m1 is the initial body weight;
m2 = 4 * m1 – the body weight was doubled.
It is required to determine E2 / E1 – the change in kinetic energy.
Since the condition of the problem is not specified, we assume that the speed of the body is constant and equal to v. Then:
The kinetic energy in the first case will be equal to:
E1 = m * v ^ 2/2.
The kinetic energy in the second case will be equal to:
E2 = m ^ 2 * v ^ 2/2 = 4 * m1 * v ^ 2/2.
E2 / E1 = (4 * m1 * v ^ 2/2) / (m * v ^ 2/2) = 4, that is, it will increase by 4 times.
Answer: the kinetic energy of the body will also quadruple.
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