The banging of a door against its stop can break the hinges. However, by properly choosing...

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The banging of a door against its stop can break the hinges. However, by properly choosing the placement of the doorstop, the impact forces on the hinges can be made to vanish. Consider a uniform door pivoted at its end. • At what distance I from the hinges should the doorstop be placed to minimize the impulse on the hinges? Hints: Begin by drawing a freebody diagram illustrating the forces that are acting as the door hits the stop. Next, write down an expression for the change in angular momentum of the door as it hits the door stop and equate this to an integral over the applied torque. Assume that the door hits the stop and stops. Next, write a similar expression for the change in the linear momentum and equate this to an integral over the applied force the impulse. Combine the expressions to derive an expression for the distance from the hinges the stop should be placed. This distance is called the center of percussion. Doorstop والي The banging of a door against its stop can break the hinges. However, by properly choosing the placement of the doorstop, the impact forces on the hinges can be made to vanish. Consider a uniform door pivoted at its end. • At what distance I from the hinges should the doorstop be placed to minimize the impulse on the hinges? Hints: Begin by drawing a freebody diagram illustrating the forces that are acting as the door hits the stop. Next, write down an expression for the change in angular momentum of the door as it hits the door stop and equate this to an integral over the applied torque. Assume that the door hits the stop and stops. Next, write a similar expression for the change in the linear momentum and equate this to an integral over the applied force the impulse. Combine the expressions to derive an expression for the distance from the hinges the stop should be placed. This distance is called the center of percussion. Doorstop والي

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