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Energy conservation with nonconservative forces: A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope and a uniform surface. When the skier reaches the bottom of the hill, her speed is 30.0 m/s. (a) How much work is done by friction as the skier comes down the hill? (b) What is the magnitude of the friction force if the skier travels directly down the hill?

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(a) -1.10 × 104 J (b) 55.3 N

Energy conservation with nonconservative forces: A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case, and air resistance is negligible. Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45° above horizontal. Case D: Thrown straight out horizontally. In which case will the speed of the stone be greatest when it hits the water below?


A) Case A
B) Case B
C) Case C
D) Case D
E) The speed will be the same in all cases.

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Power: The work performed as a function of time for a process is given by Power: The work performed as a function of time for a process is given by where What is the instantaneous power output at A) 99 W B) 69 W C) 139 W D) 208 W where Power: The work performed as a function of time for a process is given by where What is the instantaneous power output at A) 99 W B) 69 W C) 139 W D) 208 W What is the instantaneous power output at Power: The work performed as a function of time for a process is given by where What is the instantaneous power output at A) 99 W B) 69 W C) 139 W D) 208 W


A) 99 W
B) 69 W
C) 139 W
D) 208 W

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Energy conservation with conservative forces: Swimmers at a water park have a choice of two frictionless water slides as shown in the figure. Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the end of slide 1 compares with v2, the speed of a swimmer reaching the end of slide 2? Energy conservation with conservative forces: Swimmers at a water park have a choice of two frictionless water slides as shown in the figure. Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v<sub>1</sub> of a swimmer reaching the end of slide 1 compares with v<sub>2</sub>, the speed of a swimmer reaching the end of slide 2? A) v<sub>1</sub> > v<sub>2</sub> B) v<sub>1</sub> < v<sub>2</sub> C) v<sub>1</sub> = v<sub>2</sub> D) No simple relationship exists between v<sub>1</sub> and v<sub>2</sub> because we do not know the curvature of slide 2.


A) v1 > v2
B) v1 < v2
C) v1 = v2
D) No simple relationship exists between v1 and v2 because we do not know the curvature of slide 2.

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C

Energy conservation with conservative forces: A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal?


A) 0.71 m/s
B) 4.0 m/s
C) 1.4 m/s
D) 2.8 m/s
E) 1.8 m/s

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Work: A stock person at the local grocery store has a job consisting of the following five segments: (1) picking up boxes of tomatoes from the stockroom floor (2) accelerating to a comfortable speed (3) carrying the boxes to the tomato display at constant speed (4) decelerating to a stop (5) lowering the boxes slowly to the floor. During which of the five segments of the job does the stock person do positive work on the boxes?


A) (1) and (5)
B) (1) only
C) (1) , (2) , (4) , and (5)
D) (1) and (2)
E) (2) and (3

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Energy conservation with conservative forces: It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure. What is the length s of the ramp from A to B? Energy conservation with conservative forces: It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure. What is the length s of the ramp from A to B?

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Hooke's law: 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 0 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 Hooke's law: 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 0 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.


A) 18 N/m.
B) 20 N/m.
C) 22 N/m.
D) 24 N/m.
E) 26 N/m.

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Work done by variable forces: A force on a particle depends on position such that F(x) = (3.00 N/ Work done by variable forces: A force on a particle depends on position such that F(x) = (3.00 N/ ) + ( 6.00 N/m) x for a particle constrained to move along the x-axis. What work is done by this force on a particle that moves from x = 0.00 m to x = 2.00 m? A) 10.0 J B) 20.0 J C) - 48.0 J D) 24.0 J E) 48.0 J ) Work done by variable forces: A force on a particle depends on position such that F(x) = (3.00 N/ ) + ( 6.00 N/m) x for a particle constrained to move along the x-axis. What work is done by this force on a particle that moves from x = 0.00 m to x = 2.00 m? A) 10.0 J B) 20.0 J C) - 48.0 J D) 24.0 J E) 48.0 J + ( 6.00 N/m) x for a particle constrained to move along the x-axis. What work is done by this force on a particle that moves from x = 0.00 m to x = 2.00 m?


A) 10.0 J
B) 20.0 J
C) - 48.0 J
D) 24.0 J
E) 48.0 J

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Energy conservation with conservative forces: An 8.0-m massless rod is loosely pinned to a frictionless pivot at 0, as shown in the figure. A very small 4.0-kg ball is attached to the other end of the rod. The ball is held at A, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely with negligible friction in a vertical circle between A and B. The tension in the rod when the ball passes through the lowest point at D is closest to Energy conservation with conservative forces: An 8.0-m massless rod is loosely pinned to a frictionless pivot at 0, as shown in the figure. A very small 4.0-kg ball is attached to the other end of the rod. The ball is held at A, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely with negligible friction in a vertical circle between A and B. The tension in the rod when the ball passes through the lowest point at D is closest to A) 160 N. B) 200 N. C) 120 N. D) 80 N. E) 40 N.


A) 160 N.
B) 200 N.
C) 120 N.
D) 80 N.
E) 40 N.

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Energy conservation with nonconservative forces: A 5.00-kg object moves clockwise around a 50.0 cm radius circular path. At one location, the speed of the object is 4.00 m/s. When the object next returns to this same location, the speed is 3.00 m/s. (a) How much work was done by nonconservative (dissipative) forces as the object moved once around the circle? (b) If the magnitude of the above nonconservative (dissipative) forces acting on the object is constant, what is the value of this magnitude?

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(a) -17.5 ...

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Work done by variable forces: In the figure, two identical springs have unstretched lengths of 0.25 m and spring constants of 300 N/m. The springs are attached to a small cube and stretched to a length L of 0.36 m as in Figure A. An external force P pulls the cube a distance D = 0.020 m to the right and holds it there. (See Figure B.) The work done by the external force P in pulling the cube 0.020 m is closest to Work done by variable forces: In the figure, two identical springs have unstretched lengths of 0.25 m and spring constants of 300 N/m. The springs are attached to a small cube and stretched to a length L of 0.36 m as in Figure A. An external force P pulls the cube a distance D = 0.020 m to the right and holds it there. (See Figure B.) The work done by the external force P in pulling the cube 0.020 m is closest to A) 0.12 J. B) 0.060 J. C) 6.0 J. D) 12 J. E) 0.80 J.


A) 0.12 J.
B) 0.060 J.
C) 6.0 J.
D) 12 J.
E) 0.80 J.

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Force and potential energy: The plot in the figure shows the potential energy of a particle, due to the force exerted on it by another particle, as a function of distance. At which of the three points labeled in the figure is the magnitude of the force on the particle greatest? Force and potential energy: The plot in the figure shows the potential energy of a particle, due to the force exerted on it by another particle, as a function of distance. At which of the three points labeled in the figure is the magnitude of the force on the particle greatest? A) point X B) point Y C) point Z


A) point X
B) point Y
C) point Z

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Work: A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If Work: A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap? A) 75 N B) 61 N C) 85 N D) 92 N of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap?


A) 75 N
B) 61 N
C) 85 N
D) 92 N

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Energy conservation with conservative forces: A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead compress the spring a distance of 2x Energy conservation with conservative forces: A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead compress the spring a distance of 2x A) the box will go up the incline twice as high as before. B) just as it moves free of the spring, the box will be traveling twice as fast as before. C) just as it moves free of the spring, the box will be traveling four times as fast as before. D) just as it moves free of the spring, the box will have twice as much kinetic energy as before. E) just before it is released, the box has twice as much elastic potential energy as before.


A) the box will go up the incline twice as high as before.
B) just as it moves free of the spring, the box will be traveling twice as fast as before.
C) just as it moves free of the spring, the box will be traveling four times as fast as before.
D) just as it moves free of the spring, the box will have twice as much kinetic energy as before.
E) just before it is released, the box has twice as much elastic potential energy as before.

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Work-energy theorem: A 5.00-kg box slides 4.00 m across the floor before coming to rest. What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3.00 m/s?


A) 1.13
B) 0.587
C) 0.115
D) 0.229
E) 0.267

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Work-energy theorem: In the figure, two boxes, each of mass 24 kg, are at rest and connected as shown. The coefficient of kinetic friction between the inclined surface and the box is 0.31. Find the speed of the boxes just after they have moved 1.6 m. Work-energy theorem: In the figure, two boxes, each of mass 24 kg, are at rest and connected as shown. The coefficient of kinetic friction between the inclined surface and the box is 0.31. Find the speed of the boxes just after they have moved 1.6 m.

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1.9 m/s

Gravitational potential energy: You do 174 J of work while pulling your sister back on a swing, whose chain is 5.10 m long. You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest. What is your sister's mass, assuming negligible friction?


A) 22.9 kg
B) 19.5 kg
C) 26.3 kg
D) 28.4 kg

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Work: A force Work: A force = 12 N - 10 N acts on an object. How much work does this force do as the object moves from the origin to the point A) 46 J B) 266 J C) 37 J D) 62 J = 12 N Work: A force = 12 N - 10 N acts on an object. How much work does this force do as the object moves from the origin to the point A) 46 J B) 266 J C) 37 J D) 62 J - 10 N Work: A force = 12 N - 10 N acts on an object. How much work does this force do as the object moves from the origin to the point A) 46 J B) 266 J C) 37 J D) 62 J acts on an object. How much work does this force do as the object moves from the origin to the point Work: A force = 12 N - 10 N acts on an object. How much work does this force do as the object moves from the origin to the point A) 46 J B) 266 J C) 37 J D) 62 J


A) 46 J
B) 266 J
C) 37 J
D) 62 J

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Energy conservation with conservative forces: A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead use a spring having force constant 2k Energy conservation with conservative forces: A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead use a spring having force constant 2k A) the box will go up the incline twice as high as before. B) just as it moves free of the spring, the kinetic energy of the box will be twice as great as before. C) just as it moves free of the spring, the speed of the box will be times as great as before. D) All of the above choices are correct. E) None of the above choices is correct.


A) the box will go up the incline twice as high as before.
B) just as it moves free of the spring, the kinetic energy of the box will be twice as great as before.
C) just as it moves free of the spring, the speed of the box will be times as great as before.
D) All of the above choices are correct.
E) None of the above choices is correct.

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