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4.1 Newton's First Law of Motion and resultant forces

What is Newton's first law of motion?

Newton's three laws of motion are some of the earliest proposed laws of physics - indeed of science itself.

His imagination, insight and mathematical brilliance have stood the test of time since 1686 when he first proposed them - but they could not be assumed to be true i.e. valid in 1686 - repeated experimental verification is required.

BUT, countless experiments over the past few hundred years have shown them to be true and form the basis of innumerable calculations in applied physics and engineering.

Newton's First Law of Motion

Newton's First Law of Motion states that a resultant force is needed to change the motion of any object.

e.g. starting a body moving, increasing its speed (acceleration), slowing it down (deceleration), stopping it moving, changing the direction of movement (the latter is a change in velocity).

A resultant force must be an unbalanced net force of >zero on an object.

If the resultant force on a stationary body is zero, the body will remain stationary.

If the resultant force on a moving object is zero, the velocity remains unchanged, in other words the object will continue moving at the same speed and in the same direction, therefore moving with the same velocity.

If a body such as a road vehicle or an aeroplane is moving at a constant velocity (constant speed without changing direction) the driving force from the engine and the resistive forces of friction (moving parts, air resistance etc.) must be balanced i.e. the resultant force is zero.

The velocity can only be changed if a resultant non-zero force acts on the object.

A non-zero resultant force will always initially produce an acceleration or deceleration in the direction of the force (see cyclist example below).

There are five situations that you will come across when dealing with a non-zero resultant force that results in a change in velocity.

This change in velocity may involve a moving object speeding up (acceleration) or slowing down (deceleration).

The acceleration might be a stationary object being forced to move or a moving object made to stop.

These first four situations involve change in speed, and not necessarily a change in direction, but change in direction is also a 5th result of the effect on an object of a non-zero resultant force, and therefore a change in velocity.

 

See also Forces and motion section 3.

Calculating resultant forces using vector diagrams, also includes work done calculations

 

Some of these ideas are illustrated using a cyclist

On the left is a 'free body force diagram' of a cyclist showing all the forces acting on the body.

If the cyclist is moving with a constant velocity then we are dealing with uniform or constant speed and no change in direction.

There is no resultant force i.e. F1 = F3 and F2 = F4, so the cyclist continues in the same direction at the same speed.

Note the relative size and direction of the arrows and think of Newton's First Law of Motion.

F1 is the air resistance due to friction between the surface of the bike and cyclist and the air, also friction between the wheels and road, and, friction in moving parts of the bike. All three combined oppose the forward motion of the bike and rider.

F2 is the weight of the bike + cyclist combination due to gravity, weight of object acting on the road with the normal contact force

F3 is the thrust or push of the bike from the power generated by the cyclist.

F4 is the normal contact force of the atoms of the road surface pushing back up on the bike.

If the cyclist applies more power (left free body diagram), forces F1 and F2 are unbalanced, giving a resultant force of greater than zero from right to left.

Therefore the cyclist will accelerate and increase in speed. This action does not affect forces F2 and F4 which remain balanced.  The resultant force causes the acceleration. 

If the cyclist applies the brakes (left free body diagram), in doing so he will stop pedalling, reducing force F3 AND the increased friction from the brake pads acting on the wheel rim will increase force F1 (left diagram). Again, the arrows for forces F1 and F3 should be shown as unequal. The forces are now unbalanced and the bike and rider slow down (deceleration). Neither of these two actions affects forces F2 and F4 which remain balanced. The resultant force causes the deceleration. 

If another force is introduced like a sudden gust of a side wind (F5), then the cyclist and bike will change direction in the direction of the wind i.e. forced to the right since the diagram indicates a gust of wind from the left. The cyclist will then apply a correcting 'balancing' force by turning the handle bars to adjust for the extra force F5 to try to maintain the same speed and direction of the cycle.

 

You can analyse the descent of a parachutist

This is an interesting case because it involves an acceleration, a deceleration and two terminal velocities!

1.    2.    3.  

The three possible 'force' situations as the parachuting person is descending after jumping out of an aeroplane.

Note the relative size and direction of the arrows and think of Newton's First Law of Motion.

1. When drag force F1 is less than the weight force F2, the parachutist is accelerating.

2. When drag force F1 equals the weight force F2, the parachutist is descending at a steady speed - a terminal velocity.

3. When drag force F1 is more than the weight force F2, the parachutist will decelerate (to another terminal velocity).

This situation is fully analysed on Forces and Motion Part 3.5

Complex behaviour of a falling parachutist: forces & velocities

 

Any stationary object standing on a surface

The weight of an object, due to gravity, acts on the surface - normal contact force.

The atoms of the surface are compressed and push back up with an equal normal contact force.

The resultant force is zero.

Therefore from Newton's First Law of Motion, the object should stay stationary.

If there was any difference in the two forces, the object would accelerate and rise or fall.

 

Some examples involving circular motion

(i) Suppose you whirl an object around tied to the end of a string.

If you supply kinetic energy at a constant rate the object will whirl around with a constant speed in the same repeating circular path.

The object is held in a constant orbit by the tension in the string - the centripetal force, acting towards the centre of rotation, and balancing out the acceleration.

The forces are balanced, a zero resultant force, but what if the string breaks!?

The tension in the string has gone, so there is no balancing centripetal force, but the object is still moving and shoots off at a constant velocity in a linear direction at a tangent to the original orbit.

(ii) The Earth orbiting the Sun

A thought experiment! Suppose you could switch off gravity, what would happen to the Earth.

(OR imagine if the Sun suddenly disappeared, its the same effect, the Earth is NOT in a gravitational field.)

The centripetal gravitational force has gone, so I'm afraid the Earth would fly off at a tangent to its original planetary orbit and fly off in a straight line at a constant velocity.

Unless it hit or was hit, by another object, it would continue in a straight line at constant speed for ever!

 

INDEX for physics notes on Newton's Laws of Motion

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Keywords, phrases and learning objectives for Newton's 1st Law of Motion

Know and be able to Newton's First Law of Motion and resultant forces.

Know that a resultant force of >0 is needed to change the motion of any object.

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