# The 1100 kg mass of a car includes four tires

## Homework Statement

The 1100 kg mass of a car includes four tires, each of mass (including wheels) 35 kg and diameter 0.80 m. Assume each tire and wheel combination acts as a solid cylinder.
If the car is initially at rest and is then pulled by a tow truck with a force of 1500 N, what is the acceleration of the car?

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F = ma
T = I*alpha
I = 1/2*m*r^2

## The Attempt at a Solution

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It is apparent that doing acc = 1500/1100 leads to a wrong result. We must consider the tires and their accelerations. But I don't know how I can combine "ma" with "I*alpha" in the same equation, to solve for "a".

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Bystander
Homework Helper
Gold Member
diameter 0.80 m
This bit of information, and the following bit
T = I*alpha

PeroK
Homework Helper
Gold Member
Is the speed of the car not related to the rotational speed of the wheels?

This bit of information, and the following bit

Yes the right hand side of that equation(T = I*alpha) is known, but I don't think the left side can be calculated simply by F*r. Is it the whole force that contributes to torque of a tire?

Bystander
Homework Helper
Gold Member
whole force that contributes to torque of a tire?
The angular moment of inertia resists the acceleration.

Chestermiller
Mentor
Have you done a free body diagram on the car? How is the rate of rotation of the tires related to the linear speed of the car? Have you at least included the mass of the tires in the overall mass m of the car when applying F = ma.

Chet

Chestermiller
Mentor
Have you done a free body diagram on the car? Is the ground exerting a force on the car? How is the rate of rotation of the tires related to the linear speed of the car? Have you at least included the mass of the tires in the overall mass m of the car when applying F = ma.

Chet
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