A cart is placed on an inclined plane (a wooden board which is seton an angle) a

Question

A cart is placed on an inclined plane (a wooden board which is seton an angle) and attached to a pulley by a rope at the end of thewooden board. On the other side of the rope, hanging below theinclined plane is a weight. When let free the pulley system movesin a manner in which the weight moves towards the ground and thecart moves forward on the board. The question is when the cartreaches it's maximum speed and how to figure out the value for thatspeed given only the mass of the cart and weight and anydistance/length measurements required.

Explanation / Answer

M g - T = M a    where M is mass of hangingobject, T tension in rope and a acceleration of mass M T - m g sin = m a   where m is mass ofcart a = (M - m sin ) g / (M + m)     theacceleration of cart (adding equations and eliminatingT) v = a t       speed of cart atany time t s = 1/2 a t2    distance carttravels in time t

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