Newton's 1st and 2nd Law

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."

Resultant Force in a Straight Line:

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

  

  Resultant force to the right.

• Forces in the same direction: Add them together

  If a box has pushing right and pushing right

  

  Resultant force to the right.

• Forces are balanced when forces are equal and opposite

  If a box has pushing right and pushing left

  insert image

  Resultant force
  We say the forces are "balanced".

Resultant Force at Right Angles:

We know how to tackle forces in a line now, but to find the resultant of forces at right angle to each other, we require a new technique, known as tip-to-toe.

Example: two huskies are pulling a sledge, each with a force of .

Suddenly a squirrel runs in front of the sledge and distracts one of the dogs. One husky keeps pulling the sledge forwards with a force of , but the other starts running after the squirrel, pulling the sledge in that direction with a force of . Common sense tells us that the sledge will move to the left and upwards - half way between the way the two dogs are running - but we need to work out the size of the force.

To work out the resultant force on the sledge, we first need to draw them on a scale diagram. In this image below, the sledge is represented as a dot, and the arrows are each boxes long, so the scale would be .

We can now move the force arrows so that they are tip-to-toe - we need to make sure that we don't change the size or direction of the arrows, just their arrangement. In this example, the horizontal arrow is going to slide up, so the tip of the vertical arrow is now against the toe of the horizontal arrow.

Finally, we can draw a resultant force going from the bottom of the vertical arrow to the head of the horizontal arrow

The direction of the arrow tells us the direction of the resultant force (which can be measured with a protractor) and the length of the arrow would tell us the size of the force. In this example, the line is long, so in my scale of , the resultant force would be:

Newton’s Law tells us what happens when an object has no resultant force acting on it. It is very rare that an object has no forces acting on it, so this normally occurs when the forces on an object are balanced - 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

• Or keep moving at the same velocity (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: the resultant force on an object is directly proportional to the acceleration, and inversely proportional to the mass. This can be written as an equation.

Formula:

This equation tells us that if you double the force, you double the acceleration. For example, if you kick a football, it will accelerate away from you. If you kick it twice as hard, it will accelerate at twice the rate. It also tells us that the force and the acceleration are in the same direction - if resultant force and movement are in the same direction and object will speed up (accelerate), if the movement and aceleration are in different directions then the object will slow down (decelerate).

This equation also tells us that the acceleration is inversely proportional to the mass, . This means if you double the mass of an object and apply the same force, the rate of acceleration will halve. For example, a car filled with luggage and five people will accelerate at a slower rate than an empty car.

Example: a bicycle is carrying a person and all their camping kit, so it has a mass of . The thrust force on the bicycle is , and the resistive forces on the bicycle combine to .

If we wanted to calculate the acceleration of the bicycle, we could use Newton's Second Law - but first we need to calculate the resultant force on the bicycle:

Because this resultant force is in the same direction as the motion of the bicycle, then the it's velocity will increase (accelerate).

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. For example, an elephant has a much greater inertial mass than a mouse. If you kick a mouse, it will change velocity very quickly - if you kick an elephant - not so much!

Formula:

This is just rearranged.

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. We can find the size of these forces by drawing the diagram to scale and measuring the length.