**Q1: **

A spanner is used by a mechanic to tighten a nut. The spanner is 20 cm long and to tighten the nut it must apply a torque of 12 N⋅m. What force must the mechanic apply to the end of the spanner that is opposite to the end that tightens the nut? The spanner turns through a horizontal circle to tighten the nut.

**Q2: **

A ladder that stands vertically upward is used by firefighters to reach high windows in a burning building. The ladder is 25 m long, and a firefighter is standing on the ladder 20 m from its base. The firefighter leans horizontally to reach into a window beside the ladder, pulling horizontally on the ladder with a force of 35 N. What magnitude of torque is produced about the base of the ladder when the firefighter leans?

**Q7: **

A pole that is 15 m long and has a weight of 25 N is balanced at rest on a fulcrum halfway along its length. On the right-hand end of the pole, a vertically downward force of 10 N acts. On the left-hand end, a vertically downward force of 15 N acts. Find the distance from the fulcrum to the pole’s center of mass.

**Q8: **

How much torque is produced by a 30 N force acting on an object at a distance of 0.15 m from the point about which the object can rotate?

**Q9: **

A waiter is balancing a large serving tray at rest on his arm. The tray is 50 cm long and the waiter’s arm supports the tray 15 cm from its right-hand end. The tray’s weight is 10 N, which is spread evenly along its length, and 20 cm from the left-hand end of the tray is a serving of food that has a weight of 20 N. The waiter uses his spare hand to push down on the right-hand end of the tray to keep the tray horizontally level. What magnitude force does the waiter’s arm supporting the tray apply to the tray? Round your answer to one decimal place.

**Q10: **

A horizontal flagpole has a mass of 15 kg that is equally distributed along its 4 m length. The left-hand end of the flagpole is secured firmly into the wall of a building, and the right-hand end of the flagpole supports a flag of mass 5 kg. The flagpole is stable in its horizontal position. What is the magnitude of the torque produced by the flagpole’s wall mounting?

**Q11: **

A seesaw consists of a horizontal plank of wood 5 m long, with its mass equally distributed along its length. The fulcrum of the seesaw is positioned at the center of the plank. A child of mass 28 kg sits at the right-hand end of the seesaw, and a larger child with a mass of 35 kg sits at the left-hand end. The seesaw tips down on the larger child’s end, and the larger child shuffles toward the seesaw’s fulcrum until it starts to rise again. The larger child must be less than a certain distance from the fulcrum for the seesaw to start to rise again. What is this distance?

**Q12: **

A symmetrical Christmas tree is decorated with baubles. A 15 g mass bauble is hung from the tree at a horizontal distance of 20 cm to the left of its center of mass, and a 20 g bauble is hung 25 cm to the right of the tree’s center of mass. How many centimeters from the tree’s center of mass should a 50 g mass bauble be hung to produce zero net torque on the tree? Consider right to be the positive displacement direction.

**Q13: **

An object is subject to a 72 N⋅m torque about a point when a 4.5 N force is applied to a second point along the object’s length. The force is applied in a direction perpendicular to the object's length. How far apart are the two points?

**Q14: **

How much force is required to produce a 90 N⋅m torque on an object about the point about which the object can rotate? The distance between the point where the force is applied and the point about which the object can rotate is 2.5 m.