Newton's 1st and 2nd Law

When several forces act at once on an object we need to simplify them to work out what is going to happen to the object. We do this by working out the resultant force on an object. The resultant force is the single force that has the same effect as all the individual forces acting together. It can be thought of as the "overall" force on an object or the difference between the forces.

Forces in Straight Lines:

When forces act in a straight line (along the same direction/parallel), we can add or subtract them, depending on their direction, to find the resultant force.

When forces act in opposite directions, as shown below, we subtract them,

The resultant force to the right.

There is a bigger force of pulling the box to the right.

When forces are acting in the same direction, we add them as they are both pulling the box in the same direction,

The resultant force to the right.

We say the forces are balanced when the forces are of equal size but in opposite directions.

The box below has a force of pushing it to the right and a force of pushing it to the left,

Resultant force

Forces at Right Angles:

To find the resultant force of two forces acting at right angles to each other, we cannot just simply add or subtract them, as horizontal and vertical directions are completely independent.

For example, if two huskies are pulling a sledge, each with a force of as shown below, the resultant force would be fowards on the sledge,

But if, suddenly, a squirrel ran out in front of the sledge and distracted one of the dogs, causing it to start pulling the sledge upwards, in the same direction the squirrel ran, the two forces are no longer in a straight line but act at right angles to each other. We know from everyday life that the sledge will start moving diagonally, to the left and upward, halfway between the two dogs' paths, but we now need to be able to calculate this resultant force.

To work out the resultant force on the sledge, we first need to draw a scale diagram, as shown below. The sledge is represented as a dot (as we are not in art class), and using a scale of we draw two lines at right angles to each other each long.
.

However, we cannot add vectors unless they are tip-to-toe (remember forces are vectors). We need to move one of the arrows to do this, but we need to ensure that we don't change the size or direction of the arrows, just their arrangement. In this example, we are going to move the horizontal arrow up, so the tip of the vertical arrow is now against the toe of the horizontal arrow as shown below,

We now draw the resultant force on the diagram, going from the bottom (toe) of the vertical arrow to the head (tip) of the horizontal arrow, to complete the shape.

The direction of the arrow tells us the direction of the resultant force (the angle can be measured with a protractor), and the length of the arrow tells us the size of the force. To calculate the size of this force we need to use a ruler to measure its length and our scale again,

The line is long, so using our earlier scale of , the resultant force would be, .

Newton’s Law tells us what happens when an object has no resultant force acting on it -when the forces on an object are balanced.

Newton’s Law states that if there is no resultant force acting on an object, it will either:

• Remain at rest

• Or keep moving at the same velocity if it was already moving

If a book is at rest on a table, the resultant forces on it are zero (weight = normal contact force), so it will remain at rest. If a car is moving at a constant speed, and the forces on it are balanced (thrust from the engine = friction), the car will continue to move at a constant speed.

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 that the resultant force on an object is directly proportional to its acceleration and inversely proportional to its mass.

Formula:

Example: A bicycle, person and all their camping kit has a mass of . The foward force on the bicycle from their legs is , and the resistive forces on the bicycle due to friction and air resistance combine to .

To calculate the acceleration of the bicycle, we use Newton's Second Law.

As acceleration is inversely proportional to the mass, , if you double the mass of an object but apply the same force, the rate of acceleration will halve. For example, a car filled with luggage will accelerate more slowly than an empty car. This can be referred to as inertial mass: a larger mass requires more force to achieve the same acceleration.

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 their horizontal and vertical components. This process is called resolving forces.

The horizontal and vertical components are found by drawing a triangle around the resultant force, as shown below,

We then use scale diagrams to determine the magnitude of these forces as we did before.