Physics
A 2.5-kg block is sliding along a rough horizontal surface and collides with a horizontal spring whose spring constant is 320 N/m. Unstretched, the spring is 20.0 cm long. The block causes the spring to compress to a length of 12.5 cm as the block temporarily comes to rest. The coefficient of kinetic friction between the block and the horizontal surface is 0.25. a) How much work is done by the spring as it brings the block to rest? b) How much work is done on the block by friction as the block is in contact with the spring? c) What was the speed of the block when it first came into contact with the spring?
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Answers
a) The work done by the spring is 640 Joules.
b) The work done on the block by friction is 200 Joules.
c) The speed of the block when it first came into contact with the spring was 5.3 m/s. This is calculated by using the equation W = mgh, where W is the work done by friction, m is the mass, g is gravity, and h is the distance the block travels, which is calculated by subtracting the length of the unstretched spring (20 cm) from the length of the compressed spring (12.5 cm). The work done by friction is equal to the kinetic energy of the block, and so the speed can be calculated by dividing the work done by the kinetic energy of the block.
