Determine the force F required to keep the lever stationary as shown in the figure below. The mass of the object is 30 kg. Assume the gravitational acceleration to be 9.8 m/s2. Provide your answer in N to 4 decimal places.

Question

BlackTom AI · Accepted Answer

First, I identify the forces and their moments about the pivot at the right end of the lever. The upward force F is applied at the left end, 10 m from the pivot, producing a counterclockwise moment F × 10. The weight of the mass m is mg, acting downward at a point 4 m to the left of the pivot, producing a clockwise moment mg × 4.

Next, I set up the torque balance for the lever to remain stationary: sum of counterclockwise moments equals sum of clockwise moments. Therefore, F × 10 = m g × 4.

Then I substitute the given values: m = 30 kg and g = 9.8 m/s^2, so m g = 30 × 9.8 = 294 N. The moment due to the mass is 294 × 4 = 1176 N·m.

Now I solve for F: F = (m g × 4) / 10 = 1176 / 10 = 117.6 N.

Thus, the force required to keep the lever stationary is 117.6 N. If needed, I can show the intermediate steps again in a compact form: F = (30 × 9.8 × 4) / 10 = 117.6 N.

Determine the force F required to keep the lever stationary as shown in the figure below. The mass of the object is 30 kg. Assume the gravitational acceleration to be 9.8 m/s2. Provide your answer in N to 4 decimal places.数值题

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