Force & Motion
# Definition of force:
‘A force is a push or pull that one object exerts on another which produces, or tends to produce motion, stops or tends to stop motion.’
When a body is acted upon by a resultant force it will begin to move. If the body is already moving a force may alter its speed or alter its direction of motion or else bring it to rest.
The SI unit of force is Newton (N).
# Contact and non-contact forces:
Examples of contact forces are frictional forces, normal reaction forces, tensions and forces in collisions. Forces at a distance (non-contact forces) include gravitational forces of attraction between two masses, electrical forces of attraction (or repulsion) between two charged objects and magnetic forces of attraction (or repulsion) between two magnetized objects or magnetized object and a magnetic material.
# Frictional force:
Friction is the force that opposes the relative sliding motion of two surfaces in contact with one another. Walking would be impossible if there were no friction between the ground and the soles of our shoes.
# Normal force :
Any object placed in contact with another exerts on the other a force perpendicularly on to its surface in contact. These types of contact forces are called normal force. For example when a book is placed on a tabletop the table exerts a force on it in upward direction (In the adjacent figure the force is FN). At the same time the book exerts a force on the surface of the table in the downward direction by virtue of its weight (In the adjacent figure the force is FN). Here both the table and the book are acting on each other by means of two forces that are equal in magnitude but opposite in direction (FN = - FN) . Both the forces here are normal forces.
# Balanced and unbalanced forces
When the net force acting on an object is zero then the forces acting on it are balanced forces. If the net force is not zero then the forces acting on the object are unbalanced forces. In the preceding example the book is actually acted upon by two forces. One is its weight W, which is the attraction by earth in downward direction (FN = W) and the other is the normal reaction force given by the table (FN). As because FN = -W the net force on the book is zero and it stays in equilibrium. A ball released from eye-level can be observed to fall with increasing velocity (i.e. it accelerates) until it hits the ground.. Whatever it is that is responsible for accelerating the ball, or any other object, is called a force or, more correctly, an unbalanced force. Here the gravitational force is the unbalanced force. If you see an object accelerating – either speeding up or slowing down – then you must conclude that an unbalance force is acting on it.
# Gravitational force:
A ball released from eye-level can be observed to fall with increasing velocity (i.e. it accelerates) until it hits the ground. The earth exerts a force on the ball, which is called gravitational force. The force of gravity is an example of force acting at a distance, i.e. it acts even when the ball is not in contact with the earth.
Newton’s law of universal gravitation states that any two particles of the universe attracts each other with a force which is proportional to the product of their masses and inversely proportional to the square of their distance. This law is applied strictly to cases when the distance is large compared with the size of the bodies.
Newton realized that gravitational attraction was applied not only to bodies on the earth but was also responsible for holding the moon in its orbit around the earth and also the earth and the other planets in their respective orbits around the sun.
Two objects of mass M1 and M2 respectively are separated by a distance of d from each other. According to Newton’s law of gravitation. These two bodies attract each other by means of a force Fg which is given by
F21 = - F21
And F21 = F21=
Here G = 6.67 × 10-11 N m2 kg-2 is a constant called the universal gravitational constant.
The force of gravity that Earth exerts on an object placed on its surface is called its weight and depends on the objects mass.
[Radius of Earth = 6 378.1 kilometers (equatorial) = 6356.7 (polar) km, 6372.7 (mean), mass of Earth = 5.9742 × 1024 kilograms]
# Main types of forces:
There are three types of force (non-contact)
(a) Gravitational Forces
(b) Electro-magnetic Forces
(c) Nuclear Forces
The effect of forces on motion
# Newton’s laws of motion:
Isaac Newton (1642 – 1727) studied the motion of objects and formulated his famous three laws of motion.
• Newton’s First law:
‘Every object continues in its state of rest or uniform motion in a straight line unless a resultant force acts on it to change its state.’
The first law tells us two things. Firstly, if there is no resultant force acting on an object at rest, the object will remain at rest. Secondly, if there is no resulting force acting on a moving object, the moving object will continue to move at a constant speed in a straight line, i.e. with constant velocity.
The tendency of a body to remain at rest or, if moving, to continue its motion in a straight line is described as inertia. For this reason, Newton’s first law is sometimes called ‘the law of inertia’
Therefore, Newton’s First law describes the behaviour of objects when there is no resultant force acting on them. Newton’s second law explains how the motion of an object changes when the resultant force is not zero.
# Inertia
The property of a body that resists any change in its velocity is called inertia. Rest is a special case of motion with velocity equal to zero. Therefore, inertia is also the property of an object at rest that causes it to remain at rest. The amount of mass an object has is a measure of its inertia.
# Momentum:
The momentum of a body is defined as the product of its mass and its velocity, ie. p = mv.
The unit of momentum in the SI system is, Kg-m/s.
• Newton’s Second law:
‘The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts.’
Suppose a force F acts on a body of mass m for a time t, and causes its velocity to change from u to v.
The momentum changes uniformly from mu to mv in time t,
Change in momentum = mv – mu [v>u]
rate of change in momentum =
By Newton’s second law, the rate of change of momentum is proportional to the applied force, hence,
or,
but
This relationship can be turned into an equation by putting in a constant.
Thus, F = constant ma
If m = 1 kg and a = 1 m/s2, the value of the unit of force is chosen so as to make F = 1 when the constant = 1.
So, we can write,
F = ma
The SI unit of force is called the Newton (N).
1 N is the force, which produces an acceleration of 1 m/s2 when it acts on a mass of 1kg.
Newton’s Second law tells us that when there is a resultant force acting on an object, the object will either slow down (decelerate) or sped up (accelerate).
Gravitational force and weight
The force of gravity that Earth exerts on an object placed on its surface is called its weight and depends on the objects mass. According to Newton’s law of gravitation the gravitational force between two objects of mass M and m is given by
Where G is the universal gravitational constant with value 6.672 x 10-11 N m2 kg-2.
[Radius of Earth = 6 378.1 kilometers (equatorial) = 6356.7 (polar) km, 6372.7 (mean), mass of Earth = 5.9742 × 1024 kilograms]
So the force of gravity depends on the distance of the object
An object near the surface of the earth is always pulled towards the centre of the earth and its velocity increases during freefall. The rate of increase of velocity of a freely falling body because of gravity is called the acceleration due to gravity. So the force on an object or is weight is given in terms of its mass and acceleration as
F = mg
Where g is the acceleration due to gravity. Equating this with the previous equation we can write
or,
• Newton’s third law :
‘To every action there is an equal and opposite reaction.’
Or in other words, whenever a force acts on one body, an equal and opposite force acts on some other body.
Suppose body A exerts a force F on body B, then body B exerts a force of –F (of equal size but in the opposite direction) on body A.
Newton’s third law tells us four characteristics of forces. Firstly, forces always occur in pairs. These forces are called action force and reaction force.
Secondly, the action and reaction are equal in magnitude.
Thirdly, action and reaction act opposite to one another.
Lastly, action and reaction act on different bodies.
Exercise: 4 A boy pushes a box of mass 20 kg with a force of 50N. What is the acceleration of the box?
Exercise: 5 A car of mass 1000 kg accelerates from rest to 20 m/s in a time 5s. Calculate the forward thrust (force) of the car.
Exercise : 6 You hang a 5 N weight from a rubber band. Suddenly the band breaks . Describe the force(s) on the weight before and after the band broke. In each case, tell whether there is a net force or balanced forces?
Exercise: 7 in a science fiction movie, a spaceship far from any planet or star shuts off its rocket engine. It immediately stops moving. Does this obey any law of physics? If so, which law?
Exercise: 8 How much force is needed to accelerate a bicycle and rider with mass 60 kg at 1.5 m/s2 ?
Exercise: 9 The maximum acceleration of a fist in a karate blow is 3500 m/s2 . The mass of the fist is 0.7 kg. If the fist hits on a wooden block, what force does the wood place on the fist?
Exercise: 10 What is the acceleration of an airplane that has a force on it 24000 N?
Exercise: 11 An acorn( seed of oak tree) falls from the top of an oak tree to the ground in 1.5 seconds. What is the velocity of the acorn when it strikes the ground?
Exercise: 12 An object dropped from a 20 story building takes 4 second to fall. How fast it is going when it strikes the ground? [ each floor is 3.2 m high]
Exercise: 13 A cricket ball weighing 156 g is moving at 54 km/h towards a batsman. It is hit by the batsman back towards the bowler at 36\ km/h. Calculate i) the ball's impulse, and ii) the average force exerted by the bat if the ball is in contact with the bat for 0.13 s.
Exercise: 14 A cricket ball, mass 1kg is hurling down towards you at 30ms-1 . Your bat , mass 10kg, accidentally stops the ball. Ignoring your arms and hands, how quickly will the bat move backwards? (3ms-1 backwards )
Fill in the blanks
1. Force needed to accelerate a car is than the force needed toe accelerate a bicycle.
2. In order to keep a n object moving in a circular path it must be acted upon by a (friction, centripetal force)
3. When and object reaches terminal velocity, the air resistance force is equal to the
4. The momentum of a massive object at rest is
5. .
Determine whether the following sentences are true
1. Inertia stops a moving object
2. The mass of an astronaut is smaller on the moon than on the earth.
3. Acceleration may have negative value.
4. A car rounding a curve at 25 km/h is accelerating
5. An action-reaction force pair acts on same object.
6. A constant acceleration gives an object a constant velocity
7. The momentum of a football changes when it is kicked.
8. As the speed of a moving object decreases its momentum decreases.
9. Inertia causes an object to move in circular path.
Short questions
1. What is force?
2. What are contact and non-contact forces? Give examples.
3. Write down Newton’s law of gravitation.
4. Explain disadvantages and advantages of friction.
5. What is inertia? State Newton’s law of inertia.
6. State Newton second law or the law of force.
7. What are balanced forces? Why a feather drifts downward through air at a constant speed rather than accelerating at the rate of g.
