Question Video: Determining the Mass of a Moving Object from its Momentum Physics • 9th Grade

What is the mass of an object that moves at a constant velocity of 2.2 m/s if its momentum is 3.3 kg ⋅ m/s?

03:29

Video Transcript

What is the mass of an object that moves at a constant velocity of 2.2 meters per second if its momentum is 3.3 kilograms meters per second?

Okay, so we have an object. Let’s draw it here as this orange point. The question tells us that this object has a velocity, which we’ll call 𝑉, of 2.2 meters per second. But it doesn’t tell us which direction this velocity is in. Remember that velocity is a vector quantity, so it has a direction as well as a numerical value. For this question, let’s assume that the velocity is to the right. But since the question doesn’t specify the direction, this isn’t too important. So in this case, we’ll just talk about the magnitude or size of the velocity of the object, which is 2.2 meters per second. And we won’t worry about what direction this is in.

Now we’re also told that this object has a momentum, which we’ll call 𝑃, which is equal to 3.3 kilograms meters per second. Remember that we use this dot here to signify multiplication, so we’re multiplying the units of kilograms by the units of meters per second. This is different from this point here, which is our usual decimal point. So this is just 3.3. Given all this information, the velocity of the object and the momentum of the object, we’re asked to calculate the mass of the object, which we’ll call 𝑚.

Let’s remember the equation for the momentum of an object, which is that momentum 𝑃 is equal to mass 𝑚 times velocity 𝑉. Let’s also remember that since velocity is a vector quantity so is momentum and the direction associated with the momentum is the same as the direction associated with the velocity. This is because to get the momentum 𝑃, we multiply the velocity, which is a vector, by mass, which is a scalar. So mass has a numerical value but no associated direction. This means that when we do this multiplication, the direction doesn’t change and momentum has the same direction as the velocity.

Now for our object, we’ve been told in the question that its momentum is 3.3 kilograms meters per second. We don’t know the mass 𝑚, so let’s leave that exactly as it is. And we’ve also been told that the velocity is 2.2 meters per second. So we now have an equation that involves 𝑚, which we can solve to find the mass of our object. Let’s start by dividing both sides of our equation by 2.2 meters per second. Let’s look at the right-hand side of this equation first. We can see that we have 2.2 meters per second divided by 2.2 meters per second. So this cancels out, and we’re just left with 𝑚 on the right-hand side.

If we now look at the left-hand side of this equation, we can see that the numerical part of this is 3.3 divided by 2.2, which is equal to 1.5. And in the units, we have kilograms meters per second divided by meters per second. So the meters per second cancel, and we’re just left with kilograms. This means we have our equation for the unknown mass 𝑚. We can swap the order that this equation is written in without changing anything. And hence, we have our final answer. The mass of the object is equal to 1.5 kilograms.

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