A child\'s sled has rails that slide with little friction across the snow. Logan

Question

A child's sled has rails that slide with little friction across the snow. Logan has an old wooden sled with heavy iron rails that has a mass of 9.0 kg quite a bit for a 28 kg child! Logan runs at 3.7 m/s and leaps onto the stationary sled and holds on tight as it slides forward. The impact time with the sled is 0.26 s.

Immediately after Logan jumps on the sled, how fast is it moving?

What was the force on the sled during the impact?

How much energy was "lost" in the impact?

Where did this energy go?

Explanation / Answer

mass of the logan is m = 9 kg mass of child M = 28 kg initial velocity of the logan u = 3.7 m/s The impact time with the sled is t = 0.26 s ----------------------------------------------------- before impact, the momentum of the child is               P1 = Mu                     = (28 kg)(3.7 m/s)                     = 103.6 kg.m/s after impact, using , law of conservation of momentum      P1 = P2     103.6 kg.m/s = (9 kg + 28 kg)V velocity V = 2.8 m/s ------------------------------------------------------ change in momentum dP = (9 kg)(2.8 m/s)                                       = 25.2 kg.m/s force F = dP/dt            = (25.2 kg.m/s) / (0.26 s)            = 96.92 N ---------------------------------------------------- kinetic energy K1 = (1/2)(9 kg)(3.7 m/s)2                             = 61.6 J kinetic energy K2 = (1/2)(9 kg+28 kg)(2.8 m/s)2                             = 145.04 J lost in energy K = K2 - K1                          = 145.04 J - 61.6 J                          = 83.44 J ------------------------------------------------------ this energy converted into heat energy.                             = 61.6 J kinetic energy K2 = (1/2)(9 kg+28 kg)(2.8 m/s)2                             = 145.04 J lost in energy K = K2 - K1                          = 145.04 J - 61.6 J                          = 83.44 J ------------------------------------------------------ this energy converted into heat energy.                             = 145.04 J lost in energy K = K2 - K1                          = 145.04 J - 61.6 J                          = 83.44 J ------------------------------------------------------ this energy converted into heat energy.

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