5 AP Physics Uniform Circular Motion Questions (URGENT!!)

Question

1. A 5.0-kg object attached to the end of a 4.0-m rope is moving in a vertical circle. What is the object's linear velocity at the top of the circle if the tension in the rope at this point is 30 N?
2. 10 m/s
3. 8 m/s
4. 9 m/s
5. The work done by the centripetal force acting on an object moving at a constant linear speed is:
6. greater than zero since it takes energy to turn an object
7. greater than zero since a force acts and the object moves
8. equal to zero because the force and the displacement of the object are perpendicular
9. A 0.40 kg object attached to the end of a 0.50 m string rotates in a vertical circle. If the angular speed of the object at the bottom of the circle is 8.0 rad/s, what is the tension in the string at this point?
10. 10 N
11. 17 N
12. 11 N
13. A roller coaster travels around a vertical 8-m radius loop. Determine the speed at the top of the loop if the normal force exerted by the seats on the passengers is equal to ¼ of their weight.
14. 13 m/s
15. 10 m/s
16. 15 m/s
17. 7 m/s
18. A 2.0 x 10³ kg roller coaster travels around a vertical 24-m radius loop. If the coaster has a tangential speed of 18 m/s at the lowest point of the loop, what is the normal force that is exerted on the coaster by the track at this point?
19. 5.3 x 10⁴ N
20. 3.0 x 10⁴ N
21. 4.7 x 10⁴ N

I cannot understand these so can you also show work please... Thank you!!

Answer 1

Part 1) Mv²/r-Mg=30 ... yields v=8m/s

Part 2) Work = F dot r =0 since F and r are at 90 degrees

Part 3) Mv2/r+Mg= T ... yields T=16.7 Newtons

Part 4) Mv2/r-Mg = N = Mg/4 ...yields N=9.9 Newtons

Part 5) Mv2/r+Mg=N .... yields N= = 4.7*10⁴ Newtons