Newtons 3rd Law

Lets look at a scenario where a car is towing a caravan.  The car weighs 1500 kg and the caravan weighs 1000 kg.  If the car exerts a force of 7500 N, we would expect according to Newton's 2nd Law (F=ma) that the 2 objects will move off at 3 m/s/s.

However, only the car is providing the force for the forward motion, not the van.  Since the car only weighs 1500 kg, why doesn't it move off at 5 m/s/s ?

This is where Newton's 3rd law comes into play.  Simply stated, it is:

For every action there is an equal on opposite reaction.

Firstly we look at the combined system.  Using Newtons 2nd Law we calculate this correctly.

BUT.....

1. When we look at the 2 parts of this system individually, we can say that the  car has a force of 7500 N exerted by the engine to the right which will drive it forward.
2. If the caravan is accelerating at 3 m/s/s, it must have a force of 3000 N being exerted on that.

If we then apply Newtons 3rd law, the caravan must be exerting a force equal and opposite to the car (that is 3000 N from right to left, equal and opposite to the direction of the motion), the net force is now

7500 N - 3000 N = 4500 N

So when we apply this quantity of force with the mass of the car, you can now see that the acceleration of the car will be 3 m/s/s.

Just goes to show how brilliant Newton was.





Newton's 3rd law applies not only to pulling but pushing forces as well.  So if we were pushing a red Ferrari with our own red Ferrari, the car being pushed would exert and equal and opposite force on the car doing the pushing.  When something is suspended the rope etc exerts an equal and upward force on the object hanging from it.

We have all probably experienced Newton's 3rd law when we have pulled on a rope, pushed a bike or something else you have ridden or even pushed on the wall.  The classic example is when a person pushes on a wall while standing on a skateboard.

Commonsense will tell you you will move away from the wall. But this is because as they push on the wall, the wall pushes back.  When you consider the direction they travel in relation to the force they apply, Newton's 3rd Law again makes good sense.

Centripetal acceleration and forces

Centripetal acceleration describes the motion of object travelling in circles or arcs. It translates to "centre seeking".  An example of this motion is shown below with a student swinging a weight on the end of a string.  Note that if she were to let the string go, it would travel in a straight line with the same speed it has when it was spinning.  This is the instantaneous velocity of the weight.
Now because the motion is circular, while the speed can unchanging, the velocity (a vector quantity) is changing all the time.   Now lets consider this at a time interval started at t1 and finished at t2.

The acceleration of the weight can be calculated by:

When you do the vector subtraction it shows that the force is always directed into the centre of the circle or arc.  The formula for centripetal acceleration is:

It therefore follows that the formula for centripetal force is:

This means that the frictional force of the object on a surface must either exceed or be greater than the centripetal forces or a car will skid off the road when cornering.  This frequently occurs in icy or rainy conditions.

One way this overcome is by banking corners.  Just like hills they unbalance the weight of the car on the road with the reaction force of the road surface on the car.  This in turn means that even if the road was friction-less, the car should be able to take the corner (assuming its travelling below the maximum possible velocity.

The centripetal force contributed by a banked corner can be calculated as:

where theta is the angle of banking from the horizontal.

Friction

Consider a car travelling along the road.  You can see all the forces on the car in the figure below.  There are 2 frictional forces here, the contact of the tyres on the road and the air resistance of the car.

Friction always opposes the motion of an object.

You need to know how these forces compare if you are to predict what will happen to the speed of a moving object.

If the driving force is greater than the frictional forces, there is a resultant force forwards. This will make the car accelerate and increase its velocity.

If the driving force is less than the frictional forces, there is a resultant force backwards. This will make the car undergo negative acceleration (deceleration) and have lowered velocity.

If the driving force is the same as the frictional forces, there is no resultant force, and so no change in velocity.

Friction is caused by the contact between 2 surfaces.  The rougher they are, the greater the friction is.  Having said that, friction is good because it means that our grip on the ground allows for walking, riding and driving and parachuting.  It also means that you can write with a ballpoint pen and not slide off your chair as you read this.

Unfortunately there are also downsides to friction.  It creates heat and can wear materials out.  This can be solved by smoothing/polishing surfaces and/or using lubricant (in the case of engines for example).

Balanced and unbalanced forces

Up to this point we have concentrated on the idea of balanced forces and explained them using Newton's 1st Law of motion.

When an unbalance force is applied to an object it will begin to accelerate according to Newton's 2nd Law of motion.  This states that:

The acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely proportional to the mass m of the body, i.e., F = ma. 

Basically:

• The bigger the force, the larger the acceleration for a fixed mass, or 
• The bigger the mass, the lower the acceleration for a fixed force.

People intuitively know that Newton's second law is true when riding bikes, pushing objects or even driving cars.

Contact forces are when the object is in contact with the person or other object that is producing the force.. This includes cars pulling trailers etc.

Non-contact forces are those produced by electrostatic charges, magnetic fields or gravity.

Another example of unbalanced forces is where a car is on a slope.  We can show the forces are unbalance using a vector diagram.  However, we will ignore the frictional forces described here.  

The car has weight as determined by the formula F=mg where m is the mass of the car and g is acceleration due to gravity.  The direction of this force is directly down towards the center of the Earth.  However, the reaction force exerted by the road is at right angles to road surface.  If we do a vector addition of these 2 forces, we find that:

1. They don't cancel out, meaning that the forces are unbalanced.
2. The resultant is parallel to the road pointing downhill.

 As a result the car will begin rolling downhill.  The mathematical calculation of the force exerted on the car can be calculated by 

F = mg sinX

where m = mass of the car, g = acceleration due to gravity, X is the angle of the slope from the horizontal.

Forces as vectors and F=ma (amongst other stuff)

Let's consider the scenario where the pink ice skaters are pushing the blue one as pictured.



Our own experience will tell us that these skaters will end up moving diagonally upwards and to the right.  The reason for this is because the 2 forces can be added together.  Because they are in differing directions, they need to be treated as a treated as a vector addition.  When this is done, the resultant calculation corresponds to what we experience in the real world.



But what happens if no force is applied to an object? Believe it or not, just about everything on Earth is subjected to forces.  Take for example your humble physics text book sitting next to you.


There is a downwards force due to gravity, but the book does not fall.  This is because the table which it is sitting on exerts a reaction force upwards of equal value and opposite direction.  The forces are balanced.   This brings us to Newton's First Law of Motion:

A body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force.

So how does this apply to moving bodies?  Fortunately NASA posted a really nifty pic for me to borrow.



If all of these forces are in balance, then the plane will remain at a constant altitude travelling at a constant velocity.  


This is the scenario with your practical using suspended masses and vector boards.  All the forces are balanced and so nothing moves.

However, when forces are unbalanced, things start to happen.  This is summed up by Newton and his 2nd Law of Motion.

The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.

That is:

More on this in future posts.