You drop a 1.10 kg book to a friend who stands on the ground at distance D = 12.0 m below. If your friend's outstretched hands are at distance d = 1.60 m above the ground. now take U to be 100 J at ground level and again find (e) Wg, (f ) ΔU, (g) U at the release point, and (h) U at her hands.

A chain with length b and mass M is hang on ceiling under constant gravity g. Find the tension at point A when the distance between the ceiling and B is x for each casese. (1) The chain free falls. (2) Energy is conserved. A B CM T A B t=0 time t> 0 CM

You are designing a ski jump ramp for the next Winter Olympics. You need to calculate the vertical height h from the starting gate to the bottom of the ramp. The skiers push off hard with their ski poles at the start, just above the starting gate, so they typically have a speed of 2.0 m/s as they reach the gate. For safety, the skiers should have a speed of no more than 30.0 m/s when they reach the bottom of the ramp. You determine that for a 80.0 kg skier with good form, friction and air resistance will do total work of magnitude 4000 J on him during his run down the slope. 1) What is the maximum height h for which the maximum safe speed will not be exceeded?         Express your answer in meters.

A 55.4-kg box is being pushed a distance of 8.02 m across the floor by a force P whose magnitude is 169 N. The force P is parallel to the displacement of the box. The coefficient of kinetic friction is 0.249. Determine the work done on the box by (a) the applied force, (b) the friction force, (c) the normal force, and (d) by the force of gravity. Be sure to include the proper plus or minus sign for the work done by each force. (a) Number Units (b) Number i ! Units J (c) Number Units (d) Number !Units J

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A 45.9-kg box is being pushed a distance of 6.54 m across the floor by a force P whose magnitude is 168 N. The force P is parallel to the displacement of the box. The coefficient of kinetic friction is 0.208. Determine the work done on the box by (a) the applied force, (b) the friction force, (c) the normal force, and (d) by the force of gravity. Be sure to include the proper plus or minus sign for the work done by each force.

The specialty of an athlete on the women's track team is the pole vault. She has a mass of 60 kg and her approach speed is 8.7 m/s. When she is directly above the bar, her speed is 1.3 m/s. Neglecting air resistance and any energy absorbed by the pole, determine the amount(in m) she has raised herself as she crosses the bar.   Answer in Meters.

An 80.0-kg skydiver jumps out of a balloon at an altitude of 1 000 m and opens his parachute at an altitude of 200 m. (a) Assuming the total retarding force on the skydiver is constant at 50.0 N with the parachute closed and constant at 3 600 N with the parachute open, find the speed of the skydiver when he lands on the ground. (b) Do you think the skydiver will be injured? Explain. (c) At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground is 5.00 m/s? (d) How realistic is the assumption that the total retarding force is constant? Explain.

A 9.00-kg particle moves from the origin to position ©, having coordinates x = 4.50 m and y = 4.50 m as shown in the figure. One force on the particle is the gravitational force acting in the negative y direction. Using the equation (W = FAr cos e = F . Ař), calculate the work done by the gravitational force in going from O to © along the following paths. у (m) C) (x, y) х (m) (a) the purple path (o0© (b) the red path (OB© (c) the blue path (O© (d) Your results should all be identical. Why?

Keep the track tilted at 7∘∘ with the horizontal, at let the cart roll downwards. The length of the track is 75 cm. Starting from zero speed at the top of the track, what will be the speed of the cart as it reaches the bottom? Write your answer in m/s, and ignore friction. Mass of the cart = 250 grams.