Question

Show that an object with a large mass has more kinetic energy than an object with a smaller mass moving at the same speed​

Answer 1

Answer:

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

v

.

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

v

, and consequently have a higher kinetic energy, than a lighter object that goes from rest to the same velocity

v

.

Once the object reaches velocity

v

, its kinetic energy can be expressed as a function of its velocity and of its mass

mass

kinetic energy

=

1

2

×

mass

×

velocity

2

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

If you take

M

to be the mass of the massive object and

m

to be the mass of the lighter object, you can say that

KE

massive

=

1

2

⋅

M

⋅

v

2

massive

KE

light

=

1

2

⋅

m

⋅

v

2

light

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

=

1

2

⋅

M

⋅

v

2

1

2

⋅

m

⋅

v

2

which is equivalent to

KE

massive

=

M

m

⋅

KE

light

If

M

>

m

, you have

M

m

>

1

and

KE

massive

>

KE

light

−−−−−−−−−−−−−−−−

Answer 2

$\huge\red{Question}$

Show that an object with a large mass has more kinetic energy than an object with a smaller mass moving at the same speed

$\huge\red{A}\green{N}\blue{S}\pink{W}\red{E}\blue{R}\orange{--}$

Kinetic energy

$= > \frac{1}{2} \times mv {}^{2}$

So,

$kinetic \: energy \: \alpha \: mass$

As, kinetic energy is directly proportional to mass due to which it increase with increase in Mass .So,a larger object with more mass than other at the same speed,has more kinetic energy.