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Understand Forces and Elasticity

In this worksheet, students will learn Hooke's law applying the equation and graph. This worksheet will not cover the practical, but there is a related worksheet on the practical called 'Investigating Forces'

Worksheet Overview

QUESTION 1 of 10

Standing on a bridge with a river running underneath, the person to your left asks you to step off the scales and puts some numbers into a computer. They look at you and smile as they ask you ‘How much do you want to go into the water?’ You look scared, adrenaline running through your body as you say, ‘About up to my waist?’. They play with some numbers on the screen and then ask you if you are ready. You slowly nod and they start a countdown ‘3, 2, 1’. With a slight hop, you are in the air, plummeting towards the water headfirst – it feels like forever, but in only a few seconds, you feel the bungee cord pulling at your legs, slowing you down as your body dips into the water up to your waist and you get pulled back up. Bungee jump, done! It takes a lot of maths to be an expert thrill seeker -  you need to know where the limits are, so you don’t die. In this activity, we'll be looking at some of the science that allows us to perform bungee jumps – Hooke’s law and elastic forces. 

 

A bungee cord is basically a big rubber band, and it might help some of this to sink in if you have a rubber band to play with while you read this. If you apply just one force to a rubber band then it won't stretch, it will just move in the direction the force is applied. You need a minimum of two forces that will act in different directions to stretch anything. One of these forces could be stationary, such as your finger, and one could be moving, like your hand pulling the band backwards. This will apply a force to the band and make it stretch. If you release the forces,  the band will return to its original shape. All good so far? 

 

Okay, so Hooke’s law is a law that defines stretching things. It says that ‘the force applied to an object is proportional to the length of the extension’. This basically means that if you were to plot force and extension on a graph, it would make a straight line.

 

Hooke realized that he could make an equation out of this graph that could tell him, in any given circumstance, what the extension of an object would be. 

 

F = force (newtons (N))
k = spring constant – a number that tells you how hard it is to stretch the object (newtons per metre (N/m))
x = extension – how much the spring has stretched (metres (m)) This is often also written as e for extension and this is what we will be using in this activity.

 

So, the person putting the numbers into the computer at the start of the activity was just working out how much you would stretch the bungee, using this equation. 

Let’s have a go at this ourselves. 

 

Question:  A person stretches the bungee 15 m when the bungee cord has a spring constant of 40 N/m. Calculate the force applied by that person. 

 

Step 1   Highlight the numbers in the question:


A person stretches the bungee 15 m when the bungee cord has a spring constant of 40 N/m. Calculate the force applied by that person. 

 

Step 2   Write out the numbers:
F = ?
k = 40 N/m
e = 15 m

 

Step 3 Put the numbers into the equation:

F = 40 x 15

 

Step 4   Do the calculation and write out your answer:

F = 600 N

 

Don’t forget your units! 

 

Let's have a go at some questions now.

In order to squash a lump of plasticine, what is the minimum number of forces required? 

1

2

3

4

Write down the equation that links force, spring constant, and extension. 

 

[1]

Match the symbols to their values.

Column A

Column B

Force (F)
Newtons (N)
Spring Constant (k)
Newtons per metre (N/m)
Extension (e or x)
Metres (m)

Brooke stretches a rubber band. When she lets go, it returns to its original shape. Paul does the same with a lump of plasticine, but it does not return to its original shape.

 

Using the grid below, say which was elastic and which was an inelastic deformation. 

 Rubber bandplasticine
Elastic deformation
Inelastic deformation.

A spring has a spring constant of 50 N/m and is stretched 0.75 m.

 

Calculate the force on the spring.

 Rubber bandplasticine
Elastic deformation
Inelastic deformation.

An elastic band has a spring constant of 1000 N/m and an original length of 0.25 m. When it is loaded with mass, the length increases to 0.45 m.

 

Calculate the force added to the spring to cause this extension. 

 Rubber bandplasticine
Elastic deformation
Inelastic deformation.

The chart below shows extension and force data collected by a student.

 

Using the data, explain whether or not the object they were using followed Hooke's Law.  

 

[3]

 

Force (N) Extension (m)
100 0.2
200 0.4
300 0.6
400 0.8
500 1.0
600 1.2
700 1.3

 

In the previous question, the values started to change at the end.

 

Suggest what is happening to the spring at this point. 

 

[1]

 

Force (N) Extension (m)
100 0.2
200 0.4
300 0.6
400 0.8
500 1.0
600 1.2
700 1.3

 

Tom has a crossbow that is able to fire bolts. He wants to work out the force with which he can fire the bolts. On the box, it says that the bow at the front of the crossbow has a spring constant of 3 kN/m. He measures the draw distance of the crossbow as 0.5 m.

 

Calculate the force on the bolt. 

A spring in a car suspension is compressed when it goes over a bump in the ground. The spring has an original length of 0.75 m, but when it hits a bump, it compresses to a length of 0.65 m. The car is quoted as having a spring constant value of 5000 N/m.

 

Calculate the force of the car going over the bump.

  • Question 1

In order to squash a lump of plasticine, what is the minimum number of forces required? 

CORRECT ANSWER
2
EDDIE SAYS
You need to have at least two forces acting on an object in order to make it change its shape in any way - either squashing or stretching. If you want to squash it, you need a force pushing it one way and another force pushing it in the opposite direction. If you want to stretch an object, then you need two forces pulling in opposite directions. You could have more than two forces pushing or stretching in a variety of directions but the minimum number will be two.
  • Question 2

Write down the equation that links force, spring constant, and extension. 

 

[1]

CORRECT ANSWER
EDDIE SAYS
These are common questions in exams - they want to know that you can remember the equations, so get your remembering hat on! If you found it hard to remember this one, try writing it down several times in different colours so that you can picture it clearly in your mind.
  • Question 3

Match the symbols to their values.

CORRECT ANSWER

Column A

Column B

Force (F)
Newtons (N)
Spring Constant (k)
Newtons per metre (N/m)
Extension (e or x)
Metres (m)
EDDIE SAYS
Hopefully by now you are getting the hang of why we are doing these types of questions. It helps you to spot them when it comes to picking out the numbers in a maths type question. In this case, remember the capital N for newtons.
  • Question 4

Brooke stretches a rubber band. When she lets go, it returns to its original shape. Paul does the same with a lump of plasticine, but it does not return to its original shape.

 

Using the grid below, say which was elastic and which was an inelastic deformation. 

CORRECT ANSWER
 Rubber bandplasticine
Elastic deformation
Inelastic deformation.
EDDIE SAYS
Don't be put off by the use of unfamiliar words such as 'deformation'. It simply means to change form or shape. An easy way to remember which is which is to think about another name for a rubber band - elastic band. If something is elastic, then it will return to its original shape, just like an elastic band. If something is not elastic, then it will not return to its original shape - it is inelastic. This is the difference between elastic and inelastic deformation. Does that make sense?
  • Question 5

A spring has a spring constant of 50 N/m and is stretched 0.75 m.

 

Calculate the force on the spring.

CORRECT ANSWER
EDDIE SAYS
This is a simple find the numbers and plug them into the equation job! Let's go through the steps of the question together. Step 1 Find the numbers and put them next to their symbols: F = ? k = 50 N/m e = 0.75 m Step 2 Put them into the equation: F = 50 x 0.75 Step 3 Do the calculation: F = 37.5 N Don't forget to include the unit!
  • Question 6

An elastic band has a spring constant of 1000 N/m and an original length of 0.25 m. When it is loaded with mass, the length increases to 0.45 m.

 

Calculate the force added to the spring to cause this extension. 

CORRECT ANSWER
EDDIE SAYS
This one is a little more tricky because you need to do something to the length first! For this one, we need to think about the extension of the elastic band in a little more detail. A common mistake you might make is to calculate this with the length being 0.45 m, but it isn't. Let's take a look: The extension is how much the elastic band has stretched when the mass is put on it. It is originally 0.25 m long, but when it is stretched it becomes 0.45 m long. How far has it stretched ? Well 0.45 - 0.25 = 0.2, so it has stretched 0.2 m. Let's go through the steps together: Step 1 Find the numbers and write them down: F = ? k = 1000 N/m e = 0.45 - 0.25 = 0.2 m Step 2 Put the numbers into the equation: F = 1000 x 0.2 Step 3 Do the maths: F = 200 N And you're there!
  • Question 7

The chart below shows extension and force data collected by a student.

 

Using the data, explain whether or not the object they were using followed Hooke's Law.  

 

[3]

 

Force (N) Extension (m)
100 0.2
200 0.4
300 0.6
400 0.8
500 1.0
600 1.2
700 1.3

 

CORRECT ANSWER
EDDIE SAYS
For this question, you have a lot of information to take in and process - that is why it is a three mark question. Let's break it down into parts: 1 It is asking you if you can remember what Hooke's Law says. It says that a graph of extension vs force will be a straight line. This is true in this case because the numbers on the left go up by 100 each time and the numbers on the right go up by 0.2 each time. 2 It is asking you if you can use data. Can you spot the pattern in the data? Did you see that the numbers went up by 0.2 each time in the extension? This is what they are really asking you about here. It's just a case of breaking the question down and looking for what they really want you to answer.
  • Question 8

In the previous question, the values started to change at the end.

 

Suggest what is happening to the spring at this point. 

 

[1]

 

Force (N) Extension (m)
100 0.2
200 0.4
300 0.6
400 0.8
500 1.0
600 1.2
700 1.3

 

CORRECT ANSWER
EDDIE SAYS
The word suggest means you need to think of your own answer that you haven't been taught - this type of question is bound to come up in your exam at some point. In this question, you needed to think about what would happen to an elastic band or a spring if you put a whole load of force onto it. It should get to a point where it will not be able to stretch any more. This is why it is good to play with elastic bands - you will get to know where that point is. Play away - you have our permission!
  • Question 9

Tom has a crossbow that is able to fire bolts. He wants to work out the force with which he can fire the bolts. On the box, it says that the bow at the front of the crossbow has a spring constant of 3 kN/m. He measures the draw distance of the crossbow as 0.5 m.

 

Calculate the force on the bolt. 

CORRECT ANSWER
EDDIE SAYS
In this question, there is one key thing that makes it harder than the others - kN/m. Did that trip you up? It means that you need to convert from kilo newtons into newtons. 3 kN/m = 3000 N/m. Apart from that, the process is the same: F = ? k = 3000 N/m e = 0.5 F = 3000 x 0.5 F = 1500 N Did you remember the unit!
  • Question 10

A spring in a car suspension is compressed when it goes over a bump in the ground. The spring has an original length of 0.75 m, but when it hits a bump, it compresses to a length of 0.65 m. The car is quoted as having a spring constant value of 5000 N/m.

 

Calculate the force of the car going over the bump.

CORRECT ANSWER
500 N
500
EDDIE SAYS
This is a fairly simple question, with one exception, it has given you a starting length and a finishing length instead of an extension. It is also a compression instead of an extension, but this makes no difference to our maths. Step 1 Calculate the extension: e = 0.65 - 0.75 = - 0.1 This is a negative number because it is a compression rather than an extension but the difference is still 0.1 which is the number we put in for the extension. Step 2 Write down the numbers: F = ? k = 5000 N/m e = 0.1 m Step 3 Put them into the equation. F = 5000 x 0.1 F = 500 N Another activity completed! Hopefully, you are feeling really confident with stretching springs and elastic bands now.
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