Three blocks are suspended at rest by the system of strings and frictionless pulleys shown in the figure below, where W = 29.0 . What are the weights w1 and w2?
To determine the weights w1 and w2, we can use the principles of equilibrium and the concept of tension in a system of connected strings.
Let's take a step-by-step approach to solve the problem:
1. Review the figure and system description: We have three blocks connected by strings and pulleys. Block w1 is connected to the left pulley by a string, and block w2 is connected to the right pulley by another string. Both pulleys are frictionless. The system is at rest, indicating that it is in equilibrium.
2. Identify the forces acting on each block:
- w1: The downward force acting on w1 is the weight, which is given as W = 29.0.
- w2: The downward force acting on w2 is also the weight, which is unknown (w2 = ?).
3. Consider the forces due to tension in the strings:
- The tension in the string connected to w1 also acts upward on the left pulley, counteracting the weight of w1.
- The tension in the string connected to w2 acts upward on the right pulley, counteracting the weight of w2.
4. Use the principle of equilibrium:
- In an equilibrium state, the net force and the net torque (around any axis) are zero.
- Since the system is at rest, we know that the net force on each block, as well as the net torque, must be zero.
5. Apply the principle of equilibrium:
- The tensions in the strings provide the upward forces to balance the downward forces (weights).
- The tension in the string connected to w1 is equal to w1, and the tension in the string connected to w2 is equal to w2.
- The total tension in each string can be found by considering the system as a whole.
- Since the pulleys are frictionless, the tension in both strings will be the same.
6. Set up an equation based on the principle of equilibrium:
- Tension in the string connected to w1 = Tension in the string connected to w2
- Therefore, w1 = w2
7. Substitute the values given:
- Since w1 is given as W = 29.0, we have w1 = 29.0.
8. Solve for w2:
- As w1 = w2, we can substitute w1 = 29.0 into the equation.
- Therefore, w2 = 29.0.
So, the weights w1 and w2 are both 29.0.