Moments, levers & gears

The photograph shows a mechanism that can be used to open a gate.

(Source: © Photimageon / Alamy Stock Photo)

The diagram shows the gate mechanism when the handle is being pulled to the right.

The bolt is connected to the handle. When the handle is pulled to the right, the bolt also moves to the right and the gate can be opened.

The spring is compressed when the bolt moves to the right. When the handle is released, the spring pushes the bolt back to its original position.

When the handle is pulled to the right, the spring applies a force on the handle to the left.

The vertical distance between the spring and the pivot point of the handle is 22 cm.

The force from the spring is 5.2 N.

Show that the force from the spring produces a moment of approximately 1 Nm.

State what is meant by the term principle of moments.

Force F acts on the handle to keep the handle stationary so that the gate can be opened.

Force F acts at a vertical distance of 70 cm from the pivot point of the handle.

Calculate the magnitude of force F.

Give two changes to this gate mechanism that would make it easier to open the gate.

The diagram shows forces used to turn a tap.

State the formula linking moment, force and perpendicular distance from a pivot.

Calculate the total moment of the two forces required to turn the tap around the pivot.

Give your answer in N cm.

total moment =_........ N cm

The tap is used to put some water in a bucket.

Describe the arrangement and motion of the water particles in liquid water.

You may draw a diagram to help your answer.

A wrench is used to turn a nut.

(Source: https://www.shutterstock.com/image-photo/adjustable-spanner-isolated-on-white-chrome-1794553030)

The force applied to the wrench is 28 N.

Calculate the moment applied by the wrench on the nut.

Give a suitable unit.

State two changes that could be made to increase the size of the moment applied to the nut.

Diagram 2 shows the wrench as it is turned through 90°

(Source: https://www.shutterstock.com/image-photo/adjustable-spanner-isolated-on-white-chrome-1794553030)

The force is applied over a distance that is equal to a quarter of the circumference of a circle.

The circle has a radius of 15 cm.

Calculate the distance over which the force is applied. [circumference of circle = 2πradius]

Calculate the work done by the force as the wrench is turned through a quarter of the circumference of the circle.

This question is about moments.

Diagram 1 shows the raised lower leg of a person.

The moment of the weight of the lower leg about the pivot is 19 N m.

A vertical force, F, is applied to the person’s foot to keep the lower leg raised.

The lower leg does not move.

Calculate the magnitude of force F, using the formula

moment = force × perpendicular distance from pivot

Which distance is used to calculate the moment of the weight of the lower leg about the pivot?

Diagram 2 shows the person resting their lower leg on two supports.

The centre of gravity of the lower leg is 0.25 m away from support A and 0.35 m away from support B.

Explain whether force X or force Y is larger.

Ignore the weight of the upper leg.

A bag of ice is placed on the lower leg, vertically above the centre of gravity.

This causes force X and force Y to increase.

The bag is then moved towards the person’s foot.

Describe how force X and force Y change as the bag is moved towards the person’s foot.

A pencil has a weight of 0.16 N.

What is the mass of the pencil?

The diagram shows the pencil with one end resting on a small block.

A finger provides an upwards force, F, to keep the pencil horizontal.

The weight of the pencil is 0.16 N.

Calculate the moment of the weight of the pencil about the pivot.

Use the formula

moment = force × perpendicular distance from the pivot

moment =_........ N cm

State the moment of the force F.

Show that force F is 0.080 N.

Diagram 1 shows a wooden plank balanced horizontally on two supports, A and B.

A block is suspended from the plank between the supports by a cable of negligible weight.

The weight of the block is 260 N.

State the formula linking moment, force and perpendicular distance from the pivot.

By taking moments about support A, calculate force F.

Assume the weight of the plank is negligible.

Explain what will happen to the magnitude of force F if the block is moved towards support B.

The centre of gravity of the block is located at point X.

Draw an arrow on diagram 2 to show the weight of the block.

The block also experiences a force due to the tension in the cable.

Explain why the block remains stationary when it is supported by this tension force.

Explain why the forces acting on the block are not an example of Newton’s third law of motion.

Diagram 1 shows a gate fitted with a spring mechanism.

The spring mechanism shuts the gate automatically.

The graph shows some data from an investigation into how the extension of the spring changes with an increasing force.

Describe the relationship shown by the graph.

Diagram 2 shows the gate viewed from above.

The force the spring exerts on the gate is 480 N.

Show that the moment of the force the spring exerts on the gate is about 400 Nm.

The force, F, is the minimum force needed to start opening the gate.

Calculate the magnitude of force F.

The spring is removed for testing.

Explain what will happen to the spring if the force applied to extend the spring is too large.

A student investigates how the support forces acting on a metre rule are affected by the position of a mass hanger.

He uses this apparatus.

This is the student’s method.

● suspend a metre rule from its 10 cm and 90 cm marks using two newton meters

● place a mass hanger with a weight of 5 N at the 20 cm mark on the metre rule

● adjust the heights of the newton meters until the metre rule is horizontal

● record the readings on both newton meters

The student repeats the method, moving the mass hanger to a different position on the metre rule each time.

State the independent variable in the student’s investigation.

State two control variables in the student’s investigation.

Suggest how the student could improve the quality of his data.

The table shows the student’s results.

The graph shows the results for newton meter A.

Plot the results for newton meter B.

Draw the line of best fit for newton meter B.

Describe the relationships shown by the graph.

Using ideas about moments, explain why the reading on newton meter A decreases as the mass hanger is moved towards newton meter B.

The diagram shows a metal block on top of a wooden block.

The metal block is held stationary by force F.

The weight of the metal block acts through point G.

Give the name of point G.

Name a piece of apparatus that could be used to measure the weight of the metal block.

State the formula linking moment, force and perpendicular distance from the pivot.

The weight of the metal block is 0.68 N.

Show that the moment of the weight of the metal block about point P is approximately 2.9 N cm.

Force F is applied to the metal block to stop it from moving.

Calculate the magnitude of force F.

A student uses this apparatus to investigate moments.

This is the student’s method.

• attach elastic bands at 15 cm intervals on a one metre tall clamp stand

• attach a newton meter to the highest elastic band and measure the horizontal force required to tilt the stand

• repeat the method at each 15 cm interval

Name an instrument that the student should use to accurately measure the distances on the clamp stand.

The table shows the student’s results.

The photograph shows the reading on the newton meter when the distance is 45.0 cm.

Use the photograph to determine the force required to tilt the stand when the distance is 45.0 cm.

Give a reason why this newton meter is unsuitable for measuring the force for distances less than 15.0 cm.

Plot a graph of the student’s results on the grid.

Draw the curve of best fit.

The student concludes that the moment required to tilt the clamp stand does not change when the distance is varied.

Use data from the table or the graph to evaluate the student’s conclusion.

The diagram shows some of the forces acting on a large rubbish bin on wheels.

The weight of the bin acts through point G.

Give the name of point G.

The mass of the bin is 23 kg.

What is the weight of the bin?

State the principle of moments.

A person applies force F to the bin to keep it stationary.

Calculate the magnitude of force F.

State the magnitude and direction of the force applied to the person by the bin.

A builder needs to lift a large stone block.

Diagram 1 shows the stone block.

Draw an X on diagram 1 at the centre of gravity of the stone block.

State the formula linking weight, mass and gravitational field strength.

The mass of the stone block is 130 kg.

Calculate the weight of the stone block.

The builder uses a wooden plank to lift the large stone block.

The plank is uniform and pivoted at its centre.

The builder pushes down on one end of the plank to lift the stone block.

Diagram 2 shows the plank when it is horizontal and stationary.

State the principle of moments.

The builder is pushing down with a force of 520 N to keep the plank horizontal.

Calculate distance X.

Calculate the length of the plank.

This question is about a folding table.

The diagram shows some of the forces acting on the table.

The weight of the table acts through point G.

State the name of point G.

State the formula linking moment, force and perpendicular distance from the pivot.

The moment of the weight force of the table about the hinge is 92 N m.

By using the principle of moments, calculate the force S that a person applies to keep the table in equilibrium.

State Newton’s third law.

State the magnitude and the direction of the force that the table applies to the person holding the table.

The diagram shows a bottle supported by a finger.

State the name of point Z.

State the formula linking moment, force and perpendicular distance from the pivot.

The bottle does not move.

Calculate the weight of the bottle.