Newton’s laws of motion

 

Newton’s laws of motion are the basis for our understanding of the mechanical world. While students may or may not know them by name, they underpin most of the mechanics in KS3, GCSE and A Level Physics courses.

 

They are a topic many students find confusing. Newton’s laws are very simple but that doesn’t mean they are intuitive or easy to understand. Care must be taken in teaching to illustrate the differences between naïve theories of motion and the model hypothesized by Newton. Case in point: the intuitive assumption of most physics students, physics teachers even is that any motion must take place under the action of a non-zero resultant force. Newton’s laws show, this is not the case.

 

Newton’s First Law.

 

A body will remain at rest or moving with uniform velocity unless acted on by a non-zero resultant force.

 

Most of us can intuitively grasp that an object which is at rest must be subject to no forces (unusual) or to “balanced” forces with a vector sum of zero. Less obvious is the notion that an object moving with uniform velocity (unchanging speed in a straight line) must also be subject to no forces or forces which sum to zero.

 

The intuitive assumption is that forces are required for motion. Newton’s First Law is telling us that forces are required to change motion. The idea that an object can continue moving at unchanging speed with no forces acting on it is counter to our day to day experience.

 

A car or bike in motion requires a motive force to be continually applied in order to maintain motion at a uniform speed but that is because it is subject to drag forces (air resistance, friction etc.) If the vehicle moves at a uniform speed then the motive force must be equal in magnitude to the drag forces. I.e. the vehicle continues moving with uniform velocity because the resultant force acting on it is zero. If the motive force is greater than the drag forces, the vehicle will speed up, if the drag forces are greater than the motive force, it will slow down.

 

In space flight, bodies can move with (virtually) no forces acting. When the space shuttle takes off, a huge motive force is required from the thrusters to a) counter the shuttle’s weight due to gravity and drag forces and b) accelerate the shuttle from rest. Once the shuttle is in flight in deep space, the thrusters are turned off and the shuttle continues to “drift” at a uniform velocity: no motive force is acting on it but also (virtually) no gravity or drag forces.

In summary, Newton’s first law tells us: No forces or “balanced” forces with a vector sum of zero mean no change in motion. “Unbalanced” forces with a non-zero sum mean a change in motion.

 

 

Newton’s Second Law

 

Resultant force equals rate of change of momentum.

 

Newton’s first law tells us whether the motion of an object will change or not, based on the forces acting on it. Newton’s second law tells us how the motion will change.

 

The most commonly used modern form of Newton’s second law is the equation F = ma

 

F = ma can be derived quite easily from Newton’s original calculations:

F = d(mv)/dt (Resultant force equals rate of change of momentum)

F = m(dv/dt) (because mass doesn’t change)

a = dv/dt (acceleration is rate of change of velocity)

so F = ma

 

Compared to the first law, Newton’s second law is relatively intuitive.

 

Consider the equation rearranged:

a = F/m

So now we have acceleration directly proportional to resultant force and inversely proportional to the object’s mass. So if you double the force acting on an object, it will double the acceleration but if you have the same force acting on an object of double the mass, it will provide half the acceleration.

 

Furthermore, acceleration will always occur in the same direction as the resultant force.