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
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 the same 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 with the 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
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")))#