## Torque Required to Pull a Car

The amount of torque required to pull a car depends on several factors, including the car’s weight, the coefficient of friction between the tires and the road, and the incline of the road.

### Factors Affecting Torque

1. Car’s Weight:

The heavier the car, the greater the torque required to pull it. The force required to overcome the car’s inertia is directly proportional to its mass.

2. Coefficient of Friction:

The coefficient of friction between the tires and the road determines the amount of grip the car has on the surface. A higher coefficient of friction reduces the amount of torque required to pull the car.

3. Incline of the Road:

If the car is being pulled up an incline, the force required to pull it is greater than on a flat surface. The steeper the incline, the more torque is needed.

### Calculating Torque

The torque (T) required to pull a car can be calculated using the following formula:

“`

T = F r

“`

where:

T is the torque in newton-meters (Nm)

F is the force required to pull the car in newtons (N)

r is the distance from the center of the wheel to the point where the force is applied in meters (m)

### Determining Force (F)

The force required to pull the car is determined by considering the following:

1. Overcoming Inertia:

F = m a

Where m is the car’s mass in kilograms (kg)

a is the acceleration in meters per second squared (m/s²)

2. Friction:

F = μ N

Where μ is the coefficient of friction between the tire and road

N is the normal force, which is equal to the car’s weight in newtons

### Example Calculation

Consider a car with a mass of 1,500 kg, a coefficient of friction of 0.7, and is being pulled up an incline of 10 degrees.

1. Force Required:

Weight of the car = m g = 1500 kg 9.81 m/s² = 14,715 N

Normal force = 14,715 N

Force required to overcome friction = μ N = 0.7 14,715 N = 10,300 N

Acceleration due to gravity = g sin(10°) = 1.71 m/s²

Force required to overcome inertia = m a = 1500 kg 1.71 m/s² = 2565 N

Total force required = 10,300 N + 2565 N = 12,865 N

2. Torque Required:

Assuming the force is applied at the edge of the tire (r = 0.3 m)

T = F r = 12,865 N 0.3 m = 3859.5 Nm

Therefore, approximately 3860 Nm of torque is required to pull the car up the 10-degree incline.

### Important Considerations

The torque required to pull a car can be greatly reduced by using a lower gear.

The use of a winch or similar device can significantly increase the available torque.

Safety precautions must be taken when pulling a car, including proper tow bar or chain attachment and secure anchoring points.