Free Body Diagram Accelerating Car
Problem Statement
A car is accelerating at a rate of 2 m/s2 to the right. Draw a free body diagram of the car.
Solution
The forces acting on the car are:
* Weight (W): The force of gravity acting on the car, pointing downward.
* Normal force (N): The force exerted by the road on the car, pointing upward.
* Friction force (f): The force opposing the motion of the car, pointing to the left.
* Force of acceleration (F): The force causing the car to accelerate, pointing to the right.
The free body diagram is shown below:
W
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————————-> F
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N
The net force acting on the car is:
Fnet = F – f
Since the car is accelerating, the net force must be positive. Therefore, the force of acceleration must be greater than the friction force.
Additional Notes
* The weight of the car is equal to the mass of the car times the acceleration due to gravity (W = mg).
* The normal force is equal to the weight of the car (N = W).
* The friction force is equal to the coefficient of friction between the car and the road times the normal force (f = μN).
* The force of acceleration is equal to the mass of the car times the acceleration of the car (F = ma).
Example
A 1000 kg car is accelerating at a rate of 2 m/s2. The coefficient of friction between the car and the road is 0.2.
* The weight of the car is:
W = mg = (1000 kg)(9.8 m/s2) = 9800 N
* The normal force is:
N = W = 9800 N
* The friction force is:
f = μN = (0.2)(9800 N) = 1960 N
* The force of acceleration is:
F = ma = (1000 kg)(2 m/s2) = 2000 N
* The net force acting on the car is:
Fnet = F – f = 2000 N – 1960 N = 40 N
