Question

Two bodies with masses m1 and m2 are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2. The magnitude of the velocity of the center of mass of this system of two bodies is:_________
a. less than v1.
b. equal to v1.
c. equal to theaverage of v1 and v2.
d. greater than v1 and less than v2.
e. greater than v2.

Answer 1

Answer:

the correct one is D

Explanation:

The velocity of the center of mass of a body is

          $v_{cm} = \frac{1}{M } \ \sum m_i v_i$vcm = 1 / M sum mi vi

          M = $\sum m_i$ sum my

in this case we have two bodies

          v_{cm} = $\frac{1}{m1+m2} \ ( m_1v_1 +m_2v_2)$1 / m1 + m2 (m1 v1 + m² v2)

          v_{cm} = $\frac{m_1}{m1+m2} \ v_1 + \frac{m2}{m_1+m_2} \ v_2$

we can see that the velocity is an average between v₁ and v₂, but the exact value depends on the ratio of the masses of the bodies

when checking the answers the correct one is D