# Mechanics Tutorial 10 - Newton’s Laws of Motion

Newton I

Newton’s First Law states:

Every object continues in its state of rest or uniform motion in a straight line, unless it is compelled to change that state by an external force acting on it.

A car will maintain a constant speed if the drive force and the drag are balanced.   The total force is zero.

 The graph below shows the acceleration of a car up to its maximum speed. (a)  Why is the graph a straight line at low speeds? (b) Use Newton I to explain why the car reaches a maximum speed which it cannot exceed.  Assume it’s on a test track, so it can exceed the 115 km h-1 national speed limit.

##### Newton II

Newton's Second Law states:

Rate of change of momentum is proportional to the total force acting on a body, and occurs in the direction of the force.

An object of mass, m, is acted on with a constant force, F, so that its velocity increases from an initial value, u, to a final value, v, in time, t.

Momentum is the product of mass and velocity.  It is a vector and has units of kilogram metres per second (kg m s-1).

Change in momentum = momentum at end - momentum at start

Therefore:

Therefore

Now we know that acceleration:

So we can write:

Therefore:

The term k is a constant with no units. k = 1)

Force (N) = Mass (kg) × acceleration (m s-2)

F = ma

Make sure you use the right units:

• Force in N,

• Mass in kg,

• Acceleration in m s-2.

Acceleration is always caused by a total force, the vector sum of all the forces.  The acceleration is always, without exception, in the same direction as the total force.

 Question 2 A 70 kg athlete accelerates to his maximum speed of 9.5 m s-1 in a time of 2.5 s.  What is the average force he applies to the track?

If you have a vehicle providing a force to accelerate another vehicle, you must add the mass of the towing vehicle to that being towed.

 Question 3 A locomotive of mass 100 tonnes is hauling a train of wagons of mass 1200 tonnes with a pulling force (tractive effort) of 180 kN.  What is the acceleration of the train? (1 tonne = 1000 kg) Question 4 A horse of mass 800 kg is pulling a barge of mass 5000 kg as shown in the diagram below: The barge is initially at rest. (a) Calculate the acceleration. (b) The horse reaches a maximum speed of 1.5 m s-1.  Calculate the time taken to reach this speed. Question 5 (Challenge) This is part of an examination question A trolley of mass 1.0 kg is set up on a friction compensated runway, and attached to a 1 N slotted mass, which is released.   The trolley moves down the runway, and its motion is recorded with a ticker tape timer. Further slotted masses are added, and the motion measured. Describe how this experiment can be used to verify Newton’s Second Law of Motion. Explain why this is a bad question.
##### Newton III

Newton’s Third law states that:

If body A exerts a force on body B, body B must exert an equal and opposite force on body A.

In other words, forces always act in pairs.  This is true whether the forces are in equilibrium, moving, stationary or accelerating.

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This boy is sitting on a simple hovercraft.  The motor drives a fan which forces air downwards onto the floor. The force of the air going down produces a reaction force that lifts the machine off the ground.  A simplified diagram of the machine is shown below:

This picture shows a small hovercraft that can skim on water or dry land.  It is powered by a small (10 kW) petrol motor.

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Hover mowers are very simple small hovercraft.  Some transport hovercraft are enormous machines of mass several hundred tonnes.  They move easily across flat ground.  The problem with hovercraft is that their performance on hills is hopeless.  Can you think why?

Picture by Andrew Berridge, Wikimedia Commons

 Newton I and III are often confused.