Torque & Equilibrium Practice Problems

A female worker in the workplace has a safe limit to lift objects weighing 160 N (16 kg) at places of work. The worker can lift weights greater than 160 N using a trolley. You may consider a 1.5 m long trolley, weighing 100 N, and the center of gravity located at 0.6 m from the axle. Assume the load's center of mass is located 0.6 m from the axle. What is the source of the force that enables the worker to lift more weight using the trolley?

A male person has a safe limit to lift objects weighing 250N (25 kg) at the workplace. How much load can the person lift using a 1.5 m long trolley weighing 100 N? The center of mass of the trolley is located 0.6 m from the axle supporting the wheels. Take the center of gravity of the load to be located at 0.6 m from the axle. 

A 400 N hatch is located at the upper end of a stairway. Determine the total upward force a person standing on the staircase must apply to initiate door opening and the net force applied on the hatch by the hinges. Take the upward force to be applied midway of the edge opposite to the hinges. 

A 180 N hatch in the ceiling is free to rotate about hinges on one of its ends. What net upward force applied at the door's center is required to start opening the door? What net force is exerted on the door by the hinges?

Consider a long thin wooden slab 5m in length. The slab is of negligible mass and is in equilibrium. The forces acting on it are shown in the figure below. Find the magnitudes of forces F₁ and F₂.

A 5.0-meter-long plank rests upon a fulcrum (pivot/midpoint). On one end of the plank, there is a 4.0 kg backpack, while on the opposite end, there is a 1.5 kg lunchbox. In order to maintain equilibrium on the plank, determine the distance at which a 2.5 kg rat should be positioned to the left of the plank's midpoint.

The limb in a cast weighs 16.0 kg and its centre of gravity is 36.0 cm from the pivot point. Calculate the mass required to balance the limb if the suspension cord is attached 79.0 cm from the pivot point.

A clamp is designed to secure a lightweight metal tube. When both the finger and the thumb are applied with equal forces of F_F=F_T=12.0 N, calculate the resulting force that the clamp's ends exert on the metal tube.

The effort needed to pull a stopper from a bottle's neck varies between 300 and 500 N. Determine the range of forces F needed to uncork a bottle using the lever-based opener.

Determine the normal force exerted by the ground on the rear tires at point A and the vertical load transmitted through the hitch at point B of a tractor, which has a 2400-kg freight container secured at hitch point B.

A banner weighing 6.2 kg is suspended from a horizontal beam extending from the front wall of a building. The banner is attached 2.3 m away from the beam connection to the building. Determine the torque exerted by the banner about the point where the beam joins the building.

A beam extends horizontally from the front of a store, and a 6.2-kg banner is suspended from it, 2.3 m from where the beam is attached to the building. There must be opposing torque to prevent the beam from tipping due to the banner's weight. What provides this balancing torque?

You are aboard a treasure-seeking vessel and compelled to tread the plank at point C. The plank is affixed at point A and supported 0.76 m from A, with its center mass at point B. You have a mass of 66 kg, and the plank a mass of 46 kg. Determine the minimum downward force the fixings at point A must exert on the plank to hold it in place.

An industrial crane lifts a maximum load of 800 kg at the end of a horizontally set boom. The boom is 12.0 meters long and has a uniform mass of 100 kg. The cable attaches to the boom at a point 2.0 meters from the pivot at the base and forms a 60-degree angle with the boom. Calculate the maximum tension $\vec{F}_T$ that the cable exerts on the boom. Assume the boom's center of gravity is at its midpoint.

Consider a person weighing 70 kg standing on tiptoes, using the toes as the pivot point. The calf muscle applies an upward force at the Achilles tendon, located 1.8L from the pivot point (toes), where L is the distance from the toes to where the leg bone exerts its force downward. The leg bone applies its force downward at point L from the toes. This setup maintains the foot in static equilibrium while arched on tiptoe. Assuming the person's weight is supported by the leg bone, calculate the forces exerted by the leg bone and Achilles tendon to keep the foot stable and arched in static equilibrium.

An artist holds a 2.0 m long, uniformly distributed 11.0-kg rod for a performance. Determine the forces (both in magnitude and direction) he needs to apply with each hand to keep the rod balanced. Further, find out where he should shift his left hand so that the force required by either hand does not exceed 151 N and 86 N.

A flagpole is attached to the side of a building. A 5.0-kg flag hangs from the pole at a point 3.0 m from the wall. Discuss whether compression, tension, and/or shear play a role in this scenario.