Understanding your Exam
Understanding your Calculator
Newton's 1st and 2nd Law
Brook Edgar & Hannah Shuter
Teachers
Contents
Explainer Video
Resultant Force
Before we dive into Newton's Laws, we need to understand what happens when multiple forces act on an object. In real life, objects rarely have just one force acting on them - there are usually several forces at once.
The resultant force is the single force that has the same effect as all the individual forces acting together. It's sometimes called the "net force."
Calculating Resultant Force:
When forces act in a straight line (along the same direction), we can add and subtract them to find the resultant force.
Forces in opposite directions: Subtract the smaller from the larger
If a box has pushing right and pushing left
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Resultant force to the right.
Forces in the same direction: Add them together
If a box has pushing right and pushing right
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Resultant force to the right.
Forces are balanced when forces are equal and opposite
If a box has pushing right and pushing left
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Resultant force
We say the forces are "balanced".
Remember: Force is a vector quantity, so the direction of the forces on an object influence whether they need to be added or subtracted.
No answer provided.
Worked Example:
A boat moves through the ocean. There is a force on the boat West, and a force towards South.
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Find the magnitude of the resultant force on the boat using a vector diagram to scale and counting the squares.
The force towards South increases. What affect does this have on the resultant force on the boat?
Answer:
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The resultant force becomes larger. Additionally, the resultant force now tilts more towards the south, as there is a larger component in that direction.
Newton's First and Second Laws
There are 3 Laws of Motion. Here we look at Newton's and Laws of Motion.
Newton’s Law tells us what happens when forces are balanced on an object. When we say forces are "balanced," we mean the resultant force is zero - all the forces acting on an object cancel each other out completely.
Newton’s Law states: If the forces on an object are balanced, the object will either:
Remain at rest (this means it is stationary or not moving).
Or keep moving at the same speed (if it was already moving).
Newton's Law tells us what happens when forces are unbalanced -> when there is a resultant force acting on an object.
Newton’s Law states: If there is a resultant force acting on an object, the object will change its velocity. It will either:
Accelerate (speed up).
Decelerate (slow down).
Formula:
This equation tells us that acceleration is directly proportional to the resultant force, (double the force, double the acceleration). For example, if you apply the same amount of force required to push a bike on a lorry, the lorry won't move.
Acceleration is inversely proportional to the mass, (double the mass, half the acceleration for the same force). For example, a car carrying double the mass (filled with luggage) will accelerate less than an empty car.
Inertia
Inertia is a measure of how difficult it is to change the velocity of an object.
The greater the inertial mass, the harder it is to accelerate or decelerate the object.
Formula:
This is just rearranged.
Worked Example:
The car was initially stationary, is the car now…
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Stationary
Moving at a constant speed.
Speeding up (Accelerating)
Slowing down (Decelerating).
Answer:
The forces on the care are balanced, so it remains stationary.
Worked Example:
Describe what happens to each box. All are initially stationary.
(insert image b)
Answer:
Remains stationary at as there are no forces acting on the box.
Resultant Force . Resultant force is , so box B remains stationary -> Newton’s Law.
Resultant Force . Resultant Force is to the left, so the box will accelerate to the left.
Teacher Tip: Use these key words and phrases when answering questions; Stationary, Resultant Force, Constant Velocity, Accelerate, Decelerate.
Worked Example:
Explain what happens to each box. These boxes are initially moving to the right at .
(insert image c)
Answer:
No forces acting on the box, so it continues with a constant speed of .
Resultant Force , so box continues at a constant speed of .
Resultant Force to the right, so the box accelerates to the right.
Resultant Force to the left. Box accelerates to the left.
Worked Example:
(insert image f)
The swimmer is moving forward at a constant speed. If Force A is , state the size of Force B.
As Force A increases to , the swimmer accelerates. Calculate the resultant force on the swimmer.
The resultant force eventually decreases to zero even though the swimmer keeps Force A at . Explain why.
Answer:
Resultant force must be for the swimmer to be moving at a constant speed, so force B is .
Drag eventually balances the driving force, reducing the resultant force to .
Resolving Forces
Sometimes forces don't act purely horizontally or vertically - they act at an angle. We need to break these forces down into horizontal and vertical components. This process is called resolving forces. Any single force acting at an angle can be split into:
A horizontal component (parallel to the ground)
A vertical component (perpendicular to the ground)
These two components together have the same effect as the original single force.
Image suggestion: A force arrow at an angle with dotted lines showing horizontal and vertical components forming a right-angled triangle, with labels for "original force," "horizontal component," and "vertical component"
Worked Example:
If the resultant force on the box is in the direction shown below, in what directions are the horizontal and vertical components of the resultant force?
(insert image d)
Answer:
Resultant force in the North-East or top-right direction.
Vertical component must be upwards and the horizontal component to the right.
Worked Example:
Use the vector diagram below to determine the size of the vertical component of the resultant force.
Scale:
(insert image e)
Answer:
Practice Questions
A car travels along a straight road at a constant speed of .
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State the resultant force acting on the car and explain your answer.
-> Check out Brook's video explanation for more help.
Answer:
The car is moving at a constant speed in a straight line, so resultant force is .
A small vehicle of mass accelerates when a horizontal force is applied.
A resultant force of acts on the vehicle. Calculate its acceleration.
The same force is applied to a second vehicle of mass . Explain how its acceleration compares to the first vehicle.
-> Check out Brook's video explanation for more help.
Answer:
The acceleration is smaller. Because for the same force, acceleration decreases when mass increases.
Common Errors & Exam Tips
Students sometimes forget to convert grams to kilograms in calculations.
Students sometimes forget the units for acceleration ().
Remember to acknowledge and state the direction of forces.
Remember that according to Newton's 1st Law, balanced forces → no acceleration.