A Car Being Towed: Free Body Diagram

Introduction

When a car is being towed, it is important to understand the forces acting on the car in order to ensure that it is towed safely. A free body diagram is a useful tool for visualizing these forces.

Free Body Diagram

A free body diagram is a diagram that shows all of the forces acting on an object. In the case of a car being towed, the forces acting on the car are:

• Weight (W): The weight of the car is the force of gravity acting on the car. It is directed downwards.
• Normal force (N): The normal force is the force exerted by the ground on the car. It is directed upwards and perpendicular to the ground.
• Tension (T): The tension is the force exerted by the tow rope on the car. It is directed forwards and parallel to the ground.
• Friction (F): Friction is the force that opposes the motion of the car. It is directed backwards and parallel to the ground.

The free body diagram for a car being towed is shown below.

Equations of Motion

The equations of motion for a car being towed are:

• ΣF_x = ma_x: The sum of the forces in the x-direction is equal to the mass of the car times its acceleration in the x-direction.
• ΣF_y = ma_y: The sum of the forces in the y-direction is equal to the mass of the car times its acceleration in the y-direction.

In the case of a car being towed, the acceleration in the x-direction is:

a_x = T – F

And the acceleration in the y-direction is:

a_y = N – W

Example

A car with a mass of 1000 kg is being towed by a tow truck. The tension in the tow rope is 5000 N and the coefficient of friction between the car and the ground is 0.2. Calculate the acceleration of the car.

Solution:

First, we need to calculate the force of friction.

F = μN = 0.2 * 1000 * 9.81 = 1962 N

Next, we can use the equations of motion to calculate the acceleration of the car.

a_x = T – F = 5000 N – 1962 N = 3038 N

a_y = N – W = 1000 * 9.81 N – 1000 * 9.81 N = 0 N

Therefore, the acceleration of the car is 3038 m/s² in the x-direction and 0 m/s² in the y-direction.

Conclusion

Free body diagrams are a useful tool for understanding the forces acting on an object. In the case of a car being towed, the free body diagram can be used to calculate the acceleration of the car.