An auto transmission of mass 165 kg is located 1.00 m from one end of a 2.50 m bench. What weight must each end of the bench support?

Question

24-06-2025
Chemistry

High School

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An auto transmission of mass 165 kg is located 1.00 m from one end of a 2.50 m bench. What weight must each end of the bench support?

Answer :

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Nick00897 Nick00897 · Answer 1 · 2023-08-20T10:11:39-04:00

Final answer:

The question deals with balancing torques in physics. The weight of the auto transmission results in a force of 1617 N on one end of the bench, but this weight is evenly divided between the two ends of the bench, meaning each end supports approximately 808.5 N.

Explanation:

This is a problem related to the concept of torsion or balanced torques in physics. The auto transmission serves as the fulcrum of a lever arm, with the bench being the lever. We can balance the forces by setting the weight on one end of the bench equal to the weight on the other end. The center of mass of the auto transmission adds to the weight on one side of the bench, which is 1 meter away from one end. We can calculate this as follows: the weight of the auto transmission is given by multiplying the mass, 165 kg, by the acceleration due to gravity, approximately 9.8 m/s^2. This gives a weight of 1617 N, which is supported by the bench on the side where the auto transmission is closer.

The total weight supported by the bench is then split evenly between the two ends, so each end must support half the total weight. Thus, each end of the bench must support (1617 N)/2, or approximately 808.5 N.

Learn more about balanced torques here:

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