# Work, Energy & Power

The motor of a ski boat generates an average power of 6.90 x 10^4 W when the boat is moving at a constant speed of 15 m/s. When the boat is pulling a skier at the same speed, the engine must generate an average power of 8.70 x10^4 W. What is the tension in the tow rope that is pulling the skier?

The drawing shows the force-versus-displacement graph for two different bows. These graphs give the force that an archer must apply to draw the bowstring.

(a) For which bow is more work required to draw the bow fully from s = 0 to s = 0.50 m?

(b) Estimate the additional work required for the bow identified in part (a) compared to the other bow.

A net external force is applied to a 7.58-kg object that is initially at rest. The net force component along the displacement of the object varies with the magnitude of the displacement as shown in the drawing. What is the speed of the object at s = 20.0 m?

Two pole-vaulters just clear the bar at the same height. The first lands at a speed of 8.60 m/s, and the second lands at a speed of 8.90 m/s. The first vaulter clears the bar at a speed of 1.00 m/s. Ignore air resistance and friction and determine the speed at which the second vaulter clears the bar.

(Please refer to the attachment for detailed problems with figs.)

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#### Solution Summary

The work, energy and power in physics are analyzed.Net external force is applied to an object.

7 Physics problems: Kinetic Energy, work, force, magnitude, speed

1. A luge and its rider, with a total mass of 85 kg emerges from a downhill track onto a horizontal straight track with an initial speed of 37 m/s. If they stop at a constant deceleration of 2.0 m/s^2, (a) What magnitude F is required for the deceleration force, (b) what distance "d" do they travel while decelerating (c) what work "W" is done on them by the decelerating force are (d) "F", (e) "d", and (f) "W" for deceleration of 4.0 m/s^2?

2. The only force acting on a 2.0 kg canister that is moving an xy plane has a magnitude of 5.0 N. The canister initially has a velocity of 4.0 m/s in the positive x direction and some time later has a velocity of 6.0 m/s in the positive y direction How much work is done on the canister by the 5.0 N force during this time?

3. The figure a cord runs around two massless, frictionless pulleys; a canister with mass m= 20 kg hangs from one pulley ; and you exert a force "F" on the free end of the cord (a) what must be the magnitude of "F" if you lift the canister at a constant speed ? (b) To lift the canister by 2.0 cm how far must u pull the free end of the cord ? During that lift, what is the work done on the canister by (c) your force ( via the cord ) and (d) the gravitational force on the canister ? (HINT when the cord loops around a pulley as shown it pulls on the pulley with a net force that is twice the tension of the cord).

4. A cord is used to vertically lower an initially stationary block of mass M at a constant downward acceleration of g/4. When the block has a fallen distance "d", find (a) the work done by the cords force on the block. (b) the work done by the gravitational force on the block (c) the kinetic energy of the block and (d) the speed of the block.

5. A 250 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 2.5 N/cm. The block becomes attached to he spring and compresses the spring 12 cm before momentarily stopping. While the spring is being compresses what work is done on the block by (a) the gravitational force on it and (b) the spring force ? (c) What is the speed of the block just before it hits the spring ? (assume friction is negligible ) (d) If the speed at impact is doubled what is the maximum compression of the spring?

6. A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 12 degrees with the horizontal. The rope moves parallel to the slope with a constant speed of 1.0 m/s. The force moves a distance and does 900J of work on the skier as the skier moved a distance of 8.0m up the incline. (a) If the rope moved with a constant speed of 2.0 m/s how much work would the force of the rope on the skier as the skier moved a distance of 8.0 m up the incline. What rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) 1.0 m/s (c) 2.0 m/s.

7. An initially stationary 2.0 kg object accelerates horizontally and uniformly to a speed of 10 m/s in 3.0s. (a) IN that 3.0 s interval how much work is done on the object by the force accelerating on it. What is the instantaneous power due to that force (b) at the end of the interval and (c) at the end of the first half interval.

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