Work-Energy for a System of Particles - Example Problem 7.7-1

 

A ball (m₁ = 4 kg) is attached to a light rod which is pinned at O. The rod is free to rotate in the vertical plane. It is desired to determine the velocity of the ball when θ is 90 degrees when the system is released from rest at position A. Calculate the velocity for the two cases shown in the figure. The first case has a block (m₂ = 10 kg) attached to the end of the rod. The second case includes a constant force (F = m₂g) that pulls down on the end of the rod. The force remains vertical throughout the motion. The total length of the rod is 450 mm, where l₁ = 300 mm and l₂ = 150 mm.

 

 

Given:

• m₁ = 4 kg
• m₂ = 10 kg
• θ_B = 90^o
• l₁ = 0.3 m
• l₂ = 0.15 m
• F = m₂g
• v_A = 0

 

Find: v_1,B

 

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:

 

For case 1, which is the correct energy equation between states A and B? Set the datum at the height of the pivot point.

 

0 = (1/2)m₁v_1,B² + (1/2)m₂v_2,B² + m₁gl₁ - m₂gl₂
0 = (1/2)m₁v_1,B² + (1/2)m₂v_2,B² + m₁gl₁ + m₂gl₂
0 = (1/2)(m₁ + m₂ )v_1,B² + m₁gl₁ - m₂gl₂