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Classical Mechanics Level 1

You are pushing a piano up a ramp and into a truck. The ramp is 5 m 5~\mbox{m} long and the truck bed is 1 m 1~\mbox{m} high. Nearing the top, you slip, releasing your hold on the piano, which begins to slide back down the ramp. If there is no friction between the piano and the ramp, then what is the magnitude of the acceleration of the piano in m/s 2 \mbox{m/s}^2 ?

Details and assumptions

  • The acceleration due to gravity is − 9.8 m/s 2 -9.8~\mbox{m/s}^2 .


The answer is 1.96.

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David Mattingly by David Mattingly

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1 solution

David Mattingly Staff
May 13, 2014

The component of the gravitational acceleration along the ramp is g sin ⁡ θ g \sin \theta where θ \theta is the angle the ramp makes with the horizontal. Since the ramp is 1 m 1~\mbox{m} high and 5 m 5~\mbox{m} long, sin ⁡ θ = 1 / 5 \sin \theta=1/5 . Therefore the acceleration down the ramp is 9.8 / 5 = 1.96 m/s 2 9.8/5=1.96~\mbox{m/s}^2 .

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