# 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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#### Solution Summary

With good explanations, the problems are solved showing the calculations.