Question

A person holds two bricks together in one hand, pinching them as indicated by the arrows in the -figure to the left. As can be seen, the bricks have a tendency to swing apart at the bottom, contacting only at their top edges. We want to analyze the system to better understand its behavior and stability conditions (i.e. the bricks are not swinging around or falling out of the person's hand). This is done by analyzing a free body diagram of just one of the bricks, representing the pinching of the person's hand by P and the reaction of the second brick on the brick shown as R, as seen in the figure to the right. Answer the following questions to analyze this system. Ya Ya Fr Note that the weight, W, is acting at the center of the brick Note that the position at which the brick is being gripped, Yp, is fixed (because the person does not adjust their grip), but the position of the reaction force, yr. is not. You will have the opportunity to observe why this is while you are constructing the equations of equilibrium for the brick 1. What is the friction force required to support the brick (keep it from falling)? Equations Equilibriuw 2. Consider the position, direction, sense, and magnitude of Fr and W. What do we call this type of force system? provide the friction force required to F E N 3. What is the minimum force P required to provide the friction force required to support the brick? 4. What is the magnitude of the resultant, R? 5. For the bricks to keep from flipping out of the person's hand, R and P must NOT line up. Sum the moments around point C to find the equation used to determine if the system will resist its tendency to rotate. 6. Using the equation from the previous question, at what position, y, is P a minimum while still ensuring that the brick does not rotate? 7. What is the minimum force P required to ensure that the brick does not rotate? 8. Knowing the minimum P required to prevent the brick from slipping out of the person's hand and the minimum P required to prevent the brick from rotating, describe the process you would use to determine the minimum force P required to ensure the brick neither slips nor rotates out of the person's hand. In other words, how do you determine if friction or rotation is the limiting factor on the stability of the system? Suppose that the person is holding the bricks with sufficient force to maintain equilibrium, but then they begin to squeeze harder (in other words, P becomes P). 9. Show the new equilibrium in the x-direction 10. Show the new friction force 11. Show the new equilibrium in the y-direction. Does this differ from the force? Why or why not? how the new equilibrium with a sum of the moments around point C. What must change for equilibrium to be maintained? What is the new value?

Answer 1

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