your answer in volts. Vab = V
Part A Find the current through the battery in the circuit shown in (Figure 1). Express your answer in amperes. I = A Submit Request Answer Part B Find the current through the resistor R1 in the circuit. Express your answer in amperes. I = A Part C Find the current through the resistor R2 in the circuit. Express your answer in amperes. Submit Request Answer Part D Find the current through the resistor R3 in the circuit. Express your answer in amperes. Part E Find the current through the resistor R4 in the circuit. Express your answer in amperes. I = A Submit Request Answer Part F Find the current through the resistor R5 in the circuit. Express your answer in amperes. I = A Part G What is the equivalent resistance of the resistor network? Express your answer in ohms. R =
In the circuit shown in (Figure 1) all the resistors are rated at a maximum power of 1.90 W. Figure Part A What is the maximum emf E that the battery can have without burning up any of the resistors? Express your answer in volts.
(Figure 1) employs a convention often used in circuit diagrams. The battery (or other power supply) is not shown explicitly. It is understood that the point at the top, labeled "18.0 V ," is connected to the positive terminal of a 18.0−V battery having negligible internal resistance, and that the "ground" symbol at the bottom is connected to the negative terminal of the battery. The circuit is completed through the battery, even though it is not shown on the diagram. Figure 1 of 1 Part A What is the potential of point a with respect to point b in the figure when switch S is open? Express your answer in volts. Vab = V Submit Request Answer Part B Which point, a or b, is at the higher potential? point a point b Part C What is the final potential of point b with respect to ground when switch S is closed? Express your answer in volts. Vb = V Submit Request Answer Part D How much does the charge on each capacitor change when S is closed? Express your answer in coulombs separated by a comma.
In the circuit shown in (Figure 1), C = 5.90 μF, E = 28.0 V, and the emf has negligible resistance. Initially the capacitor is uncharged and the switch S is in position 1. The switch is then moved to position 2 , so that the capacitor begins to charge. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Charging a capacitor. Figure 1 of 1 Part A What will be the charge on the capacitor a long time after the switch is moved to position 2 ? Express your answer in coulombs. Submit Request Answer Part B After the switch has been in position 2 for 3.00 ms, the charge on the capacitor is measured to be 110 μC. What is the value of the resistance R ? Express your answer in ohms. Part C How long after the switch is moved to position 2 will the charge on the capacitor be equal to 99.0% of the final value found in part A ? Express your answer in seconds.
Capacitors are not perfect, and will not hold their charge indefinitely. Consider a parallel plate capacitor with area A and plate separation d, filled with a uniform material of electric permittivity ϵ and resistivity ρ (Figure 1). Suppose we place a voltage V across the capacitor. Figure 1 of 1 Part A What is the charge on the plates? Express your answer in terms of V, A, d, ϵ and ρ. Q = Submit Request Answer Part B Find the current flowing through the capacitor. Express your answer in terms of V, A, d, ϵ and ρ. I = Part C Suppose we now disconnect the battery. The charge on the capacitor dissipates through the resistor, exactly like an RC circuit. Find the RC time constant τ for this capacitor. Express your answer in terms of A, d, ϵ and ρ. Part D Suppose the dielectric material is quartz, for which ϵ = 4.43×10−11 Nm2 /C2 and ρ = 7.5×1017 Ωm. What is the value of the time constant for such a capacitor?
The capacitor in (Figure 1) is initially uncharged. The switch is closed at t = 0. Figure Part A Immediately after the switch is closed, what is the current through the resistor R1 ? Express your answer in amperes. I = Submit Request Answer Part B Immediately after the switch is closed, what is the current through the resistor R2 ? Express your answer in amperes. I = A Part C Immediately after the switch is closed, what is the current through the resistor R3 ? Express your answer in amperes. I = A Submit Request Answer Part D What is the final charge on the capacitor? Express your answer in coulombs. Q = C
In the circuit in (Figure 1) the capacitors are all initially uncharged, the battery has no internal resistance, and the ammeter is idealized. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Charging a capacitor. Figure 1 of 1 Part A Find the reading of the ammeter just after the switch S is closed. Express your answer in amperes. I = A Submit Request Answer Part B Find the reading of the ammeter after the switch has been closed for a very long time. Express your answer in amperes. I = A
Consider the 12 edges of a cube. Along each of the edges we place a 1 Ω resistor, and at each vertex we solder together the three wires that meet there. Part A If we connect a 12 V battery to two vertices that are at opposite corners of one of the square faces of the cube (across a face diagonal), what is the total current that flows? I = Part B If we connect a 12 V battery to two vertices that are at opposite corners of the cube (across a body diagonal), what is the total current that flows? I = A Submit Request Answer Part C Suppose we take 6 resistors (all 1 Ω) and put them along the edges of a tetrahedron. If we connect a 12 V battery to any two vertices, what is the total current that flows? I = A
A light string can support a stationary hanging load of 22.6 kg before breaking. An object of mass m = 2.79 kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.815 m, and the other end of the string is held fixed as in the figure below. What range of speeds can the object have before the string breaks? 0 ≤ v ≤ m/s
Engineers and science fiction writers have proposed designing space stations in the shape of a rotating wheel or ring, which would allow astronauts to experience a sort of artificial gravity when walking along the inner wall of the station's outer rim. (a) Imagine one such station with a diameter of 109 m, where the apparent gravity is 3.60 m/s2 at the outer rim. How fast is the station rotating in revolutions per minute? rev/min (b) What If? How fast would the space station have to rotate, in revolutions per minute, for the artificial gravity that is produced to equal that at the surface of the Earth, 9.80 m/s2 ? rev/min
Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 323 km above the surface of the Moon, where the acceleration due to gravity is 1.20 m/s2. The radius of the Moon is 1.70×106 m. (a) Determine the astronaut's orbital speed. m/s (b) Determine the period of the orbit. s
(a) A stuntman with a mass of 86.5 kg swings across a pool of water from a rope that is 10.5 m. At the bottom of the swing the stuntman's speed is 8.05 m/s. The rope's breaking strength is 1, 000 N. Will the stuntman make it across the pool without falling in? Yes No (b) What If? What is the maximum speed (in m/s ) that the stuntman can have at the bottom of the swing on this vine to safely swing across the river? m/s
A 43.0-kg child swings in a swing supported by two chains, each 2.98 m long. The tension in each chain at the lowest point is 342 N. (a) Find the child's speed at the lowest point. m/s (b) Find the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.) N (upward)
A roller-coaster car has a mass of 514 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points (A) and (B) are parts of vertical circles of radius r1 = 10.0 m and r2 = 15.0 m, respectively. (a) If the vehicle has a speed of 19.1 m/s at point A, what is the force exerted by the track on the car at this point? N (b) What is the maximum speed the vehicle can have at B and still remain on the track? m/s
A woman lies on her back and raises her head up off the floor. When doing so, the total tension force in her neck muscles is 56.0 N. The same woman now is sliding feet first down a water slide. The slide makes a circular curve, where the outside wall of the slide is vertical but the curve itself is in the horizontal plane, and the radius of the curve is 2.40 m. While sliding along this curve, the woman's speed is 2.55 m/s. The woman raises her head from the wall of the slide and holds it steady, looking forward. At this moment, what is the total tension (in N ) in the woman's neck muscles? N
A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 594 N. As the elevator later stops, the scale reading is 394 N. Assume the magnitude of the acceleration is the same during starting and stopping. (a) Determine the weight of the person. N (b) Determine the person's mass. kg (c) Determine the magnitude of acceleration of the elevator. m/s2
A small container of water is placed on a carousel inside a microwave oven, at a radius of 10.5 cm from the center. The turntable rotates steadily, turning through one revolution each 6.75 s. What angle does the water surface make with the horizontal?
(a) A sphere made of wood has a density of 0.810 g/cm3 and a radius of 8.50 cm. It falls through air of density 1.20 kg/m3 and has a drag coefficient of 0.500 . What is its terminal speed (in m/s )? m/s (b) From what height (in m ) would the sphere have to be dropped to reach this speed if it fell without air resistance? m
The mass of a sports car is 1400 kg. The shape of the car is such that the aerodynamic drag coefficient is 0.260 and the frontal area is 2.00 m2. Neglecting all other sources of friction, calculate the initial acceleration of the car, if it has been traveling at 100 km/h and is now shifted into neutral and is allowed to coast. (Take the density of air to be 1.295 kg/m3.) m/s2
You can feel a force of air drag on your hand if you stretch your arm out of the open window of a speeding car. [Note: Do not endanger yourself by performing this experiment. ] Calculate this force, supposing that D = 0.950, ρ = 1.20 kg/m3, A = 1.60×10−2 m2, and v = 23.5 m/s. N
A shopper in a supermarket pushes a cart with a force of 34.0 N directed at an angle of 25.0∘ below the horizontal. The force is just sufficient to balance various friction forces, so the cart moves at constant speed. (a) Find the work done by the shopper on the cart as she moves down a 55.0-m-long aisle. J (b) The shopper goes down the next aisle, pushing horizontally and maintaining the same speed as before. If the work done by frictional forces doesn't change, would the shopper's applied force be larger, smaller, or the same? larger smaller the same (c) What about the work done on the cart by the shopper? The work is larger in part (a). The work is larger in part (b). The work is the same in both parts.
Spiderman, whose mass is 72.0 kg, is dangling on the free end of a 11.2-m-long rope, the other end of which is fixed to a tree limb above. By repeatedly bending at the waist, he is able to get the rope in motion, eventually getting it to swing enough that he can reach a ledge when the rope makes a θ = 58.6∘ angle with the vertical. How much work was done by the gravitational force on Spiderman in this maneuver? kJ
Let B→ = 5.40 m at 60.0∘. C→ and A→ have equal magnitudes. The direction angle of C→ is larger than that of A→ by 25.0∘. Let A→⋅B→ = 27.0 m2 and B→⋅C→ = 36.9 m2. Find the magnitude (in m ) and direction (in degrees) of A→. magnitude m direction
Find the scalar product of the vectors in the figure below, where θ = 114∘ and F = 32.0 N. J
The force acting on a particle varies as shown in the figure below. (The x axis in the graph has its tickmarks marked in increments of 5.00 m. Find the work done by the force on the particle as it moves across the following distances. (a) from x = 0 m to x = 40.00 m J (b) from x = 40.00 m to x = 60.00 m J (c) from x = 0 m to x = 60.00 m J
When a 5.00-kg object is hung vertically on a certain light spring that obeys Hooke's law, the spring stretches 2.00 cm. (a) If the 5.00−kg object is removed, how far will the spring stretch if a 1.50−kg block is hung on it? cm (b) How much work must an external agent do to stretch the same spring 4.00 cm from its unstretched position? J
A rock with a mass of 2.40 kg is moving with velocity (6.60 i^ − 2.40 j^)m/s. (HINT: v2 = v→⋅v→. ) (a) What is the rock's kinetic energy (in J) at this velocity? J (b) Find the net work (in J) on the rock if its velocity changes to (8.00 i^+4.00 j^)m/s. J
A 8.35−kg particle is subject to a net force that varies with position as shown in the figure. The particle starts from rest at x = 0. What is its speed at the following positions? (a) x = 5.00 m m/s (b) x = 10.0 m m/s (c) x = 15.0 m m/s
A 0.27−kg stone is held 1.1 m above the top edge of a water well and then dropped into it. The well has a depth of 4.7 m. (a) Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone-Earth system before the stone is released? J (b) Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone-Earth system when it reaches the bottom of the well? J (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well? J
An object is subjected to a friction force with magnitude 4.26 N, which acts against the object's velocity. What is the work (in J) needed to move the object at constant speed for the following routes? (a) the purple path O to A followed by a return purple path to O J (b) the purple path O to C followed by a return blue path to O J (c) the blue path O to C followed by a return blue path to O J (d) Each of your three answers should be nonzero. What is the significance of this observation? The force of friction is a nonconservative force. The force of friction is a conservative force.
A single conservative force acts on a 4.70−kg particle within a system due to its interaction with the rest of the system. The equation FX = 2 x+4 describes the force, where FX is in newtons and x is in meters. As the particle moves along the x axis from x = 0.96 m to x = 5.70 m, calculate the following. (a) the work done by this force on the particle (b) the change in the potential energy of the system J (c) the kinetic energy the particle has at x = 5.70 m if its speed is 3.00 m/s at x = 0.96 m J
A right circular cone can theoretically be balanced on a horizontal surface in three different ways. Sketch these three equilibrium configurations and identify them as positions of stable, unstable, or neutral equilibrium. (Submit a file with a maximum size of 1 MB. ) Choose File No file chosen This answer has not been graded yet.
A particle with kinetic energy equal to 236 J has a momentum of magnitude 23.5 kg⋅m/s. Calculate the speed (in m/s ) and the mass (in kg ) of the particle. speed m/s mass kg
A baseball approaches home plate at a speed of 47.0 m/s, moving horizontally just before being hit by a bat. The batter hits a pop-up such that after hitting the bat, the baseball is moving at 58.0 m/s straight up. The ball has a mass of 145 g and is in contact with the bat for 1.60 ms. What is the average vector force the ball exerts on the bat during their interaction? (Let the +x-direction be in the initial direction of motion, and the +y-direction be up. ) F→on bat = N
In a research facility, a person lies on a horizontal platform which floats on a film of air. When the person's heart beats, it pushes a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. Assume that the blood's speed is 45.0 cm/s. The mass of the person + platform is 54.0 kg. The platform moves 5.45×10−5 m in 0.160 s after one heartbeat. Calculate the mass (in g ) of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person, and the person + platform is initially at rest. (Also assume that the changes in velocity are instantaneous.) g
An estimated force-time curve for a baseball struck by a bat is shown in the figure below. Let Fmax = 19,000 N, ta = 0.5 ms, and tb = 2 ms. From this curve, determine the following. (a) the magnitude of the impulse delivered to the ball N⋅s (b) the average force exerted on the ball kN
As shown below, a bullet of mass m and speed v is fired at an at rest sphere. The bullet goes through the sphere, and exits with a speed of v/2. The sphere is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the sphere will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the sphere.)
An object of mass 3.09 kg, moving with an initial velocity of 4.91 i^m/s, collides with and sticks to an object of mass 2.86 kg with an initial velocity of −3.53 j^m/s. Find the final velocity of the composite object. v→ = (i^ + j^)m/s
Four objects are situated along the y axis as follows: a 1.99−kg object is at +3.08 m, a 3.05−kg object is at +2.41 m, a 2.58−kg object is at the origin, and a 3.95−kg object is at −0.495 m. Where is the center of mass of these objects? x = m y = m
Romeo (81.0 kg) entertains Juliet (45.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m away from Juliet, who is in the front of the boat. After the serenade, Juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on Romeo's cheek. (a) How far (in m) does the 83.0 kg boat move toward the shore it is facing? m (b) What If? If the lovers both walk toward each other and meet at the center of the boat, how far (in m) and in what direction does the boat now move? magnitude m direction
A ball is attached to a cord of length L, which is tied to a frame attached to a truck bed as shown in figure (a), below. The ball-truck system is initially traveling to the right at constant speed vi, with the cord vertical. The truck suddenly stops when it undergoes an inelastic collision with a low wall as shown in figure (b), below. The suspended ball swings through an angle θ. a a (i) b (i) (a) Show that the original speed of the truck can be computed from vi = 2 gL(1−cos(θ)). When the truck stops, the ball begins moving like a -- Select--- ∇. The truck's initial velocity can be derived using ---Select-- . Implementing this derivation method results in which following equation? 12−mvi2+mgL = 0+mgLcos(θ)12−Lvi2+0 = 0+mgL(1−cos(θ))12−mvi2+mg(−L) = 0+mg(−Lcos(θ))12−Lvi2+mgLcos(θ) = 0+mgL Solving this equation for vi gives vi = 2 gL(1−cos(θ)). (b) If the wall is still exerting a horizontal force on the truck when the hanging ball is at its maximum angle forward from the vertical, at what moment does the wall stop exerting a horizontal force? somewhere between the maximum angle forward and the lowest point of the ball the lowest point of the ball somewhere between the lowest point of the ball and the maximum angle backward the maximum angle backward never
A girl launches a toy rocket from the ground. The engine experiences an average thrust of 5.26 N. The mass of the engine plus fuel before liftoff is 24.8 g, which includes fuel mass of 12.1 g. The engine fires for a total of 1.90 s. (Assume all the fuel is consumed. ) (a) Calculate the average exhaust speed of the engine (in m/s ). m/s (b) This engine is located in a rocket shell of mass 57.0 g. What is the magnitude of the final velocity of the rocket (in m/s) if it were to be fired from rest in outer space with the same amount of fuel? Assume the fuel burns at a constant rate. m/s
Consider the two pucks shown in the figure. As they move towards each other, the momentum of each puck is equal in magnitude and opposite in direction. Given that vi, green = 12.0 m/s, and mblue is 30.0% greater than mgreen , what are the final speeds of each puck (in m/s ), if 12 the kinetic energy of the system is converted to internal energy? (i) vgreen = m/s vblue = m/s
Starting from rest, a 58.0 kg woman jumps down to the floor from a height of 0.560 m, and immediately jumps back up into the air. While she is in contact with the ground during the time interval 0 < t < 0.800 s, the force she exerts on the floor can be modeled using the function F = 9,200 t − 11,500 t2 where F is in newtons and t is in seconds. (a) What impulse (in N⋅s) did the woman receive from the floor? (Enter the magnitude. Round your answer to at least three significant figures.) N⋅s (b) With what speed (in m/s ) did she reach the floor? (Round your answer to at least three significant figures.) m/s (c) With what speed (in m/s ) did she leave it? (Round your answer to at least three significant figures. ) m/s (d) To what height (in m) did she jump upon leaving the floor? m