Force and Newton’s Laws

P2.2-1 Force

Force: is either a pull or a push applied on an object by another object, and has a unit of newtons (N). And there are 2 types: contact forces and non-contact forces.

Force diagrams: 

Note: when drawing force diagrams, the size of the arrow shows the magnitude of the force, and direction should be correct too! (Forces are vectors after all!)

Free Body Diagram: Just draw the forces and ignore the shape of the object.

P2.2-1-1 Resultant force

Resultant force: or the net force, is a single force that is equivalent to all forces applied on an object.

The apple is hanging from the tree. It means it is stationary. It means tension in the stalk is equal to the weight and as it is in opposite direction the resultant force is zero!

The net force on the car is 500 N to the left à the car is accelerating to the left.

If the thrust decreases to 1000 N, the resultant force = zero à the car is moving with a constant velocity! 

P2.2e (Higher Tier)

P2.2-1-2 Scale Diagrams

Find resultant of two perpendicular forces:

1. Draw the free body diagram and choose a scale: e.g. 1 cm = 1 N
2. After drawing the first force, start the second one, at the end point of the first one
3. Connect beginning of the first to end of the last, this is the resultant force!
4. Measure the length (magnitude) of the force with a ruler, and the angle that it makes with the horizontal (Θ), with a protractor.

Resolving a force into two perpendicular components:

Now we have a force and want to see what two perpendicular forces would add up to give the first one:

1. Draw the force starting from the origin of x-y axes with a proper scale e.g. 10 N = 1cm;
2. From the end point of the vector draw perpendicular lines to x and y axis (as if you were trying to find the x and y coordinates of end point of the vector);
3. Draw vectors from the origin to the points on x and y from the previous step (F_x and F_y);

Example: find the two perpendicular components of a force of 50 N which makes an angle of 30^o to the horizontal:

P2.2-2 Newton’s First Law

Newton’s first law: if the resultant force on an object is zero:

1. The object is moving with constant velocity;

or

2. It is stationary. 

Note we say constant velocity, not speed! Constant velocity means constant speed plus no change in direction! As velocity is a vector (refer to P2.1d and P2.1h). 

Circular motion (Higher Tier):

The resultant force on an object moving in a circular path with constant speed, is not zero! There is always a force on this object towards the centre of the circle. Hence the velocity is not constant and the object is accelerating.

Terminal velocity (Higher Tier):

There are two forces applied on a falling object: weight and drag. Drag depends on the speed, and as the object falls, speed increases so does the drag. There will be a point where drag will get equal to the weight of the object, hence resultant force will be zero and the object will stop accelerating downwards and it will continue with a constant velocity, which we call the terminal velocity!

P2.2-3 Newton’s 2^nd Law

Which means if the resultant force is not zero, the object accelerates, and the rate of acceleration depends on the mass.

P2.2-3-1 Inertia (Higher Tier)

Inertia: natural reluctance of objects to change velocity. 

Inertial mass: In our universe, the value of inertial mass is the same as gravitational mass (the mass that you always worked with!). But they are different concepts. 

Force of gravity between two objects exists, because they have mass! This is the gravitational mass! But inertial mass tells you how reluctant an object is to change velocity.

P2.2-3-2 Momentum  (Higher Tier)

Momentum is mass times velocity, and it is a vector.

Change in momentum:

If momentum changes, assuming mass does not change, it means velocity has changed. Change in velocity means acceleration, and that means resultant force on the object is not zero! (Newton’s 2^nd Law):

If we increase time of collision, the force applied on objects involved in the collision decreases! All safety features in car intend to do this! 

Crumple zones: increase the time from the first impact and car stopping;

Seat belts stretch a little and increase the time the passenger’s momentum change;

Airbags both increase the time passengers head stops and protects the head against hitting the steering wheel.

Example 1:

A car moving at a speed of 12 m/s and mass of 800 kg hits a wall and comes to a stop. If the force of impact on the car is 3200 N, find the time it takes for the car to stop after hitting the wall.

Note: Force, velocity, and momentum are all vectors and their negative sign means they are in the reverse direction that we have assumed positive. In the question above we assume positive direction to the right. So u is positive and force applied on the car (F) is negative. 

Principal of conservation of momentum

The total momentum before a collision is equal to the total momentum after the collision. 

Example 2:

A toy car of mass 2 kg moving at 8 m/s collides with a stationary toy car of mass 6kg. Both objects move together after the collision. Determine their velocity after the collision.

Example 3: 

A cricket ball of mass 0.15 kg has a velocity of 30 m/s before hitting a bat and leaves the bat with the same speed but in the reverse direction. If the ball is in touch with the bat for 0.3 s, find the force applied on the ball by the bat.