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What is the magnitude of the total torque, in newton meters, exerted on the longer rod due to the force of gravity? assume that the axis extends perpendicularly out of the page and is located at the collar, which has negligible length.

User Meka
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1 Answer

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Final answer:

The magnitude of the torque on a rod due to gravity is determined by the force and the lever arm's length. To produce an 8.0 kN·m torque on a 2.0 meters long rod, a force of 4.0 kN applied at the rod's end is needed.

Step-by-step explanation:

The magnitude of the total torque exerted on a rod due to the gravitational force can be calculated using the lever arm to the point where the force is applied. If a rod is placed along the x-axis and has to produce a given amount of torque about an axis located at one of its ends, we can use the formula τ = rF, where τ is the torque, r is the distance from the axis to the point where the force is applied, and F is the force. For instance, if we need to produce 8.0 kN·m of torque on a 2.0 meters long rod, we can calculate the force that needs to be applied at the end of the rod. In a hypothetical example where the axis is at the collar, and we assume it to have negligible length, the lever arm would be the entire length of the rod. Hence, for a rod of length 2.0 meters, a force of 4.0 kN would need to be applied at the end to create the required torque of 8.0 kN·m.

User Wildhorn
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