A block rests on a rough plane whose inclination θ to the horizontal can be varied. Which of the following graphs indicates how the frictional force F between the block and the plane varies as θ is in

Question

A block rests on a rough plane whose inclination θ to the horizontal can be varied. Which of the following graphs indicates how the frictional force F between the block and the plane varies as θ is increased?

TestHub · Accepted Answer

While the block stays at rest the static friction balances the component of gravity along the plane
$F = m g sin θ$
which rises with $θ$ .
Once $tan θ$ exceeds $μ_{s}$ the block slides and the friction becomes kinetic
$F = μ_{k} m g cos θ$
which falls as $θ$ grows.
So $F$ first rises, peaks at the angle of repose and then falls to zero at
$θ = 90^{\circ}$
- graph (B).

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