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Pressure and moments

Calculate pressure and turning effects.

Start here

The key idea

A moment is the turning effect of a force around a pivpivot.

Equation to know

moment = force x perpendicular distance

Pressure And Moments
forceforcemoment = force x perpendicular distance

Use the labels to explain the scientific relationship shown.

Revision notes

The bit that matters

Short notes first. Learn the idea, then use the worked example and questions to check it properly.

1

Pressure on a surface

Pressure is the force acting at right angles to a surface per unit area: pressure = force / area (p = F / A), measured in pascals (Pa), where 1 Pa = 1 N/m2.For the same force, a smaller area gives a larger pressure, which is why sharp knives and drawing pinpins work.A larger area, such as on snowshoes or tractor tyres, spreads the force and lowers the pressure.

2

Pressure in fluids

In a liquid, pressure increases with depth because there is a greater weight of liquid above.The pressure due to a column of liquid is p = h x rho x g, where h is depth, rho is density and g is gravitational field strength.This pressure acts equally in all directions at a given depth.A submarine or dam must be built stronger at greater depths because of this increased pressure.

3

Upthrust and floating

A submerged or floating object experiences an upward force called upthrust, caused by the pressure being greater on the bottom of the object than on the top.The upthrust equals the weight of the fluid displaced.An object floats when the upthrust equals its weight; it sinks when its weight is greater than the maximum upthrust.Objects float if their average density is less than that of the fluid.

4

Moments and the principle of moments

A moment is the turning effect of a force: moment = force x perpendicular distance from the pivpivot (M = F x d), measured in newton metres (Nm).When an object is balanced (in equilibrium), the total clockwise moment about a pivpivot equals the total anticlockwise moment.Levers and gears use moments to multiply force: a longer lever arm produces a larger moment for the same force.

Key terms

Definitions to learn

Pressure

Force per unit area acting at right angles to a surface, in Pa (N/m2).

Upthrust

The upward force on an object in a fluid, equal to the weight of fluid displaced.

Density

Mass per unit volume of a substance, in kg/m3.

Moment

The turning effect of a force, equal to force x perpendicular distance from the pivpivot.

Principle of moments

For a balanced object, total clockwise moment = total anticlockwise moment.

Worked example

A force of 40 N acts 0.30 m from a pivpivot. Calculate the moment.

1

Use moment = force x distance.

2

Use the perpendicular distance.

Final answer

12 Nm

Exam habit

State moments = force × perpendicular distance before calculating.For balanced beams, write clockwise moment = anticlockwise moment explicitly.Pressure must include area in m² — convert cm² by dividing by 10,000.

Watch out

Do not use a sloping distance when the perpendicular distance is required.

Examiner tips

How to score full marks

  • 1For pressure, the area must be at right angles to the force; convert cm2 to m2 by dividing by 10000.
  • 2In moments problems always use the perpendicular distance from the pivpivot, not the distance along a tilted bar.
  • 3State equilibrium clearly: set clockwise moments equal to anticlockwise moments, then solve.
Practice questions

Try these yourself

Start with the core skill, then open the answer only after you have attempted the full question.

1A force of 150 N acts on an area of 0.025 m2. Calculate the pressure.
Mark scheme
  1. 1.Use pressure = force / area.
6000 Pa
2A balanced beam has a 20 N force 0.50 m from the pivpivot. What force is needed 0.25 m from the pivpivot on the other side?
Mark scheme
  1. 1.Set clockwise moment equal to anticlockwise moment.
40 N
3Explain why snowshoes reduce the pressure on snow.
Mark scheme
  1. 1.Relate area to pressure.
They increase the contact area, so the same force produces less pressure.
4A force of 200 N acts on an area of 0.5 m2. Calculate the pressure.[2 marks]
Mark scheme
  1. 1.Use p = F / A.
  2. 2.Substitute.
p = F / A = 200 / 0.5 (1) = 400 Pa (1).
5Explain why a person wearing snowshoes is less likely to sink into soft snow.[2 marks]
Mark scheme
  1. 1.Snowshoes have a large area.
  2. 2.Same weight/force.
  3. 3.Lower pressure.
Snowshoes increase the area in contact with the snow (1), so for the same weight the pressure (force / area) is lower (1) and the person is less likely to sink.
6A force of 30 N acts at a perpendicular distance of 0.4 m from a pivpivot. Calculate the moment.[2 marks]
Mark scheme
  1. 1.Use M = F x d.
  2. 2.Substitute.
M = F x d = 30 × 0.4 (1) = 12 Nm (1).
7Calculate the pressure at a depth of 5 m in seawater. (density = 1030 kg/m3, g = 9.8 N/kg)[3 marks]
Mark scheme
  1. 1.Use p = h x rho x g.
  2. 2.Substitute.
  3. 3.Evaluate.
p = h x rho x g = 5 × 1030 × 9.8 (1) = 50470 Pa (1) (about 50500 Pa) (1).
8A uniform beam is balanced on a central pivpivot. A 40 N weight is placed 0.6 m to the left of the pivpivot. A second weight is placed 0.8 m to the right. Calculate the size of the second weight needed to balance the beam, and state the principle you used.[4 marks]
Mark scheme
  1. 1.State principle of moments.
  2. 2.Anticlockwise moment = 40 × 0.6.
  3. 3.Set equal to clockwise W x 0.8.
  4. 4.Solve for W.
Principle of moments: total clockwise moment = total anticlockwise moment (1). Anticlockwise = 40 × 0.6 = 24 Nm (1). Clockwise = W x 0.8, so W x 0.8 = 24 (1), giving W = 24 / 0.8 = 30 N (1).
9A woman stands on two identical bathroom scales, one under each foot. The left scale reads 280 N and the right reads 320 N. Calculate her total weight and mass. (g = 9.8 N/kg)[2 marks]
Mark scheme
  1. 1.Total weight = sum of both readings.
  2. 2.Mass = weight / g.
Total weight = 280 + 320 = 600 N (1); mass = 600 / 9.8 = 61.2 kg (accept 61 kg) (1)
10A syringe has a cross-sectional area of 2.0 cm2 at the plunger. A nurse applies a force of 10 N to the plunger. Calculate the pressure exerted on the liquid in the syringe. (Convert area to m2.)[3 marks]
Mark scheme
  1. 1.Convert area: 2.0 cm2 = 2.0×10−42.0 \times 10^{-4} m2.
  2. 2.p = F / A.
  3. 3.Substitute and evaluate.
A = 2.0×10−42.0 \times 10^{-4} m2 (1); p = 10 / (2.0×10−42.0 \times 10^{-4}) (1) = 50000 Pa = 50 kPa (1)
11An object of weight 25 N is fully submerged in water and experiences an upthrust of 30 N. State whether the object sinks, floats or accelerates upward, and explain why.[3 marks]
Mark scheme
  1. 1.Compare weight and upthrust.
  2. 2.Resultant force direction.
  3. 3.Link to motion.
The upthrust (30 N) is greater than the weight (25 N) (1); the resultant force is 5 N upward, so the object accelerates upward towards the surface (1); it will rise until it partially emerges and the upthrust decreases to equal the weight, at which point it floats (1)
12A diver descends from the surface to a depth of 30 m in the sea. The density of seawater is 1025 kg/m3 and atmospheric pressure at the surface is 101 000 Pa. Calculate the total pressure the diver experiences at 30 m depth. (g = 9.8 N/kg)[3 marks]
Mark scheme
  1. 1.Pressure from water = h x rho x g.
  2. 2.Total pressure = atmospheric pressure + water pressure.
P_water = 30 × 1025 × 9.8 = 301 350 Pa (1); P_total = 101 000 + 301 350 (1) = 402 350 Pa (accept 402 000 Pa) (1)
13A non-uniform plank of length 3.0 m is placed on a pivpivot 1.2 m from its left end. A 50 N weight is hung from the left end and the plank balances horizontally. Calculate the weight of the plank, stating any assumption you make about the position of its centre of gravity.[3 marks]
Mark scheme
  1. 1.Anticlockwise moment = 50 × 1.2.
  2. 2.Centre of gravity assumption: non-uniform so it is NOT at the mid-point; the plank balances, so the plank's weight acts through the pivpivot position or must be determined.
  3. 3.If it balances with pivpivot 1.2 m from the left and 50 N hangs from left, the plank's weight acts to the right of the pivpivot.
  4. 4.Anticlockwise = 50 × 1.2; clockwise = W_plank x d where d = distance from pivpivot to COG.
  5. 5.Without more information, the question is solvable only if we assume COG is at mid-point (1.5 m from left, so 0.3 m to right of pivpivot).
Assuming the plank's centre of gravity is at its midpoint (1.5 m from the left end), the plank's weight acts 1.5 - 1.2 = 0.3 m to the right of the pivpivot (1); anticlockwise moment = 50 × 1.2 = 60 Nm; clockwise moment = W x 0.3 (1); 60 = W x 0.3, so W = 200 N (1)
14Explain, using the principle of moments and the concept of upthrust, why a large cargo ship made of steel can float even though steel is denser than water. Discuss what would happen to the ship's waterline as more cargo is loaded.[4 marks]
Mark scheme
  1. 1.Steel hull is hollow so average density of ship is less than water.
  2. 2.Upthrust equals weight of water displaced.
  3. 3.Ship sinks lower until upthrust = weight of ship + cargo.
  4. 4.If overloaded, ship sinks below safe waterline.
Although steel is denser than water, the ship is hollow, so the average density of the ship (steel plus enclosed air) is less than that of seawater (1); when placed in water, the ship sinks until the weight of water displaced (upthrust) equals the total weight of the ship, at which point the net force is zero and the ship floats — Archimedes' principle (1); as cargo is added, the total weight increases, so the ship sinks lower in the water, displacing more water and increasing the upthrust until a new equilibrium is reached (1); if too much cargo is loaded, the ship's sides dip below the waterline and water floods in, causing it to sink — this is why ships have a Plimsoll line marking the maximum safe load level (1)
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