Answer to Question #162394 in Physics for Andu

Question

10. Two boys with skates weighing 50kg and 42kg hold in their hands an 8m long rope. The first boy pulls the rope with 20N forces and keeps it pulled until they meet each other. Friction is not taken into account.

Find: a) The acceleration with which each boy moves. b) After how long they meet. c) The displacement that each of them makes until they meet.

Answer 1

a) The acceleration with which each boy moves:

$$a=\frac{F}{m}=\frac{20}{50+42}=0.22\text{ m/s}^2.$$

b) They met after

$$t=\sqrt{\frac{2d}{a}}=8.5\text{ s}.$$

c) To determine the displacement, find the center of mass of the boys (because the point where they will meet is at their center of mass):

$$x_c=\frac{m_1x_1+m_2x_2}{m_2+m_2}=\\\space\\ =\frac{50·0+42·8}{50+42}=3.65\text{ m}$$

from the 50kg-boy. Thus, his displacement was 3.65 m from the point where he initially was and the the second boy's displacement was 4.35 m.