Teach Me Maths

Pressure, Force and Area

Question 12 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A box exerts a force of 84 newtons on a table.

The area of the box in contact with the table is 12 cm².

Work out the pressure on the table due to the box. Give your answer in newtons/cm².

Hint

Divide the force by the area.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A box exerts a force of 84 newtons on a table.

The area of the box in contact with the table is 12 cm².

Work out the pressure on the table due to the box. Give your answer in newtons/cm².

  1. Pressure = force ÷ area.
  2. 84\div12=7, so the pressure is 7 newtons/cm².

Question 22 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

The pressure on the floor due to a crate is 250 newtons/m².

The area of the crate in contact with the floor is 2 m².

Work out the force exerted by the crate on the floor. Give your answer in newtons.

Hint

Every square metre of the floor has a force of 250 newtons on it.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

The pressure on the floor due to a crate is 250 newtons/m².

The area of the crate in contact with the floor is 2 m².

Work out the force exerted by the crate on the floor. Give your answer in newtons.

  1. Rearrange the formula: force = pressure × area.
  2. 250\times2=500, so the force is 500 newtons.

Question 32 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A force of 90 newtons acts on an area of A cm².

The pressure is 15 newtons/cm².

Work out the value of A.

Hint

Think of how many lots of 15 newtons make 90 newtons.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A force of 90 newtons acts on an area of A cm².

The pressure is 15 newtons/cm².

Work out the value of A.

  1. Rearrange the formula: area = force ÷ pressure.
  2. 90\div15=6, so A=6.

Question 42 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A force of 30 newtons acts on an area of 0.5 m².

Work out the pressure. Give your answer in newtons/m².

Hint

Dividing by a number less than 1 makes the answer bigger.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A force of 30 newtons acts on an area of 0.5 m².

Work out the pressure. Give your answer in newtons/m².

  1. Pressure = force ÷ area =30\div0.5.
  2. There are 60 halves in 30, so the pressure is 60 newtons/m².

Question 52 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

The diagram shows a solid cuboid standing on a table.

The face of the cuboid touching the table measures 6 cm by 4 cm.

The cuboid exerts a force of 120 newtons on the table.

Work out the pressure on the table due to the cuboid. Give your answer in newtons/cm².

Hint

Only the face touching the table counts as the area, so the height is not needed.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

The diagram shows a solid cuboid standing on a table.

The face of the cuboid touching the table measures 6 cm by 4 cm.

The cuboid exerts a force of 120 newtons on the table.

Work out the pressure on the table due to the cuboid. Give your answer in newtons/cm².

  1. Area in contact with the table =6\times4=24 cm².
  2. Pressure =120\div24=5 newtons/cm².

Question 62 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A force of 250 newtons acts on an area of 35 cm².

Work out the pressure. Give your answer in newtons/cm², correct to 1 decimal place.

Hint

Divide the force by the area, then round.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A force of 250 newtons acts on an area of 35 cm².

Work out the pressure. Give your answer in newtons/cm², correct to 1 decimal place.

  1. Pressure =250\div35=7.142\ldots newtons/cm².
  2. Correct to 1 decimal place, the pressure is 7.1 newtons/cm².

Question 72 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

The base of a box is a square with sides of length 8 cm.

The box exerts a force of 192 newtons on the floor.

Work out the pressure on the floor due to the box. Give your answer in newtons/cm².

Hint

Work out the area of the square base first.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

The base of a box is a square with sides of length 8 cm.

The box exerts a force of 192 newtons on the floor.

Work out the pressure on the floor due to the box. Give your answer in newtons/cm².

  1. Area of the base =8\times8=64 cm².
  2. Pressure =192\div64=3 newtons/cm².

Question 83 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A table has 4 legs. The end of each leg has an area of 6 cm² in contact with the floor.

The table exerts a total force of 480 newtons on the floor. The force is shared equally between the 4 legs.

Work out the pressure on the floor under the legs. Give your answer in newtons/cm².

Hint

Work out the total area of the floor touched by the legs, or the force on one leg.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A table has 4 legs. The end of each leg has an area of 6 cm² in contact with the floor.

The table exerts a total force of 480 newtons on the floor. The force is shared equally between the 4 legs.

Work out the pressure on the floor under the legs. Give your answer in newtons/cm².

  1. Total area in contact with the floor =4\times6=24 cm².
  2. Pressure =480\div24=20 newtons/cm².
  3. (Or: the force on one leg is 480\div4=120 newtons, and 120\div6=20.)

Question 91 mark

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A box is standing on the floor. It is turned over onto a different face, so that the area in contact with the floor is twice as big.

The force exerted by the box stays the same.

What happens to the pressure on the floor?

Hint

The same force is now spread over twice as much area.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A box is standing on the floor. It is turned over onto a different face, so that the area in contact with the floor is twice as big.

The force exerted by the box stays the same.

What happens to the pressure on the floor?

  1. It is doubled
  2. It is halved
  3. It stays the same
  4. It goes up by 2 newtons/cm²
  1. Pressure = force ÷ area. The force stays the same and the area is multiplied by 2.
  2. Dividing by an area twice as big gives an answer half as big, so the pressure is halved.

Question 103 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

Box A exerts a force of 200 newtons on an area of 40 cm².

Box B exerts a force of 270 newtons on an area of 60 cm².

(a)

Which box exerts the greater pressure?

2 marks

(b)

How much greater is the greater pressure? Give your answer in newtons/cm².

1 mark

Hint

Work out the pressure for each box.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

Box A exerts a force of 200 newtons on an area of 40 cm².

Box B exerts a force of 270 newtons on an area of 60 cm².

Part (a)

Which box exerts the greater pressure?

  1. Box A
  2. Box B
  3. They are the same
  1. Box A: 200\div40=5 newtons/cm².
  2. Box B: 270\div60=4.5 newtons/cm².
  3. So Box A exerts the greater pressure, even though its force is smaller.

Part (b)

How much greater is the greater pressure? Give your answer in newtons/cm².

  1. 5-4.5=0.5 newtons/cm².

Question 113 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A metal block stands on the ground. It exerts a force of 600 newtons on the ground.

The pressure on the ground due to the block is 5 newtons/cm².

The face of the block touching the ground is a rectangle. One side of the rectangle is 10 cm long.

Work out the length of the other side of the rectangle.

Hint

Use the force and the pressure to find the area of the rectangle first.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A metal block stands on the ground. It exerts a force of 600 newtons on the ground.

The pressure on the ground due to the block is 5 newtons/cm².

The face of the block touching the ground is a rectangle. One side of the rectangle is 10 cm long.

Work out the length of the other side of the rectangle.

  1. Area = force ÷ pressure =600\div5=120 cm².
  2. Area of a rectangle = length × width, so the other side is 120\div10=12 cm.

Question 123 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A steel bar is in the shape of a prism. The bar is 30 cm long and its volume is 2400 cm³.

The bar stands upright on one of its ends on a table. It exerts a force of 200 newtons on the table.

Work out the pressure on the table due to the bar. Give your answer in newtons/cm².

Hint

Volume of a prism = area of its end × its length, so you can find the area of the end.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A steel bar is in the shape of a prism. The bar is 30 cm long and its volume is 2400 cm³.

The bar stands upright on one of its ends on a table. It exerts a force of 200 newtons on the table.

Work out the pressure on the table due to the bar. Give your answer in newtons/cm².

  1. Area of the end =2400\div30=80 cm². This is the area touching the table.
  2. Pressure =200\div80=2.5 newtons/cm².

Question 133 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

The diagram shows a solid cuboid. It measures 20 cm by 10 cm by 5 cm.

The cuboid exerts a force of 300 newtons on the table. It can be put down on the table on any of its faces.

(a)

On which face should the cuboid stand to give the greatest pressure on the table?

1 mark

(b)

Work out this greatest pressure. Give your answer in newtons/cm².

2 marks

Hint

The smaller the area in contact with the table, the greater the pressure.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

The diagram shows a solid cuboid. It measures 20 cm by 10 cm by 5 cm.

The cuboid exerts a force of 300 newtons on the table. It can be put down on the table on any of its faces.

Part (a)

On which face should the cuboid stand to give the greatest pressure on the table?

  1. The 20 cm by 10 cm face
  2. The 20 cm by 5 cm face
  3. The 10 cm by 5 cm face
  1. The force is always 300 newtons, so the greatest pressure comes from the smallest area.
  2. The faces have areas 20\times10=200 cm², 20\times5=100 cm² and 10\times5=50 cm².
  3. The smallest is the 10 cm by 5 cm face.

Part (b)

Work out this greatest pressure. Give your answer in newtons/cm².

  1. Pressure =300\div50=6 newtons/cm².

Question 143 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A box of books stands on the floor. The box exerts a force of 80 newtons on the floor.

The area of the box in contact with the floor is 2500 cm².

Work out the pressure on the floor due to the box. Give your answer in newtons/m².

Hint

Change the area into m² first: 1 m² =100\times100 cm².

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A box of books stands on the floor. The box exerts a force of 80 newtons on the floor.

The area of the box in contact with the floor is 2500 cm².

Work out the pressure on the floor due to the box. Give your answer in newtons/m².

  1. 1 m² =100\times100=10\,000 cm².
  2. So 2500 cm² =2500\div10\,000=0.25 m².
  3. Pressure =80\div0.25=320 newtons/m².

Question 153 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A crate stands on the floor. The base of the crate is a rectangle 0.8 m by 0.5 m.

The crate exerts a force of 350 newtons on the floor.

Some boxes are put on top of the crate. The boxes exert a force of 250 newtons on the crate.

Work out the pressure on the floor now. Give your answer in newtons/m².

Hint

The floor now has to hold up the crate and the boxes.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A crate stands on the floor. The base of the crate is a rectangle 0.8 m by 0.5 m.

The crate exerts a force of 350 newtons on the floor.

Some boxes are put on top of the crate. The boxes exert a force of 250 newtons on the crate.

Work out the pressure on the floor now. Give your answer in newtons/m².

  1. Total force on the floor =350+250=600 newtons.
  2. Area of the base =0.8\times0.5=0.4 m².
  3. Pressure =600\div0.4=1500 newtons/m².

Question 16Challenge3 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A machine stands on 4 equal feet. It exerts a total force of 1800 newtons on the floor, shared equally between the feet.

The pressure on the floor under each foot must be no more than 30 newtons/cm².

Work out the smallest possible area of each foot. Give your answer in cm².

Hint

Find the force on one foot, then the area that gives a pressure of exactly 30 newtons/cm².

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A machine stands on 4 equal feet. It exerts a total force of 1800 newtons on the floor, shared equally between the feet.

The pressure on the floor under each foot must be no more than 30 newtons/cm².

Work out the smallest possible area of each foot. Give your answer in cm².

  1. Force on each foot =1800\div4=450 newtons.
  2. Area = force ÷ pressure =450\div30=15 cm².
  3. A smaller area would make the pressure more than 30 newtons/cm², so the smallest area is 15 cm².

Question 17Challenge3 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A crate exerts a force of 600 newtons on the floor of a van. The area of the crate in contact with the floor is 1500 cm².

The crate is swapped for a bigger crate. The bigger crate exerts a force of 900 newtons on an area of 2500 cm².

Work out the percentage decrease in the pressure on the floor.

Hint

Work out the pressure due to each crate, then the decrease as a percentage of the first pressure.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A crate exerts a force of 600 newtons on the floor of a van. The area of the crate in contact with the floor is 1500 cm².

The crate is swapped for a bigger crate. The bigger crate exerts a force of 900 newtons on an area of 2500 cm².

Work out the percentage decrease in the pressure on the floor.

  1. Pressure due to the first crate =600\div1500=0.4 newtons/cm².
  2. Pressure due to the bigger crate =900\div2500=0.36 newtons/cm².
  3. Decrease =0.4-0.36=0.04 newtons/cm².
  4. Percentage decrease =\dfrac{0.04}{0.4}\times100=10\%.

Question 18Challenge4 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A solid steel cube stands on the ground.

The cube exerts a force of 640 newtons on the ground. The pressure on the ground due to the cube is 1.6 newtons/cm².

The five faces of the cube that are not touching the ground are going to be painted.

Work out the total area that is going to be painted. Give your answer in cm².

Hint

Find the area of the face touching the ground first. All the faces of a cube are the same size.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

A solid steel cube stands on the ground.

The cube exerts a force of 640 newtons on the ground. The pressure on the ground due to the cube is 1.6 newtons/cm².

The five faces of the cube that are not touching the ground are going to be painted.

Work out the total area that is going to be painted. Give your answer in cm².

  1. Area of the face touching the ground = force ÷ pressure =640\div1.6=400 cm².
  2. All 6 faces of a cube are the same size, and 5 of them are going to be painted.
  3. Area to be painted =5\times400=2000 cm².

Question 19Challenge4 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

An empty trolley exerts a force of 150 newtons on the floor. The total area of its wheels in contact with the floor is 50 cm².

The pressure on the floor under the wheels must not be more than 12 newtons/cm².

Boxes are put on the trolley. Each box exerts a force of 40 newtons.

Work out the greatest number of boxes that can be put on the trolley.

Hint

Find the greatest total force the floor can take, then how much of it is left for boxes.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

An empty trolley exerts a force of 150 newtons on the floor. The total area of its wheels in contact with the floor is 50 cm².

The pressure on the floor under the wheels must not be more than 12 newtons/cm².

Boxes are put on the trolley. Each box exerts a force of 40 newtons.

Work out the greatest number of boxes that can be put on the trolley.

  1. Greatest force = pressure × area =12\times50=600 newtons.
  2. Force left for boxes =600-150=450 newtons.
  3. 450\div40=11.25, so 11 boxes can go on, because 12 boxes would push the pressure over 12 newtons/cm².

Question 20Challenge4 marks

\text{pressure}=\dfrac{\text{force}}{\text{area}}

Two identical solid cubes each have edges of length 20 cm. Each cube exerts a force of 160 newtons.

(a)

The two cubes are put side by side on the floor. Work out the pressure on the floor due to the two cubes. Give your answer in newtons/cm².

2 marks

(b)

One cube is lifted and put on top of the other cube. Work out the pressure on the floor now. Give your answer in newtons/cm².

2 marks

Hint

The force on the floor is the total of both cubes. Think about how much floor is touched each time.

Worked solution

\text{pressure}=\dfrac{\text{force}}{\text{area}}

Two identical solid cubes each have edges of length 20 cm. Each cube exerts a force of 160 newtons.

Part (a)

The two cubes are put side by side on the floor. Work out the pressure on the floor due to the two cubes. Give your answer in newtons/cm².

  1. Area of one face =20\times20=400 cm², so the two cubes touch 2\times400=800 cm² of floor.
  2. Total force =2\times160=320 newtons.
  3. Pressure =320\div800=0.4 newtons/cm².

Part (b)

One cube is lifted and put on top of the other cube. Work out the pressure on the floor now. Give your answer in newtons/cm².

  1. The total force is still 320 newtons.
  2. Only one face touches the floor now: 400 cm².
  3. Pressure =320\div400=0.8 newtons/cm².

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