- 1. Prove the law of the lever.
Prove the law of the lever.
Answer to Problem 1MDP
The law of the lever is proved.
Explanation of Solution
Consider the lever consists of rigid bar is shown in Figure 1.
According to the law of lever, in equilibrium condition the torque due to effort force is equal to the torque load.
Refer to Figure 1, write the formula for
Substitute equation (2) and (3) in equation (1)
Proof:
Consider the uniform bar ABCD suspended by middle point M as shown in Figure 2.
Refer to Figure 2; the bar is divided into two parts as AEFD and EBCF. Consider the middle point of AEFD is K and the middle point of EBCF is L.
The force of AEFD is represented as
Write the relation between two forces.
Consider the forces
Modify equation (4) for
Substitute
Consider
Write the expression for GI.
Substitute
Write the expression for IH.
Substitute
Write the expression for IH.
Substitute
Write the expression for GK.
Substitute
Write the expression for MK.
Substitute
Substitute
Substitute
Substitute
Compare equations (8) and (9).
Compare equation (7) and (10), which satisfies the law of the lever.
Conclusion:
Thus, the law of the lever is proved.
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