Stacking Blocks

Stacking Blocks - the rotation axis O. The torque of the...

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Stacking Blocks Two bricks of length L and mass m are stacked. Using conditions of static equilibrium we can determine the maximum overhang of the top brick (see Figure 13.4). The two forces acting on the top brick are the gravitational force F g and the normal force N, exerted by the bottom brick on the top brick. Both forces are directed along the y-axis. Since the system is in equilibrium, the net force acting along the y-axis must be zero. We conclude that Figure 13.4. Two stacked bricks. If the top block is on the verge of falling down, it will rotate around O. The torque exerted by the two external forces with respect to O can be easily calculated (see Figure 13.5). The gravitational force F g acting on the whole block is replaced by a single force with magnitude m g acting on the center of mass of the top block. The normal force N acting on the whole contact area between the top and the bottom block is replaced by a single force N acting on a point a distance d away from
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Unformatted text preview: the rotation axis O. The torque of the normal force and the gravitational force with respect to O is given by The net torque acting on the top brick is given by If the system is in equilibrium, then the net torque acting on the top brick with respect to O must be zero. This implies that Figure 13.5. Forces acting on top brick. or This equation shows that the system can never be in equilibrium if a > L/2 (since d < 0 in that case). The system will be on the verge of losing equilibrium if a = L/2. In this case, d = 0. We conclude that the system can not be in equilibrium if the center of mass of the top brick is located to the right of the edge of the bottom brick. the system will be on the verge of losing equilibrium if the center of mass of the top brick is located right over the edge of the bottom brick. Finally, if the center of mass of the top brick is located to the left of the edge of the bottom brick, the system will be in equilibrium....
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This document was uploaded on 11/25/2011.

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Stacking Blocks - the rotation axis O. The torque of the...

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