Answer to Question #328974 in Physics for Rae

Question

6. If the mass of an object is quadrupled and the speed decreased by a factor of three, by what factor does the kinetic energy change?

(a) 4/3 (b) 16/3

(c) 4/9 (d) 16/9

Answer 1

The kinetic energy is given as follows:

$$K = \dfrac{mv^2}{2}$$

New speed and mass are: $m_1 = 4m, v_1 = v/3$. Thus, the new kinetic energy is:

$$K_1 = \dfrac{m_1v_1}{2} = \dfrac{4m(v/3)^2}{2} = \dfrac{4}{9}\cdot \dfrac{mv^2}{2} = \dfrac{4}{9}K$$

Thus, the kinetic energy change by factor of 4/9.

Answer. (c) 4/9.