Assignment:
Question 1. A 39.0 kg child is in a swing that is attached to ropes 1.60 m long.
The acceleration of gravity is 9.81 m/s 2.
Find the gravitational potential energy associated with the child relative to the child's lowest position under the following conditions:
a) when the ropes are horizontal.
b) when the ropes make a 37.0 ? angle with the vertical.
c) at the bottom of the circular arc.
Question 2. A 54 kg skier is at the top of a slope, as in the figure. At the initial point A, the skier is 7.08 m vertically above the final point B.
a) Find the difference in gravitational potential energy associated with the skier at the points A and B if the zero level for gravitational potential energy is at point B.
Question 3. Find the difference in potential energy if the zero level is at point A.
Question 4. Find the difference in potential energy if the zero level is midway down the slope, at a height of 3.54 m.
Question 5. A 1.8 kg ball is attached to a ceiling by a 3.94 m long string. The height of the room is 5.18 m .
The acceleration of gravity is 9.8 m/s 2.
What is the gravitational potential energy associated with the ball relative to the ceiling?
Question 6. What is its gravitational potential energy relative to the floor?
Question 7. What is its gravitational potential energy relative to a point at the same elevation as the ball?
Question 8. In an arcade game a 0.09 kg disk is shot across a frictionless horizontal surface by compressing it against a spring and releasing it.
If the spring has a spring constant of 248 N/m and is compressed from its equilibrium position by 4 cm, find the speed with which the disk slides across the surface.
Question 9. A(n) 139 g arrow is shot straight up into the air with a speed of 16 m/s. It reaches a maximum height of 12.0612 m.
The acceleration of gravity is 9.8 m/s 2.
Find the initial kinetic energy.
Question 10. Find the potential energy at its highest position.
Question 11. Find the magnitude of the energy lost due to air resistance.
Question 12. A bead slides without friction around a loop-the-loop. The bead is released from a height 24.2 m from the bottom of the loopthe-loop which has a radius 9 m.
What is its speed at point A ?
Question 13. How large is the normal force on it at point A if its mass is 4 g?
Question 14. A block starts at rest and slides down a frictionless track (as shown in the figure below).
It leaves the track horizontally, flies through the air, and subsequently strikes the ground.
The acceleration of gravity is 9.81 m/s 2.
What is the speed v of the ball when it leaves the track?
Question 15. What is the horizontal distance x the block travels in the air?
Question 16. What is the speed of the block when it hits the ground?