Why Does Kinetic Energy Depend on Both Mass and Velocity?

[Bashyboy]

Hello,

I just read an article using math to prove that kinetic energy does indeed depend on both mass and velocity. But I was wondering if there was an intuitive explanation to accompany this mathematical one?

 

[sankalpmittal]

Hello,

I just read an article using math to prove that kinetic energy does indeed depend on both mass and velocity. But I was wondering if there was an intuitive explanation to accompany this mathematical one?

Why do you need the intuitive explanation ? Its itself contained in mathematical derivation.

Let a body be moving with initial velocity "v" be brought to rest by applying a certain force. Then displacement in the body while constant force is being applied on it is : 0 = v²-2as or s=v²/2a

But force applied on it is given by : F=ma

And Work done = Fs = mav²/2a
Work done : mv²/2
So kinetic energy of body is
mv²/2

Now intuitively , kinetic energy means energy of a body by virtue of its motion. Word kinetic itself means motion. Now body can only be in motion when it has a certain velocity (or momentum).Hence kinetic energy of a body depends on its velocity. Also kinetic energy can only be possessed when the work is being done on it (or in fact when it do work). But there could be no work done in absence of force. So kinetic energy depends on force. But without mass , force has no meaning. So in fact kinetic energy depends on mass also.

 

[bhat.vaibhav]

i think that the force by which an object is accelerated determines its speed apart from its mass.
as acceleration is directly dependent on the force applied.

for ex- if an object of less mass is pushed with a force of 10N and a heavier object with a force of 15N then the heavier one will have more kinetic energy.

but mass of the object opposes this explanation as acceleration is inversely dependent on mass and if mass is there then only the force exists

 

[CWatters]

intuitive explanation...

Dropping a brick on your foot hurts more than a bath sponge -> Energy is proportional to mass.

Shooting yourself in the foot hurts more than dropping a bullet on your foot - > Energy is proportional to velocity.

 

[PJC01]

Yes, there is an intuitive explanation for why kinetic energy depends on both mass and velocity. Kinetic energy is the energy an object possesses due to its motion. When an object is in motion, it has the ability to do work and cause changes in its surroundings. The amount of work an object can do is directly related to its mass and velocity.

To understand this, think of a moving object as a force that is exerted on its surroundings. The greater the mass of the object, the more force it can exert, and the more work it can do. Similarly, the faster the object is moving, the more force it can exert in a shorter amount of time, resulting in more work being done. This is why kinetic energy is directly proportional to both mass and velocity.

Additionally, the relationship between mass and velocity is not linear, but rather exponential. This means that a small increase in mass or velocity can result in a significant increase in kinetic energy. This is why it is important to consider both factors when calculating kinetic energy.

In summary, the intuitive explanation for the dependence of kinetic energy on mass and velocity is that the energy an object possesses due to its motion is directly related to its ability to do work, which is determined by its mass and velocity.