A large sled of mass 12kg is at rest on a horizontal, frictionless sheet of ice,

Question

A large sled of mass 12kg is at rest on a horizontal, frictionless sheet of ice, when a heavy rock with a mass of 7.5 kg is thrown onto it from behind. The rock is moving purely horizontally at a speed of 2.4 m/s when it comes into contact with the sled, and it skids across the rough top surface of the sled until it and the sled are moving forward together at the same speed. The scrape marks on the sled indicate that the rock skidded across it a distance of 1.6 m. Find the final speed of the sled.

Explanation / Answer

a) Applying conservation of momentum

   Here, 7.5 * 2.4 = (12 + 7.5) * v

=> v = 0.923 m/sec

=> final speed of sled = 0.923 m/sec

b)   Here, applying , v2 - u2 = 2as

=>    0 - 0.9232 = 2 * a * 1.6

=> a = - 0.2662 m/sec2

=> magnitude of frictional force = 7.5 * 0.2662

                                                 = 2 N

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