Question 1: A spring with a spring constant of 15 N/m is initially compressed by

Question

Question 1:

A spring with a spring constant of 15 N/m is initially compressed by 3.0 cm. How much work is required to compress the spring an additional 4.0 cm?
Answers:

1- 0.0068 J
2- 0.012 J
3- 0.024 J
4- 0.030 J
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Question 2

A 60-kg skier starts from rest from the top of a 50-m high slope. If the work done by friction is -6.0 x 103 J, what is the speed of the skier on reaching the bottom of the slope?
Answers:

1- 28 m/s
2- 24 m/s
3- 34 m/s
4- 31 m/s
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Question 3

A 0.20-kg particle moves along the x axis under the influence of a stationary object. The potential energy is given by , where x is the coordinate of the particle in m. 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:
Answers:

1- 0
2- 2.5 m/s
3- 5.7 m/s
4- 11 m/s
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Question 4

A pendulum is drawn aside until the ball has risen 0.50 m above its lowest position. It is then given an initial speed of 3.0 m/s. The speed of the ball at its lowest position is:
Answers:

1- zero
2- 0.89 m/s
3- 3.7 m/s
4- 4.3 m/s
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Question 5

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 force of the cord when the object is at the lowest point of its swing?
pendulum_semisphere
Answers:

1- 3mg
2- 2mg
3- mgR
4- mg
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Question 6

The potential energy of a body of mass m is given by . The corresponding force is:
Answers:

1- -mg + kx
2- mg - kx
3- mgx2/2 - kx3/6
4- -mgx2/2 + kx3/6
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Question 7

A 25-g ball is released from rest 80 m above the surface of the Earth. During the fall the total thermal energy of the ball and air increases by15 J. Just before it hits the surface its speed is
Answers:

1- 19 m/s
2- 36 m/s
3- 40 m/s
4- 45 m/s
5- 53 m/s
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Question 8

A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5 m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200 N/m, the thermal energy of the block and the table top must have:
Answers:

1- not changed
2- decreased by 1.9 J
3- decreased by 2.6 J
4- increased by 1.9 J
5- increased by 2.6 J
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Explanation / Answer

Now, Work Needed to compress the string x = 3cm : W3 = -0.5 kx^2 = -0.5 x 15 x (0.03)^2 = -0.00675 Joules Work Needed to compress the string x = 3+4 = 7 cm : W7 = -0.5 kx^2 = -0.5 x 15 x 0.07^2 = -0.03675 Joules Work needed to be done = W7- W3 = - 0.03 Joules Hence Option 4 is correct !!!

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