Question 1
LEVEL 4
A force of 156 N is being applied to a rectangle with sides of length 5 cm and 6 cm.
Calculate the pressure on the rectangle.
Select the correct answer from the list below:
A: 31.2 N/cm^2
B: 5.2 N/cm^2
C: 26 N/cm^2
D: 4680 N/cm^2
CORRECT ANSWER: B: 5.2 N/cm^2
WORKED SOLUTION:
We are looking for pressure, and we can see that by covering up p in the triangle above we need to divide F by A to get what we want. Before we can do this calculation however, we need to work out the area of the rectangle:
\text{Area of Rectangle }=\text{ length }\times\text{ width }=5\times6=30 cm^2
Now that we have the area, we can work out the pressure.
\text{Pressure }=\dfrac{F}{A}=\dfrac{156}{30}=5.2 N/cm^2
Question 2
LEVEL 4
A cube is resting on the ground.
The cube is pressing into the ground with a force of 213 N.
The pressure on the face of the cube touching the ground is 27 N/m^2.
Select the correct answer from the list below:
A: 22.2 m^3
B: 2.81 m
C: 45.1 m^3
D: 13.2 m^2
CORRECT ANSWER: A: 22.2 m^3
WORKED SOLUTION:
To find the volume of a cube we have to know how long each side is, but we don’t know this. However, we can find the side lengths from the area, which we can find from pressure and force.
We are looking for area, and we can see that by covering up A in the triangle above, we need to divide F by p to get what we want.
\text{Area }=\dfrac{F}{p}=\dfrac{213}{27}=7.89 m^2 (3sf)
Note: The units here will be m^2 because the N in force and pressure cancel each other.
Now that we know the area of the face touching the ground, we just need to square root this (because it is a square) to find the side length.
\text{side length }=\sqrt{7.89}=2.81 m (3sf)
And finally, to find the volume, all we need to do is cube this.
\text{volume }=2.81^3=22.2 m^3 (3sf)
Question 3
LEVEL 4
As a cyclist travels along the road and they are pushing into the ground with a force of 745.3 N.
Given that the pressure applied to the tyres is 124 N/cm^2, find the total surface area of the tyres that is in contact with the ground.
Select the correct answer from the list below:
A: 92400 cm^2
B: 7.24 cm^2
C: 0.166 cm^2
D: 6.01 cm^2
CORRECT ANSWER: D: 6.01 cm^2
WORKED SOLUTION:
We are looking for area, and we can see that by covering up A in the triangle above, we need to divide F by p to get what we want.
\text{Area }=\dfrac{745.3}{124}=6.01 cm^2 (3sf)
Note: The units here will be cm^2 because the N in force and pressure cancel each other.
Question 4
LEVEL 4
The pressure required to break a particular brand of glass is 30 N/inch^2.
A hammer with a circular head of radius 1 inch is being used to test the glass.
Work out the minimum force that should be required to break the glass with the hammer.
Select the correct answer from the list below:
A: 30 N
B: 9.55 N
C: 0.0333 N
D: 94.2 N
CORRECT ANSWER: D: 94.2 N
WORKED SOLUTION:
We are looking for force, and we can see that by covering up F in the triangle above, we need to multiply p and A. We don’t yet have the area, but we can find the area by using the formula to find the area of a circle.
\text{Area }=\pi\times r^2=\pi\times1^2=\pi\times1=\pi=3.14 N/inch^2 (3sf)
Now, to find the require force, we just need to multiply our pressure and area.
\text{Force }=p \times A=30\times 3.14=94.2 N
Note: The units here will be N because the inch^2 in pressure and area cancel each other.
Question 5
A table stands on four square based legs, with the weight evenly distributed over each leg.
Given that the table is pushing into the floor with a force of 112.8 N and the total pressure applied to the legs is 5 N/cm^2.
Select the correct answer from the list below:
A: 5.65 cm^2
B: 564 cm^2
C: 22.6 cm^2
D: 90.4 cm^2
CORRECT ANSWER: A: 5.65 cm^2
WORKED SOLUTION:
We are looking for area, and we can see that by covering up A in the triangle above, we need to divide F by p to get what we want.
\text{Area }=\dfrac{112.8}{5}=22.6 cm^2 (3sf)
Note: The units here will be cm^2 because the N in force and pressure cancel each other.
Now, this is going to give us the total area of the leg bases, but we only want one, so we need to divide this by 4.
\text{Area }=22.6\div4=5.65 cm^2 (3sf)