Question

On vacation, your 1300-kg car pulls a 530-kg trailer away from a stoplight with an acceleration of 1.30 m/s^2.

What is the net force exerted by the car on the trailer?

What force does the trailer exert on the car?

What is the net force acting on the car?

Answer 1

Concepts and reason

The concept used to solve this problem is Newton’s second law.

For the calculation of the force, use the Newton’s second law of force equation. The force is directly related to the mass of the object and its acceleration. The force exerted by the trailer on the car is calculated by using Newton’s third law of motion.

Fundamentals

From Newton’s second law, the expression of the force is,

$F = ma$

Here, $F$ is the force, $m$ is the mass of the object, and $a$ is the acceleration.

Newton’s third law states that every action has an equal and opposite reaction.

Calculate the force exerted by the car on the trailer.

The expression for the force from Newton’s second law is,

$F = ma$

Substitute $530{\rm{ kg}}$ for $m$ and $1.30{\rm{ m/}}{{\rm{s}}^2}$ for $a$ .

$\begin{array}{c}\\F = \left( {530{\rm{ kg}}} \right)\left( {1.30{\rm{ m/}}{{\rm{s}}^2}} \right)\\\\ = 689{\rm{ N}}\\\end{array}$

Calculate the force exerted by the trailer on the car.

$F = - 689{\rm{ N}}$

Calculate the net force acting on the car.

Substitute $1300{\rm{ kg}}$ for $m$ and $1.30{\rm{ m/}}{{\rm{s}}^2}$ for $a$ .

$\begin{array}{c}\\F = \left( {1300{\rm{ kg}}} \right)\left( {1.30{\rm{ m/}}{{\rm{s}}^2}} \right)\\\\ = 1690{\rm{ N}}\\\end{array}$

Ans:

The net force exerted by the car on the trailer is $689{\rm{ N}}$ .