Question

If you press an apple crate against a wall so hard that the crate cannot slide down the wall, what is the direction of (a) the static frictional force${\overrightarrow{\mathbf{f}}}_{\mathbf{s}}$on the crate from the wall and (b) the normal force ${\overrightarrow{\mathbf{F}}}_{\mathbf{N}}$on the crate from the wall? If you increase your push, what happens to (c)${\mathit{f}}_{\mathbf{s}}$, (d)${\overrightarrow{\mathbf{F}}}_{\mathbf{N}}$, and (e)${\mathit{f}}_{\mathbf{s}\mathbf{.}\mathbf{m}\mathbf{a}\mathbf{x}}$ ?

Short answer

a) The direction of the static frictional force ${\overrightarrow{f}}_s$on the crate from the wall is upwards.

b) The direction of the normal force ${\overrightarrow{F}}_N$on the crate from the wall is to the left.

c) If the push applied on the carte is increased, then ${\overrightarrow{f}}_s$remains the same.

d) If the push applied on the carte is increased, then ${\overrightarrow{F}}_N$increases.

e) If the push applied on the carte is increased, then ${\overrightarrow{f}}_{s.max}$increases.

Step-by-step solution

The given data

The press applied on the crate against a wall is so hard that the crate does not slide down.

Understanding the concept of the frictional force

To show all the forces, we have to draw a free-body diagram. Using this body diagram, we can observe the directions of the forces acting on it and their behavior if the applied press is increased on the crate.

Formula:

The static frictional force acting on a body,

${\mathbf{f}}_{\mathbf{s}\mathbf{.}\mathbf{max}}\mathbf{=}{\mathbf{\mu }}_{\mathbf{s}}{\mathbf{F}}_{\mathbf{N}}$ (1)

a) Calculation of the direction of the static frictional force

Free body diagram of blocks

From the above free body diagram acting on the crate, the static frictional force${\overrightarrow{\mathrm{f}}}_{\mathrm{s}}$ on the crate from the wall is directed to the up.

b) Calculation of the direction of the normal force from the wall

From the above free body diagram acting on the crate, the normal force${\overrightarrow{\mathrm{F}}}_{\mathrm{N}}=\mathrm{N}$ on the crate from the wall is to the left of the wall.

c) Calculation of the behavior of the static frictional force

If you increase push P on the crate then,${\overrightarrow{\mathrm{f}}}_{\mathrm{s}}$ does not depend on the push P and so it remains the same.

d) Calculation of the behavior of the normal force from the wall

The normal force${\overrightarrow{\mathrm{F}}}_{\mathrm{N}}$ is also increased if we increase push P on the crate.

e) Calculation of the behavior of the normal force from the wall

As we increase push P, the normal force${\overrightarrow{\mathrm{F}}}_{\mathrm{N}}$ is also increased and the relation between${\overrightarrow{\mathrm{f}}}_{\mathrm{s}.\max }$ and normal force${\overrightarrow{\mathrm{F}}}_{\mathrm{N}}$ considering the equation (1).

${\overrightarrow{\mathrm{f}}}_{\mathrm{s}}$is proportional to the normal force${\overrightarrow{\mathrm{F}}}_{\mathrm{N}}$ , thus as${\overrightarrow{\mathrm{F}}}_{\mathrm{N}}$ increases,${\overrightarrow{\mathrm{f}}}_{\mathrm{s}.\max }$ it also increases.