A wood block (m=4.00kg) sits on top of a steel ramp, as shown in the figure abov

Question

A wood block (m=4.00kg) sits on top of a steel ramp, as shown in the figure above. (for wood on steel ?s=0.650 ?k=0.250). The ramp is initially horizontal (theta=0degrees), but its slope, theta, is slowly icreased with time. As soon as the block starts to move, the slope stops changing. What is the acceleration of this block?

Also include free body diagram.

A wood block (m=4.00kg) sits on top of a steel ramp, as shown in the figure above. (for wood on steel ?s=0.650 ?k=0.250). The ramp is initially horizontal (theta=0degrees), but its slope, theta, is slowly icreased with time. As soon as the block starts to move, the slope stops changing. What is the acceleration of this block?

Explanation / Answer

The block will start to move when the component of the weight down the plane equals static friction

mgsin(angle) = umgcos(angle) (mass and gravity cancel)

tan(angle) = u

angle = 33.02 degrees

Then, when it is moving, kinetic friction applies

mgsin(angle) - umgcos(angle) = ma   (mass cancels)

(9.8)(sin 33.02) - (.25)(9.8)(cos 33.02) = a

a = 3.29 m/s^2

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