CBSE Class 8 Science Advanced Physics Force Notes Set 01

Force

1.1 Force

Definition

A force is a push or a pull. When it acts on a body it can change, or try to change, the body's state of rest or of uniform motion, its direction of motion, or its shape.

Mathematical form

The size of a force equals mass times acceleration: F = ma. The acceleration is the rate at which velocity changes:

\[ a = \frac{v-u}{t} = \frac{\text{final velocity} - \text{initial velocity}}{\text{time}} \]

Units of force

SI unit (newton). Using kg for mass and m/s² for acceleration, force is measured in kg m/s², which is called the newton (N). One newton is the force that gives a mass of 1 kg an acceleration of 1 m/s².

CGS unit (dyne). Using g and cm/s², force is measured in g cm/s², called the dyne. One dyne is the force that gives a mass of 1 g an acceleration of 1 cm/s².

Newton and dyne. 1 N = 1 kg × 1 m/s² = 1000 g × 100 cm/s² = 100000 g cm/s². So 1 N = 10⁵ dyne.

Effects of force

We cannot see a force; we recognise it by what it does. A force can do four things.

1. Make a stationary object move. A push on a book, a pull on a chair or a push on a handcart sets it moving. A force does not always manage this: a single student, or even the whole class, cannot move the classroom wall because their push is too small.
2. Stop a moving object or slow it down. Pulling a cycle back from behind slows it. Brakes stop a cycle, we use force to halt ourselves while running, and a fielder stops a cricket ball by pushing against its motion.
3. Change the direction of a moving object. A bat changes both the speed and the direction of a ball; a footballer redirects the ball with the foot; a rider turns a cycle by pushing the handle.
4. Change the shape of an object. A pulled spring stretches, a pressed ball or a crumpled sheet of paper is deformed.

The picture shows a spring at rest and the same spring stretched when forces pull on its two ends.

Balanced and unbalanced forces

Several forces can act on one object together. If they do not change its state of rest, its uniform motion or its direction, they are balanced forces. Examples: a person holding a briefcase, a book lying on a table, a lemon being squeezed. In the tug of war below, both sides pull with 300 N, so the rope stays where it is.

If the forces do change the state of rest or motion, or the direction, they are unbalanced forces. Examples: a briefcase let go from the hand, or a stone dropped. In the second tug of war the left side pulls with 400 N and the right side with 300 N, so the rope moves towards the stronger side.

Resultant force

When many forces act on an object, the single force that would produce exactly the same change in its motion is called their resultant force. For example, several people pushing a big almirah can be replaced by one person pushing with the resultant force.

Two forces in the same direction: the resultant is their sum. Two forces in opposite directions: the resultant is their difference, in the direction of the larger one. The three cases are shown below.

Types of force

Forces are grouped into contact forces and non-contact forces.

Contact forces

A contact force acts on a body only while the body touches the object that exerts it. The three kinds are normal force, force of friction and muscular force.

Normal force. When two bodies touch, the force between them that acts perpendicular to the surface of contact is the normal force. A book on a table is pushed up by the table, and it pushes the table down, both at right angles to the surface. For the book at rest, N = W = mg.

Force of friction. Two surfaces in contact can also exert forces along the surfaces. This is friction. It always opposes the relative motion of the object.

Muscular force. The force we apply with the muscles of our body, such as pulling, pushing or kicking, is muscular force. It is a contact force, since the body must touch what it pushes or pulls.

Non-contact forces

A non-contact force acts on a body without the object exerting it touching the body. The three kinds are gravitational, electrostatic and magnetic force.

Gravitational force. Every object in the universe attracts every other object. This mutual attraction is the force of gravitation, and it acts even when the objects are not connected in any way. It is noticeable only when at least one object is very massive, because for small masses it is tiny. Between any two particles of the universe it is called gravitation or gravitational force.

Force of gravity (weight). The earth pulls every body towards its centre. This force is the weight of the body, also called force of gravity, and it acts vertically downwards. For mass m and acceleration due to gravity g, weight = mg. The value of g is 9.8 m/s². In problems, g is taken positive for a body moving downward and negative for a body moving upward.

Gravitational units of force. Since the weight of a mass m is mg, we can define units of force from it.

1. In the MKS system the unit is the kilogram force (kgf): the pull of gravity on a 1 kg mass. 1 kgf = 1 kg × g = g newton = 9.8 N.
2. In the CGS system the unit is the gram force (gf): the pull of gravity on a 1 g mass. 1 gf = 1 g × g = g dyne = 980 dyne (as g = 980 cm/s²).
3. 1 kgf = 1000 gf. As an approximation, 1 kgf ≈ 10 N, so 1 N = 0.1 kgf = 100 gf.

Spring balance. A spring balance measures the force acting on an object. A coiled spring stretches when a force is applied, and a pointer moving over a scale shows how much it stretches. The reading on the scale gives the size of the force.

Mass and weight compared.

Electrostatic force. The force a charged body exerts on another charged or uncharged body is electrostatic force. A plastic comb rubbed with silk becomes charged and can pick up small bits of paper. It acts from a distance, so it is non-contact, and a charged body can attract or repel another charged body. It is used in factories to remove solid pollutant particles from smoke.

Magnetic force. A magnet attracts objects of iron, steel, nickel and cobalt, such as iron filings and nails. Magnets attract or repel other magnets. This force acts from a distance, so it is also non-contact.

Solved Examples

Illustration 1.1. A force produces an acceleration of 5.0 cm/s² in a body of mass 20 g. Find the force acting on the body in newton.
Answer:
a = 5 cm/s² = 0.05 m/s² and m = 20 g = 0.02 kg.
F = ma = 0.05 × 0.02 = 10⁻³ N.

Illustration 1.2. A force of 15 N acts on a body of mass 5 kg for 2 s. What is the change in velocity of the body?
Answer:
a = F ÷ m = 15 ÷ 5 = 3 m/s².
Change in velocity v − u = at = 3 × 2 = 6 m/s.

Illustration 1.3. Find the weight of an object of mass 25 kg in newton, dyne, kgf and gf. (g = 10 m/s²)
Answer:
Weight W = mg = 25 × 10 = 250 N.
In dyne: 250 × 10⁵ = 2.5 × 10⁷ dyne.
In kgf: 250 ÷ 10 = 25 kgf (1 kgf = 10 N).
In gf: 25 × 1000 = 25000 gf (1 kgf = 1000 gf).

Add to Your Knowledge

1. The idea of force comes from pushing, pulling or hitting an object.
2. Balanced forces on a moving body leave it moving in the same direction at the same speed. Moving with constant velocity needs no net external force.
3. The SI unit of force is the newton (N), equal to kg m s⁻². A force of 1 N gives an acceleration of 1 m s⁻² to a mass of 1 kg.
4. An unbalanced force on a body at rest sets it moving in the direction of that force. On a moving body it changes the velocity, that is, it speeds up or slows down the body.
5. Only four fundamental forces are known in nature: gravitational, electromagnetic, weak and strong. Weak forces appear in radioactivity, and strong forces hold the nucleus of an atom together.
6. All other forces, such as friction and muscular force, come from the fundamental ones. At the atomic scale they arise mainly from the electrical attraction and repulsion between the electrons and nuclei of the atoms.

Summary

1. Force is a push or a pull that changes or tries to change the state of rest or uniform motion, the direction or the shape of a body; F = ma.
2. Forces that produce no change are balanced forces.
3. Forces that produce a change are unbalanced forces.
4. A contact force perpendicular to the touching surfaces is the normal force.
5. Muscular force is the force we apply using our muscles; it is a contact force.
6. A non-contact force acts without touching.
7. Gravitation is the attraction between any two objects.
8. The pull of the earth on a body is its weight or force of gravity.
9. The force of gravity on a mass m is F = mg.
10. A charged body exerts an electrostatic force on other bodies.

Concept Map

1. Types of force are balanced and unbalanced forces (for example, 100 N against 100 N on a truck is balanced, while 100 N against 60 N is unbalanced and the truck moves towards the larger force).
2. Contact forces: normal force (the table pushes the book up, the book pushes the table down), frictional force and muscular force.
3. Non-contact forces: magnetic force (like poles repel, unlike poles attract), electrostatic force (a charged comb attracts paper bits) and gravitational force.