# Does a moving massive object have more kinetic energy than a lighter object?

##### 1 Answer

Maybe.

#### Explanation:

The problem doesn't specify this, but if are to assume that both the massive object and the lighter object are moving **with the same velocity**, then the answer would be **yes**.

An object's **kinetic energy** is simply the *energetic cost* paid, i.e. work done on the object, in order to accelerate it from rest to a given velocity, let's say

Now, an object's *mass* comes into play here because it will affect the amount of work we do in order to accelerate the object, i.e. give it kinetic energy.

More specifically, a more massive object will require **more work** in order to get from rest to a velocity **higher kinetic energy**, than a lighter object that goes from rest to the same velocity

Once the object reaches velocity

#color(blue)(ul(color(black)("kinetic energy" = 1/2 xx "mass" xx "velocity"^2)))#

If you take

#"KE"_"massive" = 1/2 * M * v_"massive"^2#

#"KE"_ "light" = 1/2 * m * v_"light"^2#

If you take

#v_"massive" = v_"light" -># the two objects are moving with thesame velocity

then you can say that

#"KE"_ "massive"/"KE"_ "light" = (color(red)(cancel(color(black)(1/2))) * M * color(red)(cancel(color(black)(v^2))))/(color(red)(cancel(color(black)(1/2))) * m * color(red)(cancel(color(black)(v^2)))#

which is equivalent to

#"KE"_"massive" = M/m * "KE"_"light"#

If

#color(darkgreen)(ul(color(black)("KE"_ "massive" > "KE"_"light")))#

This means that when two objects are moving withthe same velocity, the object that has the greater mass will have the higher kinetic energy

Let's take a numerical example to illustrate this idea. Let's assume that you have a bicycle of mass

You will have

#"KE"_"car" = 1/2 * "1000 kg" * "10 m s"^(-1) = "5000 J"#

#"KE"_"bicycle" = 1/2 * "10 kg" * "10 m s"^(-1) = "50 J"#

Notice that

#"KE"_ "car"/"KE"_ "bicyle" = (5000 color(red)(cancel(color(black)("J"))))/(50color(red)(cancel(color(black)("J")))) = 100#

The car has a kinetic energy is **times higher** than the kinetic energy of the bicycle, which means that it took **times more work** to accelerate the car from rest to

You can test this yourself by trying to push a bicycle and a car to the same velocity. The one that is harder to push will have the higher kinetic energy once it gets to that velocity.

#color(red)(ul(color(black)("more work needed to accelerate to the same velocity " = " higher kinetic energy")))#