Question

The wheels of a midsize car exert a force of 2100 N backward on the road to accelerate the car in the forward direction. If the force of friction including air resistance is 2150 N and the acceleration of the car is 1.80 m/s^2, what is the mass of the car plus its occupants? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton's laws of motion. For this situation, draw a free-body diagram and write the net force equation.

Answer 1

The mass of the car plus its occupants = 1027.78 kg.

Step-by-step explanation:

The first step in solving the question is to draw the free body diagram for the question, indicating all the forces acting on the car.

The forces include:

- The frictional force including air resistance which is acting in the opposite direction to motion.

- The road exerts an equal and opposite reaction on the car to drive the car forward in response to the backward force exerted on the road by the wheels of the car.

- The weight of the car and occupants of the car, acting downwards.

- Normal reaction on the car as a response to the force of gravity/weight of the car.

- And finally, the net force acting on a body accelerates the body in the same direction as that in which the resultant is applied.

The free body diagram is shown on the image attached to the solution.

Then, we take the force balance in the vertical and horizontal axis.

For the vertical axis

N = mg

For the horizontal axis

The motion-causing force = 2100 - Frictional force

The motion-causing force = ma

ma = 2100 - 250

1.8m = 1850

m = 1027.78 kg.