Question

The cord AB has a length of 5 ft and is attached to the end B of the spring having a stiffness k = 10 lb/ft. The other end of the spring is attached to a roller C so that the spring remains horizontal as it stretches. If a 10-lb weight is suspended from B, use the free-body diagram for the ring at B to determine the necessary unstretched length of the spring, so that θ = 40◦ for equilibrium.

Solution

1. Imagine the ring at B to be separated or detached from the system.

2. The (detached) ring at B is subjected to three external forces caused by:

i.

ii.

iii.

3. Draw the free-body diagram of the (detached) ring showing all these forces labeled with their magnitudes and directions. Include any other relevant information e.g. lengths, angles etc.

4. Establish an xy-axes system on the free-body diagram and write down the equilibrium equations in each of the x and y-directions + ↑ Fy = 0: + → Fx = 0:

5. Determine the stretch in the spring BC and solve for the necessary unstretched length:

Answer 1