Pure Translation - Example Problem 6.5-1

 

The figure shows a system that consists of three identical 5-kg spheres connected by rigid bars of negligible mass. If the system is initially at rest on a smooth horizontal surface, determine the velocity of the system’s mass center after the system has been acted on by the two external constant forces (constant magnitude and direction) shown for a period of 4 seconds. Will the system of particles rotate as well as translate? Explain.

 

 

Given:

• m = 5 kg
• v_Go = 0
• t_f = 4 s
• L = 10 m
• F₁ = 50 i N
• F₂ = 100 j N

 

Find: v_Gf

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

Draw a free-body diagram of the system. On this FBD, locate the system's overall center of gravity. Click on the figure to see the FBD.

 

Apply Newton's second law to the system as a whole to find the acceleration of the system's center of mass (G).

 

a_G = (10 i + 20 j) m/s²
a_G = (20 i + 10 j) m/s²
a_G = (10/3 i + 20/3 j) m/s²