Phyllis Fleming Physics Physics 104
 Review - Work and Energy
 1 Show that the work done on an object equals (a) the product of the displacement and the component of the force in the direction of the displacement or (b) the product of the force and the component of the displacement in the direction of the force.
 2 A box rests on a horizontal, frictionless surface. A girl pushes on the box with a force of 18 N to the right and a boy pushes on the box with a force of 12 N to the left. The box moves 4.0 m to the right. Find the work done by (a) the girl, (b) the boy, and (c) the net force.
 3 You support an object and move it to the right with a constant velocity. You exert a force F on it (Fig. 1 below) to oppose the gravitational attraction mg of the earth for the object. If you do not raise the object or increase its velocity, there is no increase in the object’s potential energy or in its kinetic energy. Do you do work on the object?
 4 An object attached to a string, fixed at one end, lies on a horizontal, frictionless surface. The object is given an initial velocity v and moves in a circle with uniform circular motion. Does the tension in the string do work on the object?
 5 As illustrated in Fig. 2 below, an object of mass m = 2.0 kg is pulled along a surface by a horizontal force F of 12 N to the right a distance s of 4.0 m. The coefficient of friction between the object and the surface is 0.5. Find the work done by (a) F, (b) the normal force FN, (c) the weight mg of the object, (d) the frictional force f, (e) the net force.
 6 A raindrop (m = 3.35 x 10-5 kg) falls vertically at constant speed under the forces of gravity and air resistance. In falling through 100 m, what is the work done by (a) gravity and (b) air resistance?
 7 A 52-kg skier moves down a slope at a speed of 14.0 m/s (31.3 mph). Determine the kinetic energy of the skier.
 8 An object, initially at rest, is pulled up an incline that makes an angle of 370 with the horizontal by a force F = 30 N parallel to the incline. The mass of the object is 2.0 kg and the coefficient of friction between the object and the surface is 0.5. The object moves up the incline a distance s = 4.0 m. Find (a) the frictional force, (b) the work done by F, (c) the work done by the normal force, (d) the work done by the weight of the object, (e) the work done by friction, (f) the work done by the net force and (g) the velocity of the object after it has moved 4.0 m.
 9 A 2.0-kg object is pushed along a horizontal surface a distance s = 4.0 m by a force F = 30 N to the right and down at an angle of 370 to the horizontal. The coefficient of friction between the object and the surface is 0.50. Find (a) the frictional force, (b) the work done by the frictional force, (c) the work done by force F, (d) the work done by the normal force FN, (e) the work done by the weight of the object, (f) the net work done on the object, and (g) the speed of the object after it moves through s = 4.0 m if its initial speed = 0.
 10 A constant force of 10 N is exerted to lift a l.0-kg mass a vertical height of 1.0 m. Find (a) the work done by the person, (b) the work done by the gravitational force, (c) the increase in its gravitational energy, and (d) the increase in its kinetic energy. Take g = 10 m/s2.
 11 Repeat Problem #10 for a constant force of 12 N.
 12 A box of mass 12 kg slides at a speed of 10 m/s across a smooth level floor, where it enters a rough portion 3.0 m in length. In the rough portion, the box experiences a horizontal frictional force of 72 N. (a) How much work is done by the frictional force? (b) What is the velocity of the box when it leaves the rough surface? (c) What length of rough surface brings the box completely to rest? Take g = 10 m/s2.
 13 (a) How much work is required to push a 2.0-kg object up a frictionless inclined plane whose length is 2.0 m and whose height is 1.0 m, if the velocity of the object remains constant? (b) How much work is required to push the object up the plane while increasing its velocity from zero to 3.0 m/s? (c) How much work is required to push the object up the plane at a constant speed if there is a frictional force of 3.0 N between the object and the plane? Take g = 10 m/s2.
 14 A block of mass 1.0 kg is placed at the top of an incline of length 125 m and height 62.5 m. The plane has a rough surface. When the block arrives at the bottom of the plane it has a velocity of 25 m/s. What is the magnitude of the constant frictional force acting on the block?  Take g = 10m/s2.
 15 Assume that the total energy of an electron bound to a proton in the hydrogen atom is -21.7 x 10-19 J. What is the kinetic energy of the electron (we assume the proton is at rest) when the potential energy of the atom is -43.4 x 10-19 J?
 16 A 2000-kg car is at rest on a level frictionless track. A constant force acts on it for one-half second, after which the car is moving with a speed of 0.20 m/s. Find (a) the magnitude of the force, (b) the kinetic energy of the car, (c) the work done on the car, and (d) the displacement of the car.
 17 Find (a) i · i, (b) i · j = j · i, (c) j · j, (d) the work done if the force F = 20 N j and the displacement s = 4 m i and (e) the work done if the force F = (3i + 4j)N and the displacement s = (2i - 2j) m.
 18 An object of mass m = 2.0 kg is released from rest at the top of a frictionless incline of height 3 m and length 5 m. Taking g = 10 m/s2, use energy considerations to find the velocity of the object at the bottom of the incline.
 19 Repeat #29 when µk between the object and the plane is 1/4.
 20 Figure 3 below is a plot of the potential energy U of a freely falling object as a function of the height y above the ground. E = 16.0 J (shown by the dashed horizontal line) is the total mechanical energy of the object. Find (a) the potential energy and (b) the kinetic energy of the object for y = 0.75 m. Find (c) mass of the object and (d) v when y = 0.75 m. Take g = 10 m/s2.
 21 A small block of mass m slides along the frictionless loop-the-loop shown in Fig. 4 below. Find (a) the minimum height h above the bottom of the track which you must release the block so that it will not leave the track at the top of the hoop and (b) the force of the track on the sphere at P in Fig. 4 when it is released from the height h found in (a). Take g = 10 m/s2.
 22 In Fig. 5 below, the first block has a mass m1 = 2.0 kg and the second block has m2 = 4.0 kg. The pulley and string are massless. There is no friction in the pulley, but the coefficient of kinetic friction between the first block and the incline is µk = 0.55. The blocks are released from rest. Use energy considerations to find the speed of the two blocks when the second block has moved down 2.5 m. Take g = 10 m/s2.
 23 A very light rod of length L has a ball of mass m attached to one end. The other end rotates about a pivot without friction. The system rotates in a vertical circle starting at position A in Fig. 6 below with downward velocity vo. When the ball reaches D, it stops and swings back down in a clockwise direction. Find (a) an expression for vo in terms of L, m, and g and (b) the tension in the rod at position B. A little sand gets into the pivot and then the ball only reaches C when launched from A. Find (c) the work done by friction during the motion from A to C and (d) how much total work is done by friction when the ball finally comes to rest at B after oscillating back and forth a few times.

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