1. Q07. Conservation of Energy

2. A 0.20-kg particle moves along the x-axis under the influence of a stationary object. The potential energy is given by :
U(x) = (8.0 J/m2) x2 + (2.0 J/m4) x4
where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is:
2.5 m/s
5.7 m/s
7.9 m/s
11 m/s
<PowerClick><Answer>5</Answer><Option>5</Option></PowerClick>

3. 

4. A 2.2-kg block starts from rest on a rough inclined plane that makes an angle of 25° with the horizontal. The coefficient of kinetic friction is As the block goes 2.0 m down the plane, the mechanical energy of the Earth-block system changes by:
–9.8 J
9.8 J
–4.6 J
4.6 J
<PowerClick><Answer>2</Answer><Option>5</Option></PowerClick>

5.  = 0.25
2.2 kg
25

6. A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of:
(1/4) m v2
m v2 / 4k
<PowerClick><Answer>1</Answer><Option>5</Option></PowerClick>

8. A 700-N man jumps out of a window into a fire net 10 m below
A 700-N man jumps out of a window into a fire net 10 m below. The net stretches 2 m before bringing the man to rest and tossing him back into the air. The maximum potential energy of the net, compared to it's unstretched potential energy, is:
300 J
710 J
850 J
7000 J
8400 J
<PowerClick><Answer>5</Answer><Option>5</Option></PowerClick>

9. 10 m
2 m

10. A toy cork gun contains a spring whose spring constant is 10. 0 N/m
A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed 5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is:
6.32 m/s
1.63 m/s
2.00 m/s
2.08 m/s
2.45 m/s
<PowerClick><Answer>3</Answer><Option>5</Option></PowerClick>

11. 5cm
1cm

12. A small object of mass m, on the end of a light cord, is held horizontally at a distance r from a fixed support as shown. The object is then released. What is the tension in the cord when the object is at the lowest point of its swing?
m g / 2
m g
2 m g
3 m g
m g r
<PowerClick><Answer>4</Answer><Option>5</Option></PowerClick>

13. T mg 

14. A small object of mass m starts at rest at the position shown and slides along the frictionless loop-the-loop track of radius R. What is the smallest value of y such that the object will slide without losing contact with the track ?
R /4
R /2 R
2 R
zero
<PowerClick><Answer>2</Answer><Option>5</Option></PowerClick>

15.  

16. A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. The speed of the ball at the bottom of the circle is:
<PowerClick><Answer>4</Answer><Option>5</Option></PowerClick>

17. At top, T = 0 : 
E Conservation : 

18. its mechanical energy is a minimum the forces on it are balanced
A rectangular block is moving along a frictionless path when it encounters the circular loop as shown. The block passes points 1,2,3,4,1 before returning to the horizontal track. At point 3:
its mechanical energy is a minimum
the forces on it are balanced
it is not accelerating
its speed is a minimum
it experiences a net upward force
<PowerClick><Answer>4</Answer><Option>5</Option></PowerClick>

19. its mechanical energy is a minimum
the forces on it are balanced
it is not accelerating
its speed is a minimum
it experiences a net upward force