Pure Translation - Example Problem 6.5-4
What is the horizontal acceleration a of the cart that will cause a steady state deflection angle θ of the attached pendulum from the vertical? The slender rod has a length of l and a mass of m. The ball at the end of the pendulum has a mass of 2m and a radius of r. The motion of the pendulum is restricted by a torsional spring installed at the pivot O. The moment created by the torsional spring has a spring constant k and is proportional to the pendulum's displaced angle θ from the vertical in radians.
Given:
- Ms = kθ
- Rod: m, l
- Ball: 2m, r
Find: a
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 pendulum. Locate the centers of mass of both the rod and the ball. Also, locate the overall center of mass. Estimate the location of the overall center of mass. Click on the figure to see the FBD.
Which point should we sum the moments about?