A heavy bus?

Classical Mechanics Level 1

Which tires on this bus are bearing the most load assuming the mass of the bus is evenly distributed from front to back?

Front tires Rear tires The weight is evenly distributed between all tires.

2 solutions

Steven Chase
Dec 28, 2018

The front tire is pretty close to the nose of the bus. Let $L$ be the length of the bus, let $W$ be the bus weight, let $F$ be the force exerted by the rear tire, and let $D$ be the distance of the rear tire from the front. The torques about the front of the bus must cancel each other:

$W \frac{L}{2} = F D \\ F = W \frac{L/2}{D}$

From the picture, it is evident that $\frac{L/2}{D}$ is about $0.7$ or 0.8. Therefore:

$0.7 W\leq F \leq 0.8 W$

Since the forces exerted by the two tires must sum to $W$ , it is clear that the force exerted by the rear tire must be greater.

That's an unnecessarily complicated way to solve it. The question says the mass is evenly distributed, meaning the center of mass is right in the middle. All we need to know is which tires are closer to the COM, since that's where the weight will be concentrated. The back tires are clearly closer, hence they bear more of the weight.

Mikayla Eckel Cifrese - 1 year, 6 months ago

Geoff Pilling
Dec 28, 2018

The extra overhang in the rear provides extra weight that the rear tires need to bear.

A heavy bus?

2 solutions

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