A child builds a simple cart consisting of a 0.60 m by 1.20 m sheet of plywood o

Question

A child builds a simple cart consisting of a 0.60 m by 1.20 m sheet of plywood of mass 7.8 kg and four wheels, each 20.0 cm in diameter and with a mass of 2.08 kg. It is released from the top of a 15° incline that is 33 m long. Find the speed at the bottom. Assume that the wheels roll along the incline without slipping and that friction between the wheels and their axles can be neglected. (You may assume that the center of mass of the cart starts at very top of the incline.)

I used conservation of energy but I'm having a hard time setting it up

I will really appreciate your help !

Explanation / Answer

total mass of the cart = 4*2.08+7.8=16.12kg the force responsible for the acceleration of the cart = mgsin15 = 16.12*9.81*sin15 =40.9289 N this is constant force on the cart. the length of the incline = 33m hence work done by the force = 40.9289*33 = 1350.6543 work done by the force = kinetic energy = mv^2/2 v^2 = 1350.6543*2/16.12 = 167.5749789 hence v= 12.945 m/s

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