Question Video: Newton’s Third Law of Motion in Collisions Physics • 9th Grade

Two objects A and B are thrown into the air and collide with each other, as shown in the diagram. Object A has a weight of 12 N and object B has a weight of 20 N. In the collision, object A exerts a force of 24 N on object B. What force is applied to object A by object B during the collision? What object is given a greater acceleration due to the collision?

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Video Transcript

Two objects A and B are thrown into the air and collide with each other, as shown in the diagram. Object A has a weight of 12 newtons and object B has a weight of 20 newtons. In the collision, object A exerts a force of 24 newtons on object B. What force is applied to object A by object B during the collision? What object is given a greater acceleration due to the collision?

Okay, so in this question, we can see that we’ve got two objects: object A in blue and object B in pink. Now, we’ve been told that they’ve been tossed up into the air and they collide with each other. And additionally, during this collision, object A exerts a 24-newton force on object B. And lastly, we also know the weights of these objects. That will come in handy in a minute. But the first thing that we need to try and do is to work out what force is applied to object A by object B during the collision. In other words, we know that 24-newtons of force is applied to object B by object A. And we need to work out the opposite scenario.

What force is applied by object B to object A? To answer this question, we need to recall Newton’s third law of motion. Now, Newton’s third law tells us that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. In other words, we already know the force exerted by A onto B; it’s 24 newtons to the rightish. And then due to Newton’s third law, we know that the force exerted by B onto A is going to have the same magnitude, equal magnitude. But it is going to be in the opposite direction. In other words then, the force exerted by B onto A is going to be in this direction to the leftish. And it’s also going to have a magnitude of 24 newtons.

So coming back to this question, we see that we don’t actually have to give the direction of the force. But we’ve just been asked to find the force applied. So we can simply state the magnitude of that force, which happens to be 24 newtons. So moving to the next part of the question then, we need to find what object is given a greater acceleration due to the collision, whether it’s object A or object B.

Now to answer this, let’s first start by recalling another one of Newton’s laws of motion, Newton’s second law specifically in the situation where the mass of the object that we’re applying Newton’s second law to stays constant. In other words, the mass of the object is not changing. Well, in that scenario, we can recall that the net force on an object is equal to the mass of that object multiplied by its acceleration. Now because we’re being asked to find the acceleration on these objects due to the collision specifically, we only need to think about the collision forces. We don’t need to account for their weights because remember regardless of what their weights are, these weights always act in a downward direction and produce an acceleration of 𝑔 or in other words 9.8 metres per second squared in each of these objects. And so, we only need to worry about the acceleration caused by the collision forces.

Now, we know that the collision forces are equal in magnitude on both of these objects. There’s a 24-newton force on object A and a 24-newton force on object B. Since we’re being asked to find which one has a greater acceleration, we don’t need to worry about the directions, only the magnitude of this acceleration. So first of all, thinking about object A, we know that the force that we’re considering in this case is the 24-newton force. That’s the force due to the collision that’s causing an acceleration in the object. And then, we can say that this is equal to the mass of the object which we’ll call 𝑚 subscript A multiplied by its acceleration lowercase 𝑎 subscript A. And we can do the same thing for B. We know that the force on the object that we’re considering is 24 newtons. That’s the collision force. And this is equal to the mass of the object 𝑚 subscript B multiplied by its acceleration.

Now, what we’re trying to do in this question is compare 𝑎 subscript A to 𝑎 subscript B. Which of the objects’ accelerations due to the collision is larger? So in order to do that, we need to know what the objects’ masses are. And this is where we see why we were given the weights of these objects in the first place. If we were simply going to ignore these weights, then there would have been a red herring. But this is where they come in handy because we can recall that the weight of an object is equal to the mass of that object multiplied by the acceleration due to gravity, 9.8 metres per second squared.

And so, for object A, we can say that A’s weight — which we’ll call 𝑊 subscript A — is equal to its mass which is 𝑚 subscript A multiplied by the acceleration due to gravity which is a constant. And we can do the same for B. The weight of B is equal to the mass of B multiplied by the acceleration due to gravity. Now at this point, we can see that the weight of A is less than the weight of B. In other words, 𝑊 A is less than 𝑊 B. And therefore, the mass of A must be less than the mass of B because we’re multiplying the mass by a constant value in both cases to give us the weight. So what this means is that the lower weight for object A compared to object B means that the mass of object A must also be lower than the mass of object B. We can write this as the mass of A is less than the mass of B.

And then, we can come back to these two equations that we’ve set up here. We see that in both cases the forces applied to these objects is the same; it’s 24 newtons. However, as we’ve seen, the masses of these objects are different. And so, to compensate for that and to give us the same left-hand side in both cases, the values of these two accelerations must be different. And so, if we’re going to say that the 24-newton force on object A is equal to a lower mass multiplied by some acceleration, then in order to give us a value of 24 newtons as the force in order to compensate for the low mass, the acceleration of the object needs to be bigger. And conversely, we can say that 24 newtons, the force on object B, is equal to the larger mass of B multiplied by the smaller acceleration of B.

And so, at this point, we found the answer to our question. Because both objects have the same force exerted on them due to the collision, but object A’s mass was lower than the mass of object B, this means that object A is given a greater acceleration due to the collision.

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