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Forces and Newton's Laws of Motion 4.5 Newton's Third law of Motion - defined and examples explained

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4.5 Newton's Third law of Motion

What is Newton's third law of motion?

Newton's Third Law of motion states that when two objects interact, the forces they exert on each other are equal in numerical value, act in opposite directions and are of the same type.

This at first suggests that neither object can move anywhere, but you have two objects and two outcomes!

In general, what can you can say for the forces in a pair of objects interacting?

They are the same size.

They act in opposite directions.

They act on different objects.

They are the same type of force.

These four points will be illustrated in the following examples.

 

(Context 1) A  stationary example of Newton's 3rd Law

A bit more messy to analyse than you think !!!

Consider the flask of liquid standing motionless on a laboratory bench.

There are two sets of forces operating shown by the arrows of opposing direction, but the same length - same magnitude of force.

Both sets of forces are examples of Newton's 3rd Law, but don't mix the two up!

(i) The normal contact force due to the weight of the object acting (pushing) down on the surface of the bench (F1) is balanced by the bench under minute compression of the atoms pushing back up to an equal and opposite extent onto the flask (F2).

A similar argument applies to when you push against an object that isn't moving. The force of your push is balanced by the compressed atoms of the object pushing back!

(ii) At the same time both the flask and the Earth (including the bench) are mutually attracting each other (F3 and F4) to an equal and opposite extent due to the non-contact force of gravity.

The Earth attracts the flask and the flask attracts the Earth.

It makes no difference whether the objects are in contact or not, here gravity acts throughout everything!).

In the cases described so far there is no resultant force, everything is balanced.

If the forces were not balanced and there was some net resultant force, the object would move or be reshaped - something would change!

For stationary objects, if the resultant force acting on the object is zero the object is said to be in equilibrium (effectively means a state of balance).

Take care with equilibrium situations which might look like examples of Newton's Third Law of motion

e.g. suppose a watch is hanging on the end of gold chain in a stationary equilibrium situation.

Does this conform with Newton's Third Law.

The answer is no because the forces are not of the same type and they both acting on the watch.

The weight of the watch is acting downwards due to gravity.

The tension in the chain is acting upwards from the watch - the tension is due to atoms pulling on each other.

 

(Context 2) 'Movement' examples of Newton's 3rd Law and motion consequences

illustrating all four points listed above

Situation 1. Ice skaters on an ice rink.

Suppose two ice skaters, of similar mass, are standing next to each other, and then one of them pushes the other with a force of 80 N, what happens next?

Both skaters experience the same normal contact force of 80 N, but in opposite directions.

Both skaters will accelerate away from each other in opposite directions.

However, they will only accelerate away from each other with the same acceleration if they of the same mass.

Since F = ma and a = F/m,

if one of the skaters has a smaller mass than the other, the skater of smaller mass will move in the opposite direction with a greater acceleration (F is a constant and a 1/m).

Situation 2. Astronaut with a rocket back pack

In 'outer space' in a zero gravity situation, an astronaut could manoeuvre around using a small jet pack attached to the back of a spacesuit.

When fired, the gases are accelerated one way and an equal and opposite force acts on the astronaut who is accelerated in the opposite direction - hopefully back to the space station or spaceship!

Situation 3. A head-on collision of two objects

Suppose two balls m1 and m2, of masses m1 and m2 collide head-on with a certain normal contact force.

Assume mass m1 is smaller than mass m2.

Let us assume, before impact, they are moving at the same velocity towards each other.

On impact they both fly backwards in the opposite direction than before impact.

According to Newton's 3rd Law, both balls experience exactly the same force, but acting in opposite directions.

However because they have different inertial masses, so, as a consequence of a = F/m (Newton's 2nd Law) ..

the smaller inertial mass, ball m1, will be accelerated more and fly off with a greater velocity than ball m2,

the larger inertial mass, ball m2, will be accelerated less and fly off with a smaller velocity than ball m1,

 

(Context 3) A head-on collision between two road vehicles

In example (ii) the balls rebounded of each other, but what are the consequences of two objects colliding head on and 'crunching' together.

So, imagine a 1000 kg car travelling crashing head-on into a 500 kg car travelling in the opposite direction.

 

(a) What can you say about the impact force experienced by each car?

According to Newton's 3rd law of motion, both cars experience the same impact force, but in opposite directions.

 

(b) What can you say about the relative deceleration of each car and their relative inertial masses?

Newton's 2nd law of motion can be stated as F = ma,

F = impact force, m = inertial mass and a = deceleration (negative acceleration).

Since the impact force is the same, mag for the 1000 kg green car = mab for the 500 kg blue car.

This means that the deceleration (negative a) for the green car of larger mass must be less than that for the blue car of smaller mass.

In fact, we can say mathematically, for the same impact force F

1000 x agreen car = 500 x ablue car

Which means that the relative deceleration of the blue/green cars is 1000/500 = 2.

So, the 'lighter' blue car decelerates at twice the rate of the 'heavier' green car.

The green car has a much greater inertial mass, and is more difficult to slow down than the blue car of much smaller inertial mass, for the same impact force.

 

(c) What are the consequences for each driver from your answers to (b)?

The consequences for the driver of the blue car are potentially much more serious than the consequences for the driver of the green car.

The blue car driver will be accelerated forwards at twice as much as the green car driver, with potentially greater impact injuries - although all should be wearing safety belts, there is still the possibility of 'whiplash' injuries.

You could also presume, in the case of either driver, the smaller the mass of the driver, the more the would be accelerated forwards.

 

(d) If the cards were travelling at the same speed prior to impact, and the crunch combination continued moving as a single object, which direction would the 'wreck' move and why?

(i) The 'combination wreck' would continue moving to the right.

Eventually it would come to a halt due to friction with the road.

(ii) The 'combination wreck' would continue moving to the right because of he heavier mass of the green car.

The green car has twice the momentum (mass x velocity) of the blue car.

For more on (d) see Q2.7 on momentum calculations and Newton's 2nd law of motion

 

(Context 4) A cat leaping up from the ground to catch a butterfly!

The 'force' sequences (neglecting air resistance)

  1. At the start a pair of equal non-contact gravitational forces operate - the Earth attracts the cat and the cat attracts the Earth.

  2. Coincident are the normal contact forces operating - the weight of the cat pushes down on the ground via the cat's paws and the compressed ground pushes back up with an equal opposite action force.

  3. On leaping up, the cat's muscles exert an increased normal contact force on the ground through its back legs and, again, the ground pushes up with an increased equal an opposite normal contact force.

  4. The normal contact forces are no longer operating and the upward acting force generated by the cat's muscles must initially exceed the weight of the cat due to gravity - the cat's acceleration must exceed the Earth's gravitational pull on it - otherwise it can't leave the ground.

  5. The cat's kinetic energy store (KE) decreases and its gravitational potential energy store (GPE) increases to a maximum at the maximum height the cat reaches into the air - the KE is zero just for a moment, then as it falls the cat's GPE is converted back to KE.

  6. The cat is attracting the Earth and the Earth is equally attracting the cat, which now falls to the ground.

  7. The normal contact force of the cat's impact on the ground is equalled by the atoms of the ground pressing back up.

See also Forces and Motion Section 6.

Elastic/non-elastic collisions, momentum calculations, Newton's 2nd law

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Keywords, phrases and learning objectives for Newton's 3rd law of motion

Be able to define and quote Newton's Third law of Motion that when two objects interact the forces exerted on each other are numerically equal and act in opposite directions

Be able to analyse and explain what happens when two objects interact and the forces they exert on each other in terms of Newton's third law of motion.


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