Newton’s Laws of Motion Force is usually assumed push/pull – not easy to describe actual force, but effects of force can be described e.g. movement. Force will tend to cause movement. If from stationary to a given velocity then force causes acceleration. The unit of force is defined from this concept. It is the acceleration produced when a force acts upon a given mass of 1 kg. Definition of unit:- the force required to give a mass of 1 kg an acceleration of 1 ms -2.The unit of force is therefore the kg. m/s 2 or kg. ms -2 Unit changed to the Newton in honour of Sir Isaac Newton 17th century. In 1687 Newton produced book called “ The mathematical principles of natural philosophy” known as The Principia. The text provides a series of three laws to sum up the basic principles of motion.

Newton’s Laws of Motion Newton’s 1st Law of motion states: Every body continues in its state of rest or uniform motion in a straight line unless compelled by some external force to do otherwise. Objects do not move by themselves! This law suggests that objects when moving with constant velocity in a straight line will continue to do so indefinitely. This is not so due to the influence of external forces such as friction, air resistance, gravity. The concept of reluctance of an object to change is known as inertia. The first law is often called the inertia law. A heavy object will need a greater force to accelerate/decelerate it than a light object. A heavy moving object has a greater amount of motion than a light object. The amount of motion/mass of a body is defined as momentum. Momentum is taken as the product of mass & velocity of a body. The unit of momentum is therefore kilograms x metres per second kg ms -1 or kg m/s For the same given force a light body can obtain a greater velocity than a heavy body but both may have the same value of momentum.

Newton’s Laws of Motion Newton’s 2nd Law of motion states: The rate of change of momentum of a body is proportional to the applied force and takes place in the same direction in which the force acts. For a given body momentum changes from mu to mv in a time slot t Thus change in momentum is equal to this is proportional to a the given force F. Thus F  If the expression is factorised F  m As acceleration a = Then it can be seen F = ma

Newton’s Laws of Motion If it is intended to ACCELERATE a rocket against gravity then the thrust provided by the rocket motors must:- 1.Overcome the weight of the rocket (mass x g) 2.Overcome any resistance on the rocket (air resistance etc.) 3.Provide the force needed to accelerate the rocket up to its required speed If air resistance is not included the thrust must balance mg + ma Thrust = m (g + a) Note:- a rocket must attain an escape velocity of 11.2 km/s

Newton’s Laws of Motion If it is intended to ACCELERATE a car along a flat track then the thrust provided by the car engine must:- 1.Provide the force needed to accelerate the car up to its required speed F = ma 2.Overcome any resistance on the car (air resistance, friction etc.) The resistances are grouped under the title of Tractive Resistance TR (The weight of the car is now a factor of its TR) The forward propulsion force F must be ma + TR

Newton’s Laws of Motion If it is intended to ACCELERATE a load upwards against gravity then the tension in the lifting cable must:- 1.Overcome the weight of the load (mass x g) 2.Overcome any resistance on the load (air resistance etc.) 3.Provide the force needed to accelerate the load up to its required speed If air resistance is not included the tension must balance mg + ma Tension = m (g + a) Tension in cable

Newton’s Laws of Motion Q1.what force is needed to produce an acceleration of 3 ms -2 on a 4 kg mass. Soln.F = ma = 4kg x 3 ms -2 = 12 kg.ms -2 = 12 N Q2.If a force of 2800N is applied to a mass of 120kg what acceleration results.

Newton’s Laws of Motion Q3.what force is needed to accelerate a car of mass 900kg from 2.5 ms -1 to 6.8 ms -1 in 2.7sec. Soln.(Tip:-First find rate of acceleration.)

Newton’s Laws of Motion Q4.An automatic machine operation requires a tool of mass 2.43kg to accelerate from 0.5 ms -1 to 13.2 ms -1 in a distance of 426mm. Find the minimum force needed by the machine. Soln.

Newton’s Laws of Motion Q4.An automatic machine operation requires a tool of mass 2.43kg to accelerate from 0.5 ms -1 to 13.2 ms -1 in a distance of 426mm. Find the minimum force needed by the machine. Soln. Q5.Find the minimum force required if the tool works against a frictional resistance of 100N Soln.

Newton’s Laws of Motion Q6.Calculate the weight on the floor of a lift when a mass of 120kg is placed on the floor. Soln.(Remember weight = mass x gravity) Q7.Calculate the tension in the lift cable when the lift has a total mass of ½ tonne and is held stationary

Newton’s Laws of Motion Q8.re calculate the tension if:- a.the lift is accelerated up at 2 ms -2 b. lift is accelerated down at a rate of 2 ms -2

Newton’s Laws of Motion Newton’s 3rd Law of motion states: When a force acts upon a body, an equal and opposite force acts on some other body. Often given as: To every action there is an equal but opposite reaction. A good example of this concept is the recoil experienced when firing a gun. e.g. The mass of the bullet x bullet velocity = mass of gun x recoil velocity Q1.what is the momentum of a vehicle having a mass of 900kg when moving at 6.2 ms -1 Soln.Momentum = mv = 900kg x 6.2 ms -1 = 5580 kg.ms -1

Newton’s Laws of Motion Newton’s 3rd Law of motion Q2what is the momentum of a drop hammer of mass 650kg after falling freely through a height of 3.2m Soln.First use free fall equation to find terminal velocity v.