A block of mass m is sitting at height H above the floor at the end of a rough i

Question

A block of mass m is sitting at height H above the floor at the end of a rough inclined plane that makes an angle with the horizontal and has a coefficient of friction . It is next to a spring with force constantk that is parallel to the incline's surface. The block is pushed against the spring, compressing t a distance D. The block is then launched from rest. The block travels down the incline and then flies off the edge. It strikes the ground a distance at L from the left base of the table. A fan is blowing down on the scene, producing a constant vertical force of magnitude B pushes against the block throughout its entire motion from launch to hitting the ground Use energy methods to derive an expression for the speed v at which the block hits the ground in terms of relevant system parameters

Explanation / Answer

Applying work energy theorem,

Work done by gravity + work done by B + work done by friction + Work done by spring force = change in KE

m g (Dsin(theta) + H) + BH + (-u m g cos(theta) D) + k D^2 /2 = m v^2 /2 - 0

2 m g D sin(theta) + 2 m g H + 2 B H - 2 u m g D cos(theta) + K D^2 = m v^2

v = sqrt[ 2 g D sin(theta) + 2 g H + (2 B H / m) - (2 u g D cos(theta)) + (k D^2 / m)]

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