Video: Kinetic Energy

An object that has 9 J of kinetic energy is moving at 3 m/s. What is the mass of the object?


Video Transcript

An object that has nine joules of kinetic energy is moving at three metres per second. What is the mass of the object?

Okay, in this situation, we have some object. Let’s say it’s this box here. And we’re told that this box is in motion, moving along with a velocity, we’ll call 𝑣, of three metres per second. Thanks to this motion, this object has a kinetic energy of nine joules. Based on this information, we want to solve for the mass, we can call it 𝑚, of our object. To start out doing that, let’s recall the equation for an object’s kinetic energy in terms of its mass and its velocity. Kinetic energy is equal to one-half 𝑚𝑣 squared. Now in our situation, it’s not the kinetic energy we want to solve for, but rather the mass 𝑚.

To do that, starting with this equation, we can start by multiplying both sides by the factor of two, which cancels out that two with the factor of one-half on the right-hand side. And then, second, we can divide both sides of the equation by 𝑣 squared, the square of this object’s velocity. Doing this cancels out that term also on the right-hand side. Based on our original equation then, an object’s mass is equal to two times its kinetic energy divided by its velocity squared. And that brings us back to solving for the mass of this particular object. That mass is equal to two times the object’s kinetic energy, which is nine joules, divided by its velocity, three metres per second squared. Now, looking at this denominator, we know that because this three metres per second velocity is inside parentheses and being squared, then that means we apply the squared term both to the three as well as to the units, metres per second. What results is this term, nine metres squared per second squared.

Next, if we look at the numerator, we know that two times nine joules is 18 joules. But then, let’s consider this unit joules. Recall that one joule is equal to a newton multiplied by a metre. And then, on top of that, one newton is equal to a kilogram metre per second squared. Making this substitution, we see that a joule can also be written as kilogram metre squared per second squared. But then, with that substitution made, look at this. We have metre squared divided by second squared in both the numerator and denominator of this fraction. So when we calculate this fraction, these units cancel out. We’re left simply with units of kilograms. Knowing that and the fact that 18 divided by nine is equal to two, we understand that our final answer is two kilograms. That’s the mass of this object.

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