CBSE Class 10 Physics Force and Laws of Motion Notes Set 06

Force and Its Effects

A force is a push or a pull that can change the speed or direction of a body, or change its shape and size. It is a vector quantity: it has both magnitude and direction. SI unit is the newton (N); in CGS it is the dyne, and 1 N = \( 10^5 \) dyne.

1. Forces in the same direction add; forces in opposite directions subtract. The combined effect is the net (resultant) force.
2. Contact forces need touching: muscular force, friction, tension in a string, normal force.
3. Non-contact forces act at a distance: gravitational, magnetic and electrostatic force.
4. Balanced forces have zero resultant: a body at rest stays at rest, and a moving body keeps its uniform velocity.
5. An unbalanced force changes the velocity, that is, produces an acceleration.

Inertia and Newton's First Law

Inertia is the property of a body to resist any change in its state of rest or of uniform motion in a straight line. Mass is its measure: the greater the mass, the greater the inertia. The first law says a body keeps its state unless an unbalanced external force acts on it.

1. Inertia of rest: a body at rest tends to stay at rest (dust falls from a beaten carpet).
2. Inertia of motion: a moving body tends to keep moving (passengers lurch forward when a bus brakes).
3. Inertia of direction: a body tends to keep its direction (passengers feel thrown outward on a sharp turn).

Momentum and Newton's Second Law

Linear momentum is the product of mass and velocity, \( p = mv \), a vector in the direction of the velocity. SI unit: kg m/s. The second law says the rate of change of momentum is proportional to the applied force and takes place in the direction of the force:

\( F = \dfrac{m(v-u)}{t} = ma \)

1. For a given force, acceleration is inversely proportional to mass: \( a_2/a_1 = m_1/m_2 \).
2. 1 newton is the force that gives a 1 kg mass an acceleration of 1 m/s\( ^2 \).
3. For a fixed change of momentum, a longer time means a smaller force. This is why a cricketer draws his hands back while catching and why fragile goods are packed in soft material.

Impulse

Impulse is force multiplied by the time for which it acts, and equals the change in momentum: \( J = Ft = \Delta p = m(v-u) \). Its unit is N s. The area under a force-time graph gives the impulse, counting areas below the time axis as negative.

Newton's Third Law

When one body exerts a force on another, the second exerts an equal and opposite force on the first: \( F_{AB} = -F_{BA} \). The pair acts on two different bodies, so the forces never cancel each other.

1. Walking: we push the ground backward and the ground pushes us forward.
2. Gun recoil: the gun is pushed back as the bullet goes forward; the heavy gun gets a much smaller speed.
3. Rocket and balloon: the expelled gas goes one way and the vehicle moves the other way.
4. A boat moves away from the shore when a person walks towards it.

Conservation of Momentum

If no external force acts on a system, its total momentum stays constant. Useful forms:

Connected Bodies and Lifts

1. Two masses pulled by force F on a smooth surface, joined by a string: \( a = \dfrac{F}{m_1+m_2} \), tension \( T = \dfrac{m_2F}{m_1+m_2} \) in the string pulling \( m_2 \).
2. Atwood machine: \( a = \dfrac{(m_2-m_1)g}{m_1+m_2} \), \( T = \dfrac{2m_1m_2g}{m_1+m_2} \).
3. Lift at rest or moving uniformly: apparent weight = mg.
4. Lift accelerating up: apparent weight = \( m(g+a) \); accelerating down: \( m(g-a) \); falling freely: zero.

Friction

Friction is a force along the surfaces in contact that opposes relative motion, caused by microscopic irregularities. It depends on the nature of the surfaces and the force pressing them together, and, for hard surfaces, not on the area of contact.

1. Static friction acts on a body at rest and adjusts itself to the applied force up to a maximum: \( f_s \le \mu_s N \). The maximum value is the limiting friction.
2. Sliding (kinetic), rolling, air and fluid friction are other kinds; rolling friction is smaller than sliding friction.
3. Friction is a necessary evil: it wears machine parts and wastes energy as heat, but it makes walking, braking and gripping possible.
4. Friction is increased by grooved soles and tyre treads, and reduced by lubricants and smooth surfaces.

Worked Examples

Example 1. A 1500 kg car is stopped with a retardation of 1.7 m/s\( ^2 \). The force needed is \( 1500 \times 1.7 = 2550 \) N, opposite to the motion.

Example 2. A 0.15 kg ball moving at 12 m/s is hit back at 20 m/s. The impulse is \( 0.15 \times (20+12) = 4.8 \) N s; if the contact lasts 0.02 s the average force is 240 N.

Example 3. A 100 kg gun fires a 0.02 kg shell at 80 m/s. The recoil speed is \( 0.02 \times 80/100 = 0.016 \) m/s.