Moments, levers & gears

Which of these forces keeps the Moon in orbit around the Earth?

Figure 3 shows a rock and a long lever.

The lever is used to try to move the rock.

The lever is pushed downwards at Q with a force of 375 N. Q is 1.4 m from the pivot.

Calculate the moment of the force at Q about the pivot.

Use the equation

moment of a force = force × distance from pivot

moment of force =_........

When the force of 375 N is pushed down at Q, the rock does not move.

Explain why pushing down at P with a force of 375 N may be more successful in moving the rock.

Figure 4 shows a uniform ruler that can rotate about a pivot. The ruler is balanced by adding weights to each side.

Calculate the value of X, the unknown weight, that keeps the ruler balanced.

Figure 20 shows a metal block being weighed by a newton meter (force meter).

In Figure 20a the block is hanging in a liquid. In Figure 20b the same block is hanging in air.

Explain why the reading on the newton meter is different in Figures 20a and 20b.

The density of the liquid is 1.4 × 10³kg / m³.

Calculate the density of the block. Gravitational field strength, g, = 10 N / kg

density =_........ kg / m³

*(b) Figure 21 shows a device that a person can use to lift a large load with a smaller effort force.

(Source: © Shutterstock-Pixelsquid/Shutterstock)

Figure 21

Figure 22 shows the important parts of the device. The curved arrows show the directions of rotation of the handle, the gears and the drum.

The size of the effort force needed to lift the load is determined by the sizes of the parts of the device.

Explain why this is the case.

Your answer should refer to

• the sizes of the different parts of the device

• how these sizes are used in relevant calculations

Figure 2 shows two gear wheels, P and Q.

P has 20 teeth.

Q has 10 teeth.

P rotates once.

How many times does Q rotate when P rotates once?

A third gear wheel is added to the system in Figure 2 so that this third wheel rotates in the opposite direction to Q but at the same speed as Q.

1. Draw an X on Figure 2 to show the position of this third gear wheel.

2. State how many teeth this third gear wheel has.

number of teeth =_........

Figure 3 shows a 9.0 N force acting on a ruler.

Calculate the moment of the 9.0 N force about the pivot.

Use the equation

moment = force perpendicular distance of force from pivot

moment =_........

Another ruler is balanced at its midpoint.

Figure 4 shows two forces, F and G, acting on this ruler.

The ruler is balanced (in equilibrium).

The moment of force F about the pivot = 2.4 N m.

Use the principle of moments to state the moment of force G about the pivot.

moment of force G =_........

Force F = 8.0 N.

The moment of force F about the pivot = 2.4 N m.

Calculate the distance, d, of force F from the pivot.

Use the equation

moment = force perpendicular distance of force from pivot

distance =_........

Which of these is a unit for the moment of a force?

Figure 15 shows a claw hammer about to remove a nail from a piece of wood.

State the principle of moments.

Calculate the force F₂ shown in Figure 15.

Use the following data

• F₁ = 11.4 N

• d₁ = 24.5 cm

• d₂ = 3.7 cm

Figure 16 shows a system of gears used in a clock.

Gear wheel P rotates clockwise at a rate of 1.0 revolution per minute.

Calculate the rotation rate of gear wheel Q in revolutions per hour.

rotation rate of Q =_........ revolutions per hour

Describe how a gear wheel could be added to the system to give a clockwise rotation with double the rotation rate of gear wheel Q.

Your answer should refer to

• the position of the gear wheel

• the number of teeth in the gear wheel.

Which of these is a vector?

Figure 17 shows a balanced seesaw with two children on it.

The pivot is at the centre of the seesaw.

The seesaw is balanced with no children sitting on it.

Child P has a weight of 150 N.

Calculate the moment of the weight of child P about the pivot in N m.

Use the equation

moment of a force = forcedistance to pivot

moment =_........

Figure 18 shows the same balanced seesaw, with the distance of child Q to the pivot labelled as well.

Calculate the value of W, the weight of child Q.

Use the idea of moments and the equation

the moment of W = the moment of the weight of child P

Give your answer to 2 significant figures.

*(c) Figure 19 shows a crowbar being used to lift a heavy weight.

Explain how the crowbar enables a person to lift a heavy weight.

You should include the idea of moments in your answer.

It may help to label some distances in Figure 19 and use those distances in your explanation.

Figure 11 shows a person doing a push‑up exercise.

An upward force is used to cause rotation about a pivot.

Which row of the table is correct for this rotation?

Figure 12 shows some of the bones and muscles in an arm.

The arrows show the forces on the forearm when the arm is bent.

The hand is empty.

The biceps muscle provides a force to balance the weight of the forearm.

The weight of the forearm can be represented as a single force.

Figure 13 shows a diagram representing the forces and distances involved.

Use the principle of moments to show that the system shown in Figure 13 is in equilibrium.

The person then holds a ball weighing 15 N in their hand.

Figure 14 shows the forces on the forearm and their distances from the elbow joint.

Calculate the force from the muscle that is needed to keep the system in Figure 14 in equilibrium.

Figure 15 shows a ball floating in seawater and the same ball floating in fresh water.

Compare the upthrust on the ball in seawater with the upthrust on the same ball in fresh water.

Explain why there is less of the ball below the surface of the seawater than below the surface of the fresh water.

Figure 2 shows four items of equipment that can be used in investigations.

In which of these does a force cause rotation?

spring balance plotting compass thermometer variable resistor

Figure 3 shows a force, F, acting on a ruler.

The ruler has a pivot at one end.

Calculate the moment of the force, F, around the pivot.

Give your answer in units of Nm.

Use the equation

moment of a force = force × distance from pivot

A 20 cm ruler has a pivot at its centre.

The ruler is balanced when no forces act on the ruler.

Figure 4 shows two forces, Y and Z, acting on the ruler.

Use the principle of moments to show that the ruler in Figure 4 is balanced.

Figure 5 shows an arrangement of three gears, P, Q and R.

P and R have the same number of teeth.

P rotates in the direction shown.

State how the speed and direction of rotation of R compare with the speed and direction of rotation of P.

speed

direction

Which of these is a vector quantity?

Figure 13 shows a toy that a student makes for a nursery school.

The rod hangs by a string from the ceiling.

weight of S = 2.0 N weight of R = 1.0 N

Figure 13

The moment of C about point P is 0.60 Nm.

Calculate the weight of C.

Use the equation

moment = F × d

weight of C_........

Show that the total moment of S and R about P is 0.70 N m.

Using the data in the question and the principle of moments, determine if the toy shown in Figure 13 is in equilibrium.

The rod is very light so its weight can be ignored.

Figure 14 show a rack and pinion system, used on a mountain railway.

The teeth on the rack are 8.0 cm apart.

Calculate how far along the rack the train moves when the pinion turns through one complete revolution.

Complete the following sentences using words from the box below.

The force that keeps the Earth in orbit around the sun is

The force that opposes motion between two surfaces is_........ .

The force that can move small pieces of paper towards a plastic comb

Which of these statements is true for a vector quantity?

Figure 3 shows a force of 200 N acting at the end of a plank of wood.

The force acts at right angles to the plank and at 3.0 m away from a pivot.

Calculate the moment of the 200 N force about the pivot.

State the unit of the moment of the force.

Use the equation

moment of a force = force × distance at right angles to the direction of the force

moment of the force about the pivot =_........ unit_........

A student investigates moments of forces.

Figure 14 shows the apparatus used.

The pivot is under the centre of the rod.

A magnet is fixed to one end of the rod.

A piece of modelling clay is fixed to the other end of the rod.

The system is in equilibrium.

State the relationship between the moment of the weight of the magnet and the moment of the weight of the piece of modelling clay about the pivot.

The student fixes a coil to the bench under the magnet as shown in Figure 15.

The coil of wire is connected to a d.c. power supply so that there is a current in the coil.

To bring the system back into equilibrium, the student hangs a 0.050 N weight on the rod, 8.4 cm away from the pivot, as shown in Figure 15.

Calculate the size of the force between the magnet and the coil.

Describe how the student could develop the investigation to determine if the size of the force between the magnet and the coil is directly proportional to the size of the current in the coil.

The student reverses the direction of the current in the coil. Describe how the student can bring the system back into equilibrium without making any changes to the magnet.

Figure 6 shows two gears.

Gear R and gear S can rotate.

Gear R has 20 teeth.

Gear S has 60 teeth.

Gear S rotates through 2 complete revolutions.

Calculate how many complete revolutions gear R rotates by.

gear R has rotated through_........ revolutions

Figure 7 shows two gears, S and T.

Gear S can rotate on a fixed axle.

Gear T can move up and down.

Gear S has 60 teeth.

The distance between each of the teeth on gear S and on gear T is 2 mm.

Gear S moves through one complete revolution in the direction shown.

Which of these describes the motion of gear T?

Figure 8 shows a force of 70 N turning a lever about point P.

Calculate the moment of the 70 N force about point P.

State the unit.

Use the equation

moment = force × distance normal to the direction of the force

Figure 9 shows a worker using a wheelbarrow to move some sand.

The load is equal to the total weight of the sand and the wheelbarrow.

The effort is the force that the worker applies to the wheelbarrow handles.

The worker applies just enough effort to lift the load.

Explain why the effort is smaller than the load.

Some sand falls down and sticks between the wheel and the axle.

State why it might be harder to push the wheelbarrow along when there is some sand between the wheel and the axle.

Figure 1 shows some forces acting on a seesaw.

The forces shown have the same magnitude but act in different directions.

In which of these could the forces acting on a seesaw be in equilibrium?

Figure 2 shows an open door.

Explain why it is easier to close the door by pushing at point P rather than pushing at point Q.

Figure 3 is a diagram of the forces acting on a swing.

The swing is not moving.

The seat of the swing, AB, is 0.80 m long.

A person of weight 450 N sits on the seat.

The person’s weight acts at a distance of 0.50 m from A as shown in Figure 3.

Ignore the weight of the seat.

The upward forces exerted by the ropes on the seat are F₁ and F₂.

Calculate the force F₂ by taking moments about A.

force F₂ =_........

Figure 19 shows four forces, P, Q, R and S, acting on a rod.

The rod can rotate around an axle.

Which force will make the rod rotate about the axle?

Figure 20 shows a person trying to lift a large rock using a metal bar.

The rock weighs 1800 N.

The person can only produce a downwards force of 600 N.

The person cannot lift the rock.

Explain, using calculations, why the person cannot lift the rock.

Explain one change to the arrangement that will make it possible for this person to lift the rock.

Figure 21 shows a bicycle.

The rider uses the pedals to make the large gear wheel turn.

The large gear wheel moves the chain. The chain turns the small gear wheel.

The large gear wheel has 48 teeth.

The small gear wheel has 12 teeth.

The large gear wheel turns 2 times each second.

Calculate the number of times that the small gear wheel turns each second.

_........ turns each second

Explain how the oil improves the efficiency of the bicycle.

Figure 6 shows four forces, P, Q, R and S, acting on a rod.

The rod can rotate around an axle.

Which force will make the rod rotate about the axle?

Figure 7 shows a person trying to lift a large rock using a metal bar.

The rock weighs 1800 N.

The person can only produce a downwards force of 600 N.

The person cannot lift the rock.

Explain, using calculations, why the person cannot lift the rock.

Explain one change to the arrangement that will make it possible for this person to lift the rock.

Figure 8 shows a bicycle.

The rider uses the pedals to make the large gear wheel turn.

The large gear wheel moves the chain. The chain turns the small gear wheel.

The large gear wheel has 48 teeth.

The small gear wheel has 12 teeth.

The large gear wheel turns 2 times each second.

Calculate the number of times that the small gear wheel turns each second.

_........ turns each second

Explain how the oil improves the efficiency of the bicycle.

Figure 10 shows an arrangement of gears.

Each gear turns around a fixed axle.

Gear P is turned through one complete revolution per second.

Which of the following describes the motion of gear R?

Figure 11 shows the same arrangement with gear R replaced by a rack.

The rack can move up or down when the gears turn.

The teeth on the rack are 2 mm apart.

Calculate how far the rack moves when P turns through to one complete revolution.

Figure 12 shows three toy animals hanging from a rod.

The rod hangs from the ceiling by a string tied to the centre of the rod.

The system is in equilibrium.

Use the principle of moments to calculate the mass of the toy elephant.

Figure 13 shows a diagram of a device for lifting heavy loads.

The metal tube is filled with oil.

The piston Y is pushed down with a force K.

This produces a force L on piston Z.

The pressure exerted on the oil by piston Y is the same as the pressure exerted by the oil on piston Z.

Explain the difference between the size of force K and the size of force L.