A car tows a trailer which has a mass of 182kg. The car starts from rest on a horizontal road with an acceleration of 2.40m/s^2. As soon as the trailer starts to move a friction force of 64.0N acts on the trailer. Calculate the magnitude of the force which the car exerts on the trailer. Why is the answer 501N and why is the friction positive instead of negative?
friction is not positive if pulling force is positive
total force forward = pulling force - friction force
= m a
F - 64.0 = 182 *2.40
F = 64 + 437
F = 501 N
If you are the same person who posted about velocity and distance fallen please check the reply I posted.
To calculate the magnitude of the force which the car exerts on the trailer, we need to first understand the forces acting on the trailer.
The forces acting on the trailer are:
1. The force exerted by the car on the trailer (the force we are trying to find)
2. The friction force acting on the trailer, in the direction opposite to its motion
Since the trailer is accelerating, we can apply Newton's second law of motion:
Force = Mass * Acceleration
The mass of the trailer is given as 182 kg, and the acceleration is given as 2.40 m/s^2:
Force = 182 kg * 2.40 m/s^2
Force = 436.8 N
So, the force exerted by the car on the trailer is 436.8 N.
Now, let's address the question of why the answer is 501 N instead of 436.8 N.
The friction force acting on the trailer is given as 64.0 N. This force opposes the motion of the trailer. Since it opposes the motion, it is usually considered negative.
When we take into account the direction of the friction force, we need to add it algebraically to the force exerted by the car on the trailer. If the car exerts a force of 436.8 N, and the friction force is -64.0 N (negative because it opposes motion), the total force exerted by the car on the trailer is:
Total force = Force exerted by the car + Friction force
Total force = 436.8 N + (-64.0 N)
Total force = 372.8 N
Therefore, the magnitude of the force that the car exerts on the trailer is 372.8 N, not 501 N.
It is important to note that the direction of the force determines whether it is positive or negative. In this case, the friction force is positive because it is acting in the same direction as the force exerted by the car, resulting in a larger total force.