Question

A crate (box) rests on a smooth horizontal surface and a person pulls it with a $10N$ force. Rank the situations shown below according to the magnitude of the normal force exerted by the surface on the crate, from the least to the greatest.

• A. $1$, $2$, $3$
• B. $3$, $2$, $1$
• C. $3$, $1$, $2$
• D. $1$, $3$, $2$

Answer 1

The correct option is B

$3$, $2$, $1$

Step 1: Given data

In case $\left(1\right)$ there is a horizontal force of $10N$ exerted on the crate in the right-hand direction.

In case $\left(2\right)$ there is a force of $10N$ exerted on the crate make some angle with the surface.

In case $\left(3\right)$ there is a force of $10N$ exerted on the crate in the upward direction.

Step 2: Determine the normal force exerted by the surface on the crate in case $\mathbf{\left(}\mathbf{1}\mathbf{\right)}$

For the first crate, the force is acting horizontally. It is in the same direction of motion.

So, the net force acting on the system vertically is:

$\Rightarrow N_1-mg=0$

$\Rightarrow N_1=mg$

Step 3: Determine the normal force exerted by the surface on the crate in case $\mathbf{\left(}\mathbf{2}\mathbf{\right)}$

For the second crate, the force is acting diagonally away from the ground.

Out of the total force, we notice that a component acts in the vertical direction, and the other acts on the right pulling the box.

So the net force acting on the system vertically is,

$\Rightarrow \left(N_2+10\sin \varphi \right)-mg=0$

$\Rightarrow N_2=mg-10\sin \varphi$

As $\sin \varphi$ varies from $0<\varphi <1$.

So the normal force acting on the second crate is lesser than the normal force acting on the first crate.

Step 4: Determine the normal force exerted by the surface on the crate in case $\mathbf{\left(}\mathbf{3}\mathbf{\right)}$

For the third crate, the force is acting in the vertically upward direction.

So the net force acting on the system vertically is,

$\Rightarrow \left(N_3+10\right)-mg=0$

$\Rightarrow N_3=mg-10$

So the normal force acting on the third crate is lesser than the normal force acting on the second crate.

Therefore the magnitude of the normal force exerted by the surface on the crate, from the least to the greatest is $\mathbf{3}$, $\mathbf{2}$, $\mathbf{1}$.

Hence Option B is correct.