# Understand Newton's Second law

In this worksheet, students will use the equation F = ma to understand Newton's Second law and apply that to objects.

Key stage:  KS 4

Curriculum topic:   Forces, Movement and Interactions, Explaining Motion, Motion and Forces, Forces and Motion

Difficulty level:

### QUESTION 1 of 10

Just a quick note - this is Newton's Second Law, and it will help if you have a good understanding of Newton's First Law before you start this. You might also want to refresh your understanding of acceleration.

Ever tried to push a car? It’s difficult, right? Why? Because the car is heavy, or because gravity is pulling the car down, or because you have the hand brake on? Only one of these affects how difficult it is to push the car in a straight line, and that is the hand brake. If you think about it, gravity is pulling the car down, so why would that make it difficult to push along?

Okay, so you release the hand brake and try again, but it is still difficult to push along. Much more difficult than pushing a table, and a table doesn’t even have wheels! Why? What makes pushing a car hard? This is what we are going to be looking at in this activity. We will be looking at Newton's Second Law, defining it, and then using it to explain some everyday situations (like trying to push a car…).

So here is Newton's Second Law: ‘The acceleration of an object is proportional to the force of an object’. This means that as the force goes up, so does the acceleration. This makes sense, right? If you lightly push a pen on the table, it won’t reach a very high top speed, but if you throw it with a lot of force, then it will reach a much higher top speed.

Newton also said that ‘The acceleration of an object is inversely proportional to the mass of an object’. This is where the magic happened. What he was saying was that as you increase the mass of an object,  you decrease the acceleration. So, a more massive object will accelerate slower than a less massive one. This is our car problem – because the car has a lot of mass, it accelerates a lot slower. Newton called this idea inertia -  it is the idea that the heavier the object, the more force is needed to accelerate it.

He went one step further though - he also made an equation with force, acceleration and mass in it:

F = ma

F = force (newtons (N))
m = mass (kilograms (kg))
a = acceleration (metres per second per second (m/s2))

So, let's look at an example together.

Question:  A person is attempting to push a car to get it to accelerate at 2 m/s2. The car has a mass of 900 kg. Calculate the force that will be needed by the person to achieve this acceleration.

Step 1    Highlight the numbers in the question:

A person is attempting to push a car to get it to accelerate at 2 m/s2The car has a mass of 900 kg. Calculate the force that will be needed by the person to achieve this acceleration.

Step 2    Write out the numbers:

F = ?
m = 900 kg
a = 2 m/s2

Step 3   Put them into the equation:

F = 900 x 2

Step 4    Write out your full answer:

F = 1800 N

Don't forget your units!

Are you ready to have a go at some questions now?

Match the symbols to their units below.

## Column B

Force (F)
Metres per second per second (m/s2)
Mass (m)
Newton (N)
Acceleration (a)
Kilogram (kg)

What is required to cause an acceleration?

Is force a scaler or a vector value?

Scaler

Vector

Newton's Second Law states that 'Acceleration is proportional to the ...'

Finish the sentence.

Scaler

Vector

Newton's Second Law states 'Acceleration is inversely proportional to...'

Complete the sentence.

Acceleration

Mass

Force

Heat

An object with a mass of 60 kg is accelerated at 0.5 m/s2.

Calculate the force that the object was accelerated with.

Acceleration

Mass

Force

Heat

An F1 car has an acceleration of 25 m/s2 and a minimum mass of 740 kg.

Calculate the force provided by the engine of the F1 car.

Acceleration

Mass

Force

Heat

When jumping out of a plane, you will reach a top speed on your descent.

Choose the correct name for that top speed from the list below.

Starting velocity

Ending velocity

Incredible velocity

Terminal velocity

When falling out of a plane, you will initially accelerate at 9.8 m/s2. The average person has a mass of 60 kg.

Calculate the force that the Earth is applying to that person in order to get them to accelerate at 9.8 m/s2.

Starting velocity

Ending velocity

Incredible velocity

Terminal velocity

In your own words, explain what Newton's Second Law is.

[2]

• Question 1

Match the symbols to their units below.

## Column B

Force (F)
Newton (N)
Mass (m)
Kilogram (kg)
Acceleration (a)
Metres per second per second (m/s...
EDDIE SAYS
How did you do? As always, knowing the units will help you to spot the correct numbers in the question which will, in turn, make it easier for you to solve the equation. It is also handy if it comes to actually putting the units into the equation! It will make everything so much easier if you just know them!
• Question 2

What is required to cause an acceleration?

Force
A force
EDDIE SAYS
Think about a teddy and how it can help to show you what a force is! If you hit it, then it will move, but if you leave it alone, then it will stay where it is. It needs a force to act upon it before it is able to accelerate in any direction - the same is true of all objects, they all need a force to act on them before they are able to move.
• Question 3

Is force a scaler or a vector value?

Vector
EDDIE SAYS
Now don't get depressed if you didn't have a clue what this question was asking! This is something that you might not have learned about yet or have long since forgotten about - but it is important to understand the differences between these two when looking at forces. So what do they mean? Scaler means a quantity with a size but no direction eg. speed, distance, mass, temperature or time. A vector means a quantity that has a size but also has a direction eg. velocity, acceleration or force. Force needs a direction and so it is a vector value. Does that make sense now?
• Question 4

Newton's Second Law states that 'Acceleration is proportional to the ...'

Finish the sentence.

EDDIE SAYS
Did that just roll of the tongue easily for you or did you have to look it up in the Introduction?! It is very important to know this law so make sure you spend some time getting it fixed in your head. Acceleration is proportional to the force of an object. If you hit your poor old teddy with more force, it is going to go further. If you hit it with less force then it won't go as far. Remember - proportional means as one thing goes up, then the other thing goes up as well.
• Question 5

Newton's Second Law states 'Acceleration is inversely proportional to...'

Complete the sentence.

Mass
EDDIE SAYS
This time, we are looking for something that will go down when the acceleration goes up. If you think about the car example, the less mass the car has, the easier it is to accelerate (that's why F1 cars are so light). This means that the lower the mass, the easier an object is to accelerate! This is another really important law to learn - as well as to understand!
• Question 6

An object with a mass of 60 kg is accelerated at 0.5 m/s2.

Calculate the force that the object was accelerated with.

EDDIE SAYS
This question is simple if you can remember the equation: F = ma F = ? m = 60 kg a = 0.5 m/s2 F = 60 x 0.5 F = 30 N
• Question 7

An F1 car has an acceleration of 25 m/s2 and a minimum mass of 740 kg.

Calculate the force provided by the engine of the F1 car.

EDDIE SAYS
Again a simple one if you can remember the equation: F = ma F = ? m = 740 kg a = 25 m/s2 F = 740 x 25 F = 18,500 N Done!
• Question 8

When jumping out of a plane, you will reach a top speed on your descent.

Choose the correct name for that top speed from the list below.

Terminal velocity
EDDIE SAYS
Think about the word terminal - you might have heard it before, maybe as a terminal at an airport or a bus terminal. The word terminal tends to be around where things stop. You might also have heard of people suffering from a terminal illness which means that they will not recover - it will lead to the end of their lives. So, terminal velocity is to do with the end of something. It is where the velocity will stop accelerating - it has reached its terminal. This is why we call it terminal velocity.
• Question 9

When falling out of a plane, you will initially accelerate at 9.8 m/s2. The average person has a mass of 60 kg.

Calculate the force that the Earth is applying to that person in order to get them to accelerate at 9.8 m/s2.

EDDIE SAYS
This looked like a complicated question, but it was actually just asking you about the force of gravity pulling the person towards the Earth. Again, not too tricky if you know the equation. F = ma F = ? m = 60 kg a = 9.8 m/s2 F = 60 x 9.8 F = 588 N
• Question 10

In your own words, explain what Newton's Second Law is.

[2]

EDDIE SAYS
You should now have a bit of an understanding of what Newton's Second Law is. Start by writing the equation and then explain what it means in your own words. That equation is vital! You've completed another activity. Hopefully, you are more confident with using this equation now.
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