Question

Identical green blocks are sliding down too different ramps made of the same material (same surface texture). Ramp $1$ is not a steep as ramp $2$, as can be seen in the diagram below.
Which block experiences a greater force of friction and why?

• A. The block on ramp $1$ experiences more frictional force because the normal force on block $1$ by the ramp is greater for it than for block $2$
• B. The block on ramp $2$ experiences more frictional force because the normal force on block $2$ by the ramp is greater for it than for block $1$
• C. The block on ramp $1$ experiences more frictional force because the component of the force of gravity down the ramp is greater on block $1$ than it is on block $2$, and the force of friction must be equal to this component of gravity
• D. The block on ramp $2$ experiences more frictional force because the component of the force of gravity down the ramp is greater on block $2$ than it is on block $1$, and the force of friction must be equal to this component of gravity
• E. The force of friction acting on each block is the same

Answer 1

The correct option is D The block on ramp $2$ experiences more frictional force because the component of the force of gravity down the ramp is greater on block $2$ than it is on block $1$, and the force of friction must be equal to this component of gravity

Let the angle of inclination be $\theta$.

Resolving the weight $mg$ of the block along and perpendicular to the inclined surface is shown.

Friction force acting on the block $f=mg\sin \theta$

$⟹$ $f\propto \sin \theta \propto \theta$

As the angle of inclination made by ramp 2 is more than that of ramp 1, thus component of force of gravity down the ramp is greater on block 2 than block 1. Hence the block on ramp 2 experiences more frictional force than block on ramp 1.