A car with a mass of 320 kilograms is having engine problems, so it is being towed behind a van while the driver of the malfunctioning car tries to start its engine. The van supplies a force of 960 newtons to the car, and a friction force of 160 newtons acts in the opposite direction to the car’s motion. The malfunctioning motor starts to work and provides the car with a force of 160 newtons. What is the acceleration of the car when its engine starts working?
Okay, so in this question, we’ve got a car that’s a bit dodgy. It’s kind of broken down. So here’s a little diagram of our car. Now, we know that this car is being pulled behind a van like so. We’ve been told that the van supplies a force of 960 newtons to the car. And of course, that force is going to be towards the right because the van is moving towards the right. So it’s pulling the car along. We’ve also been told that there is a friction force in the opposite direction to the car’s motion and this force is 160 newtons. Finally, we’re told that the car’s motor starts working again. The driver’s managed to make it work. And when the malfunction motor starts to work, it exerts an extra force of 160 newtons on the car. And of course, this force is gonna be towards the right because the motor is going to exert a force so that the car can move forward.
So these are the three forces that are acting on the car. And the third force — the 160-newton force forwards — only starts acting when the car’s motor starts working again. What we’ve been asked to do in this question is to find the acceleration of the car when its engine starts to work. In other words, what’s the acceleration of the car when these three forces are acting on it?
To find this out, we can first work out the resultant force on the car. Let’s call this resultant force 𝐹. And it’s the resultant force because we have to take into account all of the forces acting on the car. So if we choose that this direction towards the right is positive, which kind of make sense because the forward direction should be positive, we say that the resultant force on the car 𝐹 is equal to the 960 newtons provided by the van to the car plus the 160 newtons provided by the car’s engine when it starts working minus the 160-newton friction force.
Now as we can see here, the plus 160 and the minus 160 cancel which in effect means that the car’s motor provides enough force to exactly cancel out the frictional force. And so the resultant force on the car is going to be 960 newtons.
So now, we know the resultant force on the car. But why is this useful? Well, we can use something known as Newton’s second law of motion. What this tells us is that the resultant force on an object 𝐹 is equal to the mass of the object 𝑚 multiplied by the acceleration of that object 𝑎. In this case, we’ve just worked out what 𝐹 is for the car — the resultant force on the car — and we know the mass of the car. We’ve been told this in the question. And of course, we’re trying to work out the acceleration.
So we need to rearrange 𝐹 is equal to 𝑚𝑎. What we can do is to divide both sides of the equation by 𝑚. So the 𝑚s cancel on the right-hand side and that leaves us with 𝐹 divided by 𝑚 is equal to 𝑎. Then, we can substitute in the values of 𝐹 which is 960 newtons and 𝑚 which is 320 kilograms. And we can evaluate the fraction, which ends up being three.
And because we use the standard units of newtons and kilograms for force and mass, respectively, our answer is therefore going to be in the standard unit of acceleration, which is meters per second squared. And at this point, we have our final answer. The acceleration of the car when its engine starts working is three meters per second squared.