A block of mass m is held in place on a ramp of mass M with a slope of angle ? ,

Question

A block of mass m is held in place on a ramp of mass M with a slope of angle ?, which in turn is held in place as shown in the figure below. The ramp is free to move on the surface beneath it. There is no friction anywhere. The ramp is then pushed with a horizontal force so that the block does not slide on the ramp. Derive an expression for the magnitude of this force. (Use any variable or symbol stated above along with the following as necessary: g. Assume SI units.)
F =

A block of mass m is held in place on a ramp of mass M with a slope of angle ?, which in turn is held in place as shown in the figure below. The ramp is free to move on the surface beneath it. There is no friction anywhere. The ramp is then pushed with a horizontal force so that the block does not slide on the ramp. Derive an expression for the magnitude of this force. (Use any variable or symbol stated above along with the following as necessary: g. Assume SI units.) F =

Explanation / Answer

horizontal acceleration of the system=F/(M+m)

now for the mass m,

balancing force parallel to the plane,

macos theta=mgsin theta

or tan theta=a/g

=F/(m+M)g

or F=(m+M)*g*tan theta

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