Sample Problem

Sample Problem

A uniform beam, of length L and mass 11/ = 1.8 kg. is at rest with its ends on two scales. A uniform block. with mass M = ~.7 kg. is at rest on the beam. with its center a distance , from the beam’s left end, What do the scales read?

SOLUTION :The first steps in the solution of  problem about static equilibrium arc these: Clearly define the system to be analyzed and then draw a free body diagram of it. indicating all the forces on the system. Here, let us choose the system the beam and block taken together. Then the forces on the system are shown in the free-body diagram (Choosing the system takes experience and often there can be more than one good choice: see Problem Solving Tactic  below.)

The Key Idea here is that. because the system is in static equilibrium. we can apply the balance of forces equations  and the balance’ of torques to it. The forces have nor components. so provides no information. For the y components.

Let us choose a rotation axis through the left end of the beam. We shall also use our general rule for assigning signs to torques: If a torque would cause an initially stationary body to rotate clockwise about the rotation axis. the torque is negative. If the rotation would be counterclockwise. the torque is positive. Finally, we shall write the torques in the form r.L F, where the moment.

Notice the strategy in the solution: When we wrote an equation for the balance of force components. we got stuck with two unknowns. If we had written an equation for the balance of torques around some arbitrary axis, we would have again gotten stuck with those two unknowns. However. because we chose the axis to pass through the point of application of one of the unknown forces. here F,. we did not get stuck. Our choice neatly eliminated that force from the torque equation, allowing us to solve for the other unknown force magnitude F,. Then we returned to the equation for the balance of force components to find the remaining unknown force magnitude.

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CHECKPOINT: static equilibrium. (a) Can you find the magnitudes of unknown forces by balancing the forces? (b) If you wish to find the magnitude of force  by using a single
equation, where should you  rotational axis? (c) The magnitude of  turns out to be 65 N. What then is the magnitude of F?

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