A chain 63 meters long whose mass is 21 kilograms is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the top 2 meters of the chain to the top of the building? Use that the acceleration due to gravity is 9.8 meters per second squared.

If the net work done by external forces on a particle is zero, which of the following statements about the particle must be true? (a) Its velocity is zero. (b) Its velocity is decreased. (c) Its velocity is unchanged. (d) Its speed is unchanged. (e) More information is needed.

A boy in a wheelchair (total mass 47.0 kg) has speed 1.40 m/s at the crest of a slope 2.60 m high and 12.4 m long. At the bottom of the slope his speed is 6.20 m/s. Assume air resistance and rolling resistance can be modeled as a constant friction force of 41.0 N. Find the work he did in pushing forward on his wheels during the downhill ride.

. In the annual Empire State Building race, contestants run up 1,575 steps to a height of 1,050 ft. In 2003, Australian Paul Crake completed the race in a record time of 9 min and 33 S, Mr., Crake weighed 143 lb (65 kg) , (a) How much work did Mr., Crake do in reaching the top of the building? (b) What was his average power output (in ft-lb/s and in hp)?

A cyclist in a race must climb a 5 hill at a speed of 8 m/s. If the mass of the bike and the biker together is 80 kg, what must be the power output of the biker to achieve the goal?

The force acting on a particle is Fx = (8x 16), where F is in newtons anti x is in meters. (a) Make a plot of this force versus x from x = 0 to x = 3.00 m. (b) From your graph, find the net work done by this force on the particle as it moves from x = 0 to x = 3.00 m.

As shown in Figure P7.20, a green bead of mass 25 g slides along a straight wire. The length of the wire from point to point is 0.600 m, and point is 0.200 in higher than point . A constant friction force of magnitude 0.025 0 N acts on the bead. (a) If the bead is released from rest at point , what is its speed at point ? (b) A red bead of mass 25 g slides along a curved wire, subject to a friction force with the same constant magnitude as that on the green bead. If the green and red beads are released simultaneously from rest at point , which bead reaches point first? Explain. Figure P7.20

Two stones, one with twice the mass of the other, are thrown straight up and rise to the same height h. Compare their changes in gravitational potential energy (choose one): (a) They rise to the same height, so the stone with twice the mass has twice the change in gravitational potential energy. (b) They rise to the same height, so they have the same change in gravitational potential energy. (c) The answer depends on their speeds at height h.

For each of the situations given, state whether frictional forces do positive, negative, or zero work on the italicized object. (a) A plate slides across a table and is brought to rest by friction. (b) A person pushes a chair at constant speed across a rough, horizontal surface. (c) A box is set down on a stationary conveyor belt. The conveyor belt is then turned on and the box begins to move, being carried along by the belt. (d) A person exerts a horizontal force on a banana at rest on a counter top. The banana remains at rest.

A block is placed on top of a vertical spring, and the spring compresses. Figure P8.24 depicts a moment in time when the spring is compressed by an amount h. a. To calculate the change in the gravitational and elastic potential energies, what must be included in the system? b. Find an expression for the change in the systems potential energy in terms of the parameters shown in Figure P8.24. c. If m = 0.865 kg and k = 125 N/m, find the change in the systems potential energy when the blocks displacement is h = 0.0650 m, relative to its initial position. FIGURE P8.24