Force

If you place a ball on a flat surface, it will remain there until unless you disturb it. It will move only when either we push it or pull it. This push or pull acting on an object is known as a force. At least two objects must interact for a force to come into play. An interaction of one object with another object results in a force between the two objects.

Forces applied on an object in the same direction add to one another.  If the two forces act in the opposite directions on an object, the net force acting on it is the difference between the two forces.

Spring balance is a device used for measuring the force acting on an object. It consists of a coiled spring which gets stretched when a force is applied to it. Stretching of the spring is measured by a pointer moving on a graduated scale. The reading on the scale gives the magnitude of the force.

State of Motion

The state of motion of an object is described by its speed and the direction of motion. The state of rest is considered to be the state of zero speed. An object may be at rest or in motion; both are its states of motion.

Force can Change the State of Motion

A force applied on an object may change its speed. If the force applied on the object is in the direction of its motion, the speed of the object increases. If the force is applied in the direction opposite to the direction of motion, then it results in a decrease in the speed of the object.

A change in either the speed of an object, or its direction of motion, or both, is described as a change in its state of motion.

Force can Change the Shape of an Object

The application of force on an object may change its shape or size. For example, when you apply a force on an inflated balloon by pressing it between your palms.

Newton's Laws of Motion

By observing the motion of objects on an inclined plane Galileo deduced that objects move with a constant speed when no force acts on them. Newton further studied Galileo’s ideas on force and motion and presented three fundamental laws that govern the motion of objects. These three laws are known as Newton’s laws of motion.

Newton’s First Law of Motion

Every body continues in its state of rest or of uniform motion in a straight line until unless it is compelled by some unbalanced force to change that state.

Newton’s first law of motion tells that all bodies resist a change in their state of motion. This property of bodies is called inertia. That is why, Newton’s first law of motion is also known as the law of inertia.

Inertia

The inertia is the tendency of objects to stay at rest or to keep moving with the same velocity.

While travelling in a motor car, you tend to remain at rest with respect to the seat until the driver applies a braking force to stop the motorcar. With the application of brakes, the car slows down but our body tends to continue in the same state of motion because of its inertia.

Inertia and Mass

There is a resistance offered by an object to change its state of motion. If it is at rest it tends to remain at rest; if it is moving it tends to keep moving. This property of an object is called its inertia. Heavier or more massive objects offer larger inertia.

Quantitatively, the inertia of an object is measured by its mass.

Newton’s Second Law of Motion

The first law of motion indicates that when an unbalanced external force acts on an object, its velocity changes, that is, the object gets an acceleration.

Momentum

The force required to stop a moving body depends upon its mass. The force required to stop a body also depends upon its velocity. The impact produced by the objects depends on their mass and velocity. These two quantities define a new quantity called momentum.

The momentum, p of a moving body is defined as the product of its mass, m and velocity, v.

p = mv

SI unit of momentum is kilogram-metre per second (kg m s-1). Momentum has both magnitude and direction. Its direction is same as that of velocity.

Since the application of an unbalanced force brings a change in the velocity of the object, therefore a force also produces a change of momentum.

Second Law of Motion

Second law of motion states that the rate of change of momentum of a body is directly proportional to the force acting on it and takes place in the same direction as the force.

Newton’s second law of motion also gives a relation between force and acceleration.

Suppose the velocity of an object of mass m changes from u to v in time t by the application of a constant force F. The magnitude of initial and final momentum of the object will be

p1 = mu and p2 = mv

Rate of change in momentum = (p2 - p1)/t

According to second law of motion, the magnitude of the force F, is

F = (p2 - p1)/t

F = (mv - mu)/t

F = m(v - u)/t

F = ma

The second law of motion gives a method to measure the force acting on an object as a product of its mass and acceleration. 

For example, while catching a fast moving cricket ball, a fielder in the ground gradually pulls his hands backwards with the moving ball. In doing so, the fielder increases the time during which the high velocity of the moving ball decreases to zero. This decreases the rate of change of momentum and hence the force.

Unit of Force

The unit of force is called newton and its symbol is N. So a force of 1 newton will produce an acceleration of 1 m/s2 on an object of mass 1 kg.

The C.G.S. unit of force is dyne.

1 newton = 105 dyne

Newton’s Third Law of Motion

The first two laws of motion tell how an applied force changes the motion and provide with a method of determining the force. The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction.

Newton in his third law of motion stated a relation between action and reaction. According to this law, to every action there is an equal and opposite reaction. Action and reaction never act on the same body.

For example, when a gun is fired, it exerts a forward force on the bullet. The bullet exerts an equal and opposite reaction force on the gun. This results in the recoil of the gun. Since the gun has a much greater mass than the bullet, the acceleration of the gun is much less than the acceleration of the bullet.

Impulse

When a force F acts on a body for a small time-interval Δt, then the product of the force and the time interval is called the impulse of the force.

Impulse = F x Δt

Impulse is a vector quantity. Its unit is newton second or kg m/sec.

Conservation of Momentum

According to this law, if two or more objects collide with each other, their total momentum remains conserved before and after the collision provided there is no external force acting on them.

From the Newton’s laws of motion, the rate of change of momentum is equal to the force.

If p1 = initial momentum and p2 = final momentum after time t, then

F = (p2 - p1)/t

Now, if F = 0, then p1 = p2

Thus, the momentum of a system remains unchanged (or conserved) if no force is acting on it.

Contact and Non-Contact Forces

Contact Forces: Muscular Force, Friction

Non-Contact Forces: Magnetic Force, Electrostatic Force, Gravitational Force

Friction

A ball rolling around the ground gradually slows down and finally comes to rest. It is the force of friction between the surface of the ball and the ground that brings the moving ball to rest.

Friction exists between the surfaces of all materials which are in contact with each other. The force of friction always acts on all the moving objects and its direction is always opposite to the direction of motion. Since the force of friction arises due to contact between surfaces, it is an example of a contact force.

The substances which reduce friction are called lubricants. In some machines, it may not be advisable to use oil as lubricant. An air cushion between the moving parts is used to reduce friction.

Increasing and Reducing Friction

For a given pair of surfaces friction depends upon the state of smoothness of those surfaces. Friction depends on how hard the two surfaces press together.

Friction can be increased by making a surface rough. The sole of the shoes and the tyres of the vehicle are treaded to increase friction.

When one body rolls over the surface of another body, the resistance to its motion is called the rolling friction. Rolling reduces friction. It is always easier to roll than to slide a body over another. That is the reason it is convenient to pull the luggage fitted with rollers. Since the rolling friction is smaller than the sliding friction, sliding is replaced in most machines by rolling by the use of ball bearings. Common examples are the use of ball bearings between hubs and the axles of ceiling fans and bicycles. Fluid friction can be minimised by giving suitable shapes to bodies moving in fluids.

Static and Sliding Friction

Static friction comes into play when you try to move an object at rest. Sliding friction comes with play when an object is sliding over another. Sliding friction is smaller than static friction.

The resistive force, before the body starts moving on a surface is called static friction. Once a body starts moving on a surface the friction between them is called sliding or kinetic friction. The kinetic friction is slightly less than the static friction.

Coefficient of Friction

The ratio of the force of limiting friction F and normal reaction R between the two surfaces in contact is called the coefficient of friction μ.

μ = F/R

Angle of Friction

It is the angle between the normal reaction R and the resultant of limiting friction F and the normal reaction.

Work

If on applying a force on a body, the body is displaced, then work is said to be done. This work is equal to the product of force and displacement of the body in the direction of force.

Work = Force x Displacement

Work is a scalar quantity. Its unit is joule.

1 joule = 1 newton x 1 metre or joule = newton-metre

If the displacement (d) of the body is at an angle (θ) with the direction of force (F), then work done

W = F.d cosθ

In the force-displacement graph, the area enclosed by the force-displacement curve represents the work done by a variable force.

Power

The rate of doing work by a body is called its power. The unit of power is joule/second or watt.

1 watt = 1 joule/second

1 Horse power (H.P.) = 746 watt

Power = F.d/t = Force x Velocity

Energy

The total capacity of doing work by a body is called its energy. It is a scalar quantity. Its unit is joule.

1 watt hour = 3600 joule

1 kilowatt hour = 3600 x 1000 joule = 3.6 x 106 joule

Kinetic Energy

The energy possessed by a body by virtue of its motion is called its kinetic energy.

K = ½mv2

Potential Energy

It is the energy stored in a body by virtue of its position of state.

Gravitational potential energy, U = mgh

Law of Conservation of Energy

The magnitude of the total energy of a physical system always remains constant. Only one form of energy is transformed into the other form of energy but it can neither be created nor destroyed. The total energy of the universe remains constant.

Einstein's Mass-Energy Relation

If mass m is converted into energy, the energy obtained will be

E = mc2

where c is the speed of light

Thrust and Pressure

The force acting upon the surface of a body perpendicular to it is called thrust. The thrust on unit area is called pressure. The SI unit of pressure is Nm-2.

The force acting on a unit area of a surface is called pressure.

Pressure = Force / Area 

The area is in the denominator in the above expression. So, the smaller the area, larger the pressure on a surface for the same force. That is why shoulder bags are provided with broad straps and not thin strap. The tools meant for cutting and piercing always have sharp edges.