Question

A group of particles of total mass 35 kg has a total kinetic energy of 313 J. The kinetic energy relative to the center of mass is 81 J. What is the speed of the center of mass?

Answer 1

Answer:

The speed of center of mass is 3.64 m/s.

Explanation:

Given that,

Total mass of the group of particles, m = 35 kg

Total kinetic energy of group of particles, $K_T= 313 J$

The kinetic energy relative to the center of mass is, K = 81 J

We need to find the speed of center of mass. We know that the total kinetic energy is equal to the sum of rotational kinetic energy and the rotational kinetic energy.

$K_T=E+K\\\\E=K_T-K$

Since, $E=\dfrac{1}{2}mv_c^2$, $v_c$ is the speed of center of mass

$\dfrac{1}{2}mv_c^2=K_T-K\\\\v_c=\sqrt{\dfrac{2(K_T-K)}{m}} \\\\v_c=\sqrt{\dfrac{2(313-81)}{35}}\\\\v_c=3.64\ m/s$

So, the speed of center of mass is 3.64 m/s.