Video Transcript
An object accelerates at four meters per second squared while a force of 20 newtons is applied to it. What is the mass of the object?
Okay, so we have some object. Let’s say that’s this pink dot here. And we know that this object is accelerating. Let’s suppose that this acceleration is in this direction to the right. We’ll label the acceleration as 𝑎 so that we have 𝑎 is equal to four meters per second squared. We’re told that a force of 20 newtons is applied to the object. That force is going to be in the same direction as the object’s acceleration. And we’ll label it as 𝐹 so that we have 𝐹 is equal to 20 newtons.
The question is asking us to work out the mass of the object. Let’s label this mass as 𝑚. To work out this mass, we can recall Newton’s second law of motion. This law says that the total force acting on an object is equal to the object’s mass multiplied by the acceleration of the object. Using symbols, we can write this as force 𝐹 is equal to mass 𝑚 multiplied by acceleration 𝑎. In this case, we know the values of 𝐹 and 𝑎. We need to work out the mass 𝑚 of the object.
So, let’s take this equation from Newton’s second law and rearrange it to make 𝑚 the subject. To do this, we divide both sides of the equation by the acceleration 𝑎. Then, on the right-hand side, the 𝑎 in the numerator cancels with the 𝑎 in the denominator. And we are left with an equation that says 𝐹 divided by 𝑎 is equal to 𝑚. Of course, we can also write this the other way around to say that mass 𝑚 is equal to force 𝐹 divided by acceleration 𝑎.
We are now ready to sub our values for 𝐹 and 𝑎 into this equation to calculate the value of 𝑚. Doing this gives us an expression for 𝑚 that says 𝑚 is equal to 20 newtons divided by four meters per second squared. At this stage, it’s worth noticing that the force is in units of newtons, which is the SI base unit for force, and the acceleration is in meters per second squared, the SI base unit for acceleration. Since both of the quantities on the right-hand side are expressed in their SI base units, then the result that we’ll calculate for 𝑚 must be in the SI base unit for mass, which is the kilogram. When we evaluate this expression, we get a result of five kilograms.
And so our answer to this question is that the mass of the object is five kilograms.
