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Physics: Springs and Compression

1. A spring is compressed 10 cm by pushing a body against it. When released the spring pushes the body towards another identical spring. The body must slide over a rough floor in order to reach the second spring. When it makes contact the body compresses the opposite spring by 8 cm. Once again the body is forced back over the rough floor by the second spring towards the first spring. Determine the amount of compression produced by the body on the first spring as it collides with the spring. Also assume the work done by friction is the same for each trip.

2. Two identical objects are pressed against two different springs so that each spring stores 50 J of potential energy. The objects are then released from the rest. One spring is quite stiff (hard to compress), while the other one is quite flexible (easy to compress). Which of the following statement is or are true?
A. Both objects will have the same maximum speed after being released
B. The object pressed against the stiff spring will gain more kinetic energy than the other object.
C. Both spring are initially compressed by the same amount
D. The stiff spring has a large spring constant than the flexible spring
E. The flexible spring must have been compressed more than the stiff spring.

Solution Preview

1. The compression will be 5.29 cm. Here the potential energy of compression is given by U = 1/2 kx^2 . We have to find the energy lost in the process of traveling over the floor we have

delta U = 1/2k( (0.1m)^2 - (0.08m)^2) = 1/2k(0.0036 m^2)

Then the change in energy traveling in the opposite direction is going to be the same for the ...

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