A 50-N crate sits on a horizontal floor where the coefficient of static friction between the crate and the floor is 0.50. A 20-N force is applied to the crate acting to the right. What is the resulting static friction force acting on the crate?

(a) 20 N to the right.

(b) 20 N to the left.

(c) 25 N to the right.

(d) 25 N to the left.

(e) None of the above; the crate starts to move.

A force was applied to the resting crate. Then the frictional force that acts on the crate at the rest position.

The direction of the static frictional force on the crate is opposite to the applied force on the same crate.

The given data can be listed below as:

• The weight of the crate is $W=50\mathrm{N}$.
• The static frictional coefficient between the crate and the floor is ${\mu }_s=0.50$.
• The value of applied force is $P=20\mathrm{N}$.

The static frictional coefficient value results in the maximum value of the frictional force before the crate moves forward.

The crate is not moving as it is at rest. Thus, the static frictional force is equal to the applied force on the crate. The resulting frictional force $\left(F_s\right)$can be expressed as:

$\begin{array}{c}{F}_s=P\\ =20\mathrm{N}\end{array}$

The applied force acts in the rightward direction. So, the static frictional force acts in the opposite direction of the applied force.

For the cart's movement, the applied force (P) must be greater than the value of the frictional force.

The cart will not move for any forces less than or equal to the value of the applied force (20 N).

The static frictional force is 20 N, acting in the leftward direction. This will not induce the cart to move.

Option (a) is incorrect because even though the resulting frictional force is 20 N, it does not act in the rightward direction.

Option (b) is correct because the value of frictional force is 20 N, acting in the leftward direction.

Option (c) is incorrect because the resulting frictional force is not equal to 25 N. Also, its direction is not in the right direction.

Option (d) is incorrect because the resulting frictional force is not 25 N, although the direction of the friction force is correct; that is, leftward.

Option (e) is incorrect because the crate will not move.

So, from the above analysis of the options, it can be concluded that option (b) is correct.

Thus, the correct option is (b), 20 N to the left.