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We want to find the maximum value of the hanging mass m such that the system is in equilibrium. 1. Free body diagram (FBD): Draw a FBD for each: the Cart and the hanging mass. Clearly show all the forces. 2. Clearly write the equilibrium equations for the cart in the horizontal and vertical direction. 3. Clearly write the equilibrium equation for the hanging mass. 4. Solve the system of the three equations above for the hanging mass m. Show your calculation credit. 5. What would happen if mass m exceeds this value? Explain.

We want to find the maximum value of the hanging mass m such that the system is in equilibrium. 1. Free body diagram (FBD): Draw a FBD for each: the Cart and the hanging mass. Clearly show all the forces. 2. Clearly write the equilibrium equations for the cart in the horizontal and vertical direction. 3. Clearly write the equilibrium equation for the hanging mass. 4. Solve the system of the three equations above for the hanging mass m. Show your calculation credit. 5. What would happen if mass m exceeds this value? Explain.

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Consider the system in the picture below: a cart of mass \( M \) with a static friction coefficient \( \mu \) is connected through a massless string to a hanging mass \( m \). **\( M \) is a capital letter, \( m \) is lower case. Write them as such, or your equations will be confusing.** **Diagram Description:** A cart labeled \( M \) is placed on a flat surface. The cart is connected by a string that passes over a pulley. Over the edge of the surface, the string supports a hanging mass labeled \( m \). We want to find the maximum value of the hanging mass \( m \) such that the system is in equilibrium. 1. **Free Body Diagram (FBD):** Draw a FBD for each: the Cart and the hanging mass. Clearly show **all** the forces. 2. Clearly write the equilibrium equations for the cart in the horizontal and vertical direction. 3. Clearly write the equilibrium equation for the hanging mass. 4. Solve the system of the three equations above for the hanging mass \( m \). Show your calculation to get credit. 5. What would happen if mass \( m \) **exceeds** this value? Explain.
Transcribed Image Text:Consider the system in the picture below: a cart of mass \( M \) with a static friction coefficient \( \mu \) is connected through a massless string to a hanging mass \( m \). **\( M \) is a capital letter, \( m \) is lower case. Write them as such, or your equations will be confusing.** **Diagram Description:** A cart labeled \( M \) is placed on a flat surface. The cart is connected by a string that passes over a pulley. Over the edge of the surface, the string supports a hanging mass labeled \( m \). We want to find the maximum value of the hanging mass \( m \) such that the system is in equilibrium. 1. **Free Body Diagram (FBD):** Draw a FBD for each: the Cart and the hanging mass. Clearly show **all** the forces. 2. Clearly write the equilibrium equations for the cart in the horizontal and vertical direction. 3. Clearly write the equilibrium equation for the hanging mass. 4. Solve the system of the three equations above for the hanging mass \( m \). Show your calculation to get credit. 5. What would happen if mass \( m \) **exceeds** this value? Explain.
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