Video: Mass, Weight, and Applied Force

A car has a mass of 460 kg. The weight of the car is evenly supported by its four identical wheels. What force does each wheel apply to the ground?

02:15

Video Transcript

A car has a mass of 460 kilograms. The weight of the car is evenly supported by its four identical wheels. What force does each wheel apply to the ground?

All right, so in this question, we’ve been told that we firstly got a car. So here’s our car. Now we’ve been told that the weight of the car is evenly supported by its four identical wheels. In other words, if we said that the car has a total weight 𝑊, then because each wheel is evenly supporting the weight of the car and there are four wheels on the car, each wheel is going to apply a force of 𝑊 divided by four to the ground, because remember weight is a force. So the weight of the car is the force that the car exerts on the ground. It does this by applying a force of 𝑊 divided by four through each of its wheels.

Now we’ve specifically been asked to work out the force applied by each wheel to the ground. And we know that this is 𝑊 by four. So to work out what 𝑊 by four actually is, we first need to know what 𝑊 is. In other words, we need to know the weight of the car.

To work this out, we can recall that the weight of an object is defined as the mass of the object multiplied by the gravitational field strength of the Earth, 𝑔. Now 𝑔 is just a constant. And we can recall that the gravitational field strength of the Earth is 9.8 meters per second squared, at which point we’ve been given the mass of the car and we know the value of 𝑔. So we can work out the weight of the car.

So we say that the weight of the car is equal to the mass of the car, which is 460 kilograms as we’ve been told in the question, multiplied by the gravitational field strength of the Earth, which is 9.8 meters per second squared. And of course, because weight is a force, it’s going to have the unit of newtons.

However, we’re not gonna evaluate this expression just yet because we’re trying to find out what the value of 𝑊 divided by four is, because that’s the force applied by each wheel to the ground. So we can say that 𝑊 divided by four is equal to the right-hand side of this expression divided by four.

And let’s say that this is the force 𝐹 exerted by each wheel into the ground, at which point we can say that 𝐹 is equal to 1127 newtons because, remember, it’s a force. And hence, we’ve worked out our final answer. The force applied by each wheel to the ground is 1127 newtons.

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