A force of 10 newtons is applied to an object for three seconds, acting in the direction in which the object is moving. How much does the momentum of the object change?
Okay, so in this question, we’ve got a force of 10 newtons applied to an object for a time interval of three seconds. And we’ve been told that this force is acting in the direction in which the object is moving. So we’ve got an object here. And let’s say it’s moving in this direction, towards the right.
Now we’ve been told that there’s a force of 10 newtons acting on the object for a time interval of three seconds. So let’s say the object starts up here and ends up here. And it takes three seconds to get there. And at that point, the force stops acting.
Now because we’ve been told that the force is acting in the direction in which the object is moving, we’ve also drawn the force as acting towards the right. What we’ve been asked to do is to find out how much does the momentum of the object change by. In other words, we need to find the quantity Δ𝑝 or the change in momentum of the object.
To do this, we need to recall that an impulse on an object is defined as the force on an object, 𝐹, multiplied by the time interval for which the force acts on the object, Δ𝑡. And we can also recall that an impulse is equal to the change in momentum of the object, Δ𝑝, which means that we can find Δ𝑝 because we’ve been given 𝐹 and Δ𝑡.
And so we say that Δ𝑝, the change in momentum, is equal to the force on the object, which is 10 newtons, multiplied by the time interval, Δ𝑡, which happens to be three seconds. That’s how long the force is exerted on the object for.
And so when we evaluate the right-hand side of the equation, we find that the change in momentum is equal to 30 kilogram meters per second. Now the reason that we know that the unit is kilogram meters per second is because we’ve used standard units for both the force and the time interval. We have the force in newtons and we have the time interval in seconds.
So because we’ve got standard units on the right-hand side of the equation, we’ll also have the standard units on the left-hand side of the equation. And the standard units of momentum or change in momentum are kilogram meters per second. Hence, our final answer is that the change in momentum of the object is 30 kilogram meters per second.