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# can 2 objects of different mass have the same kinetic energy?

### 8 Answers

- Lucas CLv 71 decade agoFavorite Answer
Yes, because KE depends both on mass and velocity:

KE = 1/2 mv²

So let's say you've got a ball with a mass of 100 kg rolling at 10 m/s. It's kinetic energy is:

KE = 1/2 (100 kg)(10 m/s)²

KE = 5000 J.

Now let's say you've got another ball whose mass is only 50 kg. If its KE is 5000 J also, then:

5000 J = 1/2 (50 kg)(v²)

5000 J = (25 kg)(v²)

v² = 200 m²/s²

v = 14.1 m/s.

So the lighter ball could have the same KE if it were traveling at 14.1 m/s. I hope that hleps. Good luck!

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- bosqueLv 43 years ago
with the aid of fact the exchange in mass is linear and the exchange in velocity is exponential in the Ek formula the object with the greater suitable mass could have the greater suitable momentum for a given Ek. Examples: Mass and velocity the two 4 Ek=(a million/2)4*4^2= 32 momentum is sixteen next study 0.5 the mass for Ek=32= (a million/2)2*V^2 fixing for V = SQRT 32 = 5.657 Momentum is two * SQRT 32 or 11.314 final case double the mass to eight and resolve for V the place Ek=32 V= SQRT 8 = 2.828 Momentum is 8 * SQRT 8 = 22.627

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- oldprofLv 71 decade ago
Sure ke = 1/2 mV^2 = 1/2 Mv^2 = KE; thus V^2 = (M/m) v^2. This simply means the two kinetic energies KE and ke will be equal when mass m velocity V = sqrt(M/m) v or sqrt(M/m) times the velocity of mass M.

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- Anonymous1 decade ago
Yes they can.

Their respective kinetic energies will depend on what their velocities are. By definition,

KE = (1/2)mV^2

where

m = mass of the body

V = velocity of the body

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- Anonymous1 decade ago
Sure. The object with less mass just has to have a greater speed than the other object.

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- GaleleuLv 61 decade ago
Yes!

Say you have two object whose respective masses are m1 and m2, if their kinetics energies are equal to each other then

m1 v1^2 / 2 = m2 v2^2 /2

Therefore v1/v2 = Sqrt(m2/m1) for this to happen.

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- Anonymous1 decade ago
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