# 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.

Solving Physics Questions

1. Give an example of a situation in which there is a force and a non-zero displacement, but the force does no work. Explain why it does no work.

2. What is a conservative force?

3. (a) Calculate the work done on a 1500 kg elevator by its cable to lift it 40.0 m at constant speed, assuming friction averages 100 N. (b) What is the work done on the elevator by gravity in this process? (c) What is the total work done on the elevator?

4. A shopper pushes a grocery cart 20.0 m at constant speed on level ground, against a 35.0 N frictional force. He pushes in a direction 25.0 degrees below the horizontal. (A) What is the work done on the cart by friction? (B) What is the work done on the cart by gravity? (C) What is the work done on the cart by the shopper? (Remember the Work-Kinetic Energy Theorem.) (D) Find the force the shopper exerts, giving both the x- and y-components, and the magnitude of the force. (E) What is the total work done on the cart?

5. Compare the kinetic energy of a 20,000 kg truck moving at 110 km/h with that of an 80.0 kg astronaut in orbit moving at 27,500 km/h.

6. (a) Calculate the force needed to bring a 950 kg car to rest from a speed of 90.0 km/h in a distance of 120 m. Use the work-kinetic energy theorem (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).

7. Suppose a bicycle rolls down a hill, starting from rest. It drops an altitude of 4.0 m, ending up on level ground. The mass of the bicyclist plus bike is 70.0 kg. Assume that friction can be ignored. (A) Find the potential energy lost by the bicycle and rider. (B) Find the speed of the bicycle when it reaches level ground. (C) Repeat (B), assuming that this time the bicycle starts with an initial speed of 4.0 m/s. (D) Suppose frictional forces dissipate 400 J of energy while the bike rolls down the hill. Find the speed of the bicycle when it reaches level ground in this case. (Again, assume an initial speed of 4.0 m/s.)

8. A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.5-m-high hill as shown. (A) Find his final speed at the top, assuming no friction is involved. (Use energy methods, not the equations for constant acceleration.) (B) Now suppose the coefficient of friction between skier and snow is 0.08. Again find his speed at the top of the hill. (Don't worry about energy lost on the flat at either end --- just find the energy dissipated by friction on the 35-degree slope and use this in your calculations.)

9. A cart is rolling without friction on a platform, hooked to a hanging mass with a string which runs over a pulley, as shown in the diagram. The mass m_c of the cart is 0.35 kg, and the hanging mass is 0.050 kg. (A) How much work does the force of gravity do on the system when the hanging mass moves from a height of 0.80 m to a height of 0.30 m? (B) Assuming it starts from rest, find the speed of the cart after 0.50 m of travel. Use the information from part (A), and energy considerations. Do not use Newton's laws.

10. Suppose we have a spring whose force as a function of compression is shown in the graph. We place a ball of mass 0.600 kg on top of the spring and compress it by 0.25 m from its relaxed length. We then let the ball go. When the ball is released, its height above the floor is 0.10 m.

(A) Find the spring constant of the spring.

(B) Determine the potential energy of the spring when compressed.

(C) Find the highest point the ball reaches in its flight.

(D) Determine the velocity of the ball just as it leaves the spring: that is, just as the spring is fully relaxed.