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.
