Question

consider a moving cart of mass 120 kg with kinetic energy K if its velocity is doubled how much the mass be decreased so that the KE does not change​

Answer 1

Answer:

The equation KE = ½ mv² shows that the relationship between Kinetic Energy and mass is directly proportional. a)So if the mass triples then the KE triples too. The relationship between Kinetic Energy and velocity is also directly proportional but with the square of the velocity. ... Hence, KE is 9 times greater.

Explanation:

it becomes quadrupled.

Because KE=1/2mv^2, if V is doubled, it is

KE(2)=1/2m(2V)^2

KE(2)=1/2m4v^2

KE(2)=2mv^2

KE(2)/KE=(1/2mv^2)/(2mv^2)=1/4

KE(2)=4KE

Explanation:

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Answer 2

Answer:

Sol:

Let us consider the velocity of cart is = 1m/s

Mass of cart = 120 kg.

Then, kinetic energy of cart = ½ mass x (velocity)2

K.E of cart = ½ mv2

60

K.E of cart = ½ x 120 x (1)2

K.E = 60 x 1 x 1

K.E of cart = 60 joules.

Here if velocity is double then the velocity (V) will become 2m/s.

Then K.E of cart = ½ mass x (velocity)2

= ½ m x V2

= ½ x 120 x (2)2

60

= ½ x 120 x 4

= 240 joules

But according to questions if velocity is double then mass should be decreased so that there is no change in K.E.

We have seen if velocity is double then K.E of cart becomes 240 joules.

Therefore mass of cart should decreased so that K.E. remains same.

3

If mass is decreased to ¼ of 120 kg. Then mass of cart will become ¼ x 120= 30kg.

There kinetic energy will become (keeping the velocity double) ½ mass x velocity

K.E = ½ 30 x (2)2

K.E of cart = ½ 30 x (2)2

15

K.E = ½ x 30 x 4

K.E of cart = 60 joules

Therefore kinetic energy of cart again becomes 60 joules.