Video Transcript
An object is decelerated by an average force of 15 newtons for a time of 0.5 seconds. What is the change in the object’s momentum?
Okay, so in this question, we have some object that we’ll say is represented by this pink dot. Since we’re told that the object gets decelerated, we know that initially it must be moving. Let’s suppose that the object is moving to the right. We’ll take this direction that the object is moving in as the positive direction. We’re told that the object gets decelerated by an average force of 15 newtons and that this force is applied for a time of 0.5 seconds. We’ll label this time interval over which the force acts as Δ𝑡. So we have Δ𝑡 is equal to 0.5 seconds. Then, thinking about the object again, after the time interval Δ𝑡 has passed, we’ll find that the object’s momentum is going to have changed as a result of the force. We’ll call this change in momentum Δ𝑝. And this is exactly what the question is asking us to find.
Now, we’re told that during this time Δ𝑡, an average force of 15 newtons acts on the object. We’re also told that this force acts to decelerate the object, or in other words to reduce its speed. So, since our object is initially traveling to the right, or the positive direction, then the force must act to the left, or negative direction. This means that the force acting on the object, which we’ll label as 𝐹, is equal to negative 15 newtons.
Now, we’ve said already that when we have a force acting on an object over some time, that causes a change in momentum of the object. And it turns out that there’s an equation we can recall that’s going to be helpful. Specifically, this equation says that if we have a force 𝐹 acting on an object for a length of time Δ𝑡, then the object’s momentum changes by an amount Δ𝑝 such that 𝐹 is equal to Δ𝑝 divided by Δ𝑡. In this case, we know the value of the force 𝐹 and we know the value of the time interval Δ𝑡 for which this force acts. The quantity that we don’t know and that we’re trying to find is the change in momentum of the object Δ𝑝. This means that we need to take this equation and rearrange it to make Δ𝑝 the subject.
The first step is to multiply both sides of the equation by the time interval Δ𝑡. Then, on the right-hand side, the Δ𝑡 in the numerator cancels with the Δ𝑡 in the denominator. And this leaves us with an equation that says Δ𝑡 multiplied by 𝐹 is equal to Δ𝑝. From here, we can then notice that we can also write the equation the other way around. So we have that the change in momentum Δ𝑝 is equal to the force 𝐹 multiplied by the time interval Δ𝑡.
Now, we just need to take our values for 𝐹 and Δ𝑡 and sub them into this equation. When we do this, we get that Δ𝑝 is equal to negative 15 newtons, that’s our value for 𝐹, multiplied by 0.5 seconds, that’s our value for Δ𝑡. At this stage, it’s worth pointing out that the force is measured in units of newtons, which is the SI base unit for force, and the time is in units of seconds, which is the SI base unit for time. Since both these two quantities are measured in their SI base units, then the value that we calculate for Δ𝑝 will also be in its own SI base unit. The SI base unit for momentum is the kilogram-meter per second.
When we evaluate this expression for Δ𝑝, we get a result of negative 7.5 kilogram-meters per second. The fact that this change in momentum Δ𝑝 is negative means that the object’s momentum has decreased. This value of Δ𝑝 that we’ve calculated is exactly what the question was asking us to find. And so our answer to this question is that the change in the object’s momentum is negative 7.5 kilogram-meters per second.
