LAWS OF MOTION-QnA

Q1: Define inertia.

Inertia is the tendency of a body to resist any change in its state of rest or of uniform motion in a straight line. The greater the mass, the greater is the inertia of the body.

Q2: State Newton’s first law of motion.

Newton’s first law states that a body remains at rest or in uniform motion in a straight line unless acted upon by an external unbalanced force. This law introduces the concept of inertia.

Q3: Write the mathematical form of Newton’s second law.

Newton’s second law is written as \( \vec{F}_{\text{net}} = m\vec{a} \), where \( \vec{F}_{\text{net}} \) is net external force, \(m\) is mass, and \( \vec{a} \) is acceleration produced in the body.

Q4: What is linear momentum?

Linear momentum of a particle is the product of its mass and velocity, \( \vec{p} = m\vec{v} \). It is a vector quantity directed along the velocity of the particle.

Q5: Define impulse of a force.

Impulse is the product of a large force and the short time interval for which it acts, \( J = F\Delta t \). It is equal to the change in linear momentum of the body.

Q6: State Newton’s third law of motion.

Newton’s third law states that for every action there is an equal and opposite reaction. Action and reaction forces always act on two different interacting bodies.

Q7: What is meant by an external force?

An external force on a system is a force exerted by a body outside the system’s boundary. Only external forces can change the total momentum of the system.

Q8: Define coefficient of kinetic friction.

The coefficient of kinetic friction \( \mu_k \) is the ratio of kinetic friction \( F_k \) to normal reaction \( N \), that is \( \mu_k = F_k/N \). It is dimensionless and depends on the nature of surfaces in contact.

Q9: What is centripetal force?

Centripetal force is the net inward force required to keep a body moving in a circular path of radius \( r \) with speed \( v \). Its magnitude is \( F_c = mv^2/r \) and it is directed towards the centre of the circle.

Q10: Give one example of rolling friction.

When a car tyre rolls over the road, the resistive force opposing its motion is rolling friction. Rolling friction is generally smaller than kinetic friction for the same pair of surfaces.

Q11: State the law of conservation of linear momentum.

The total linear momentum of an isolated system of interacting particles remains constant in time, if no external force acts on the system. Internal forces cannot change the total momentum.

Q12: What is a free-body diagram (FBD)?

A free-body diagram is a simplified sketch of an object showing only the object and all the external forces acting on it. Drawing an FBD helps in applying Newton’s laws systematically.

Q13: Define equilibrium of a particle.

A particle is said to be in equilibrium when the vector sum of all forces acting on it is zero. In this condition, the particle has no acceleration.

Q14: Write the SI unit of force and define it.

The SI unit of force is newton (N). One newton is the force that produces an acceleration of \( 1 \,\text{m s}^{-2} \) in a body of mass \( 1 \,\text{kg} \).

Q15: What is limiting friction?

Limiting friction is the maximum value of static friction just before the body on a surface starts sliding. It equals \( \mu_s N \), where \( \mu_s \) is the coefficient of static friction and \( N \) is normal reaction.

Q1: A force of 20 N acts on a body of mass 5 kg at rest on a frictionless surface. Find the acceleration produced.

Using Newton’s second law, \( a = F/m = 20/5 = 4 \,\text{m s}^{-2} \). The body starts moving in the direction of the applied force with this acceleration.

Q2: A body of mass 3 kg moves with velocity 6 m s\(^{-1}\). Calculate its momentum and state the direction of momentum.

Momentum \( p = mv = 3 \times 6 = 18 \,\text{kg m s}^{-1} \). The direction of momentum is the same as the direction of the velocity vector of the body.

Q3: Distinguish between static and kinetic friction.

Static friction acts when a body is at rest and opposes the initiation of motion, increasing from zero up to a limiting value. Kinetic friction acts when the body is sliding, has nearly constant magnitude, and is usually smaller than the limiting static friction.

Q4: Why is it easier to push a loaded trolley after it has started moving than to start it from rest?

To start motion, the applied force must overcome limiting static friction, which is relatively large. Once the trolley is in motion, only kinetic friction, which is smaller, needs to be balanced, so a smaller force is sufficient.

Q5: State two differences between mass and weight.

Mass is the amount of matter in a body, is scalar, and remains constant everywhere, measured in kilograms. Weight is the gravitational force on the body, is vector, depends on local acceleration due to gravity, and is measured in newtons.

Q6: A 2 kg block is pulled on a horizontal frictionless table by a force of 10 N making an angle of \( 60^\circ \) with the horizontal. Find the horizontal component of the force and the acceleration.

Horizontal component \( F_x = 10\cos60^\circ = 5 \,\text{N} \). Acceleration \( a = F_x/m = 5/2 = 2.5 \,\text{m s}^{-2} \) along the table.

Q7: Explain why passengers tend to fall forward when a moving bus stops suddenly.

When the bus stops abruptly, the lower parts of passengers’ bodies in contact with the bus decelerate quickly. Due to inertia of motion, the upper parts continue to move forward, so passengers appear to fall forward.

Q8: A body of mass 0.5 kg experiences a change in velocity from 4 m s\(^{-1}\) to 10 m s\(^{-1}\) in 3 s. Find the average force acting on it.

Change in momentum \( \Delta p = m(v - u) = 0.5(10 - 4) = 3 \,\text{kg m s}^{-1} \). Average force \( F = \Delta p/\Delta t = 3/3 = 1 \,\text{N} \) in the direction of motion.

Q9: Why does a cyclist lean inward while taking a turn on a circular track?

During turning, the needed centripetal force is provided by the horizontal component of the normal reaction between tyres and road. By leaning inward, the cyclist aligns the resultant of weight and normal reaction towards the centre, preventing toppling.

Q10: Briefly explain why seat belts are important in cars using Newton’s laws.

In a sudden stop, the car’s body decelerates quickly, but the passengers’ bodies tend to continue forward because of inertia. A properly fastened seat belt provides a restraining force over a short distance, reducing acceleration and the risk of injury.

Q1: State and explain Newton’s first law of motion with an everyday example.

Newton’s first law states that a body continues in its state of rest or uniform straight-line motion unless acted upon by an external unbalanced force. For example, when a bus at rest suddenly starts, passengers tend to fall backward because their bodies tend to remain at rest while the bus moves forward; the backward fall is due to inertia of rest. This law justifies why a book lying on a table remains there indefinitely until someone applies a force to move it.

Q2: Show that impulse is equal to change in momentum and state one situation where impulse is useful.

Let a constant force \( F \) act on a body for a short time \( \Delta t \), producing acceleration \( a \). From Newton’s second law, \( F = \Delta p/\Delta t \), where \( \Delta p \) is change in momentum. Rearranging gives \( F\Delta t = \Delta p \); the left side is defined as impulse \( J \). Hence impulse equals the change in momentum produced. In sports like cricket, a fielder moves hands backward while catching a fast ball so that the time of impact increases, reducing the average force even though the impulse and momentum change remain the same.

Q3: Explain the terms static friction, kinetic friction and rolling friction.

Static friction acts between two surfaces in contact when there is no relative motion; it adjusts up to a limiting value to oppose impending motion. Kinetic friction acts when surfaces slide over each other and usually has a nearly constant value smaller than limiting static friction. Rolling friction arises when a body such as a wheel or ball rolls over a surface and is typically much smaller than kinetic friction, which is why vehicles use wheels to move efficiently.

Q4: What is centripetal force? Derive its expression for a body of mass \( m \) moving with speed \( v \) in a circle of radius \( r \).

When a body moves in a circular path at constant speed, its velocity continuously changes direction, so an inward acceleration called centripetal acceleration acts on it. For uniform circular motion, this acceleration has magnitude \( a_c = v^2/r \) directed towards the centre. Using Newton’s second law, the required inward or centripetal force is \( F_c = ma_c = mv^2/r \). This force may be provided by tension in a string, friction between tyres and road, or other interactions depending on the situation.

Q5: Explain the law of conservation of linear momentum for a system of two interacting bodies with one example.

Consider two bodies that exert equal and opposite internal forces on each other according to Newton’s third law. These internal forces produce equal and opposite changes in their momenta, so the vector sum of their momenta remains constant as long as no external force acts on the system. For instance, when a gun fires a bullet, the bullet gains forward momentum and the gun gains an equal backward momentum (recoil); the total momentum of gun plus bullet just before and just after firing remains the same.

Q1: Describe in detail the different kinds of friction and discuss their advantages and disadvantages in daily life.

Friction is a resistive force that opposes the relative motion or tendency of motion between two surfaces in contact. Static friction acts when there is no relative motion and adjusts itself from zero up to a limiting value, preventing sliding until the applied force exceeds this limit. Kinetic or sliding friction comes into play once motion has started; its magnitude is nearly constant and is usually slightly less than the limiting static friction for the same pair of surfaces. Rolling friction occurs when one body rolls over another, as in wheels or ball bearings, and is the smallest of the three because there is less microscopic interlocking of surface irregularities. Friction is useful because it enables walking without slipping, allows vehicles to move and stop, and helps us hold objects firmly. However, it also has disadvantages: it causes wear and tear of machine parts, produces unwanted heating, and wastes energy, so lubrication and smooth bearings are often used to reduce excessive friction while retaining enough grip for safe operation.

Q2: Discuss the motion of a car on a level circular road and explain the role of friction and speed limits using Newton’s laws.

When a car moves on a level circular road, it must experience an inward centripetal force to stay on the curved path. This inward force is provided by the horizontal component of static friction between the tyres and the road; if this friction is insufficient, the tyres will skid outward and the car will leave the circular track. As the speed of the car increases, the required centripetal force \( mv^2/r \) increases rapidly because it is proportional to the square of speed, while the maximum available frictional force is limited by \( \mu_s N \), where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal reaction. Therefore, for a given road and weather condition, there is an upper speed beyond which friction cannot supply the required centripetal force, which is why speed limits are imposed on sharp turns, especially when the road is wet or covered with sand. Drivers who understand this connection between friction and centripetal force intuitively slow down on curves to avoid skidding.

Q3: Explain with reasoning why a rocket can move forward in space where there is no air, using Newton’s laws of motion.

A rocket carries fuel that, when burnt, ejects exhaust gases at very high speed backward through its nozzle. According to Newton’s third law, the backward momentum of the exhaust gases is accompanied by an equal and opposite forward momentum of the rocket, so the rocket experiences a forward thrust force. Since space is nearly free of external forces like air resistance and friction, the rocket and exhaust gases together form an almost isolated system, and the law of conservation of linear momentum applies. The continuous ejection of gases keeps increasing the forward momentum and speed of the rocket even though there is no surrounding medium to “push against”, which is often misunderstood in everyday thinking.

Q4: Describe how seat belts and airbags in cars reduce injuries during collisions using the concept of impulse and Newton’s second law.

In a collision, the velocity of a car and its occupants changes rapidly, leading to a large change in momentum in a very short time. The impulse experienced by an occupant is fixed by this momentum change, but the average force can be reduced if the time over which the change occurs is increased. Seat belts restrain the body and stretch slightly, and airbags inflate to provide a soft, cushioning surface that compresses as the body moves forward. This combination increases the duration of impact from a few milliseconds to a slightly longer period, so by Newton’s second law the average force \( F = \Delta p/\Delta t \) becomes smaller. As a result, the deceleration of the body is less severe and the risk of serious injury to the chest, head, and neck is greatly reduced, which is why modern safety standards insist on proper use of these devices.

Q5: Using an example of a person walking, explain how Newton’s third law and friction together make forward motion possible.

When a person walks, each foot pushes the ground backward with a certain horizontal force at every step. According to Newton’s third law, the ground simultaneously exerts an equal and opposite horizontal reaction force on the foot, directed forward. This forward reaction force, provided by static friction between the shoe and the ground, accelerates the person’s body and produces forward motion. If the surface is extremely smooth or oily, the coefficient of static friction becomes very small, so the necessary reaction force cannot be generated and the person slips instead of walking steadily. Thus, comfortable walking depends on having enough friction so that the action–reaction pair can effectively propel the body forward.