06. Short and Long Answer Questions: How Forces Affect Motion

Short Answer Type Questions

Ques 1: What is force? State its SI unit and explain why force is called a vector quantity.

Ans: A force is a physical quantity that can make an object move from rest, change the speed and direction of motion of a moving object, and even change the shape of an object.

The SI unit of force is newton (written with a small ‘n’), and its symbol is N. One newton is defined as the force that produces an acceleration of $1{\text{ m s}}^{-2}$ on an object of mass $1\text{ kg}$.

Force is a vector quantity because we need to specify both its magnitude (strength) and its direction to fully describe it – just like position, displacement, velocity, and acceleration. If either the magnitude or direction of a force changes, the effect of the force also changes.

Ques 2: Distinguish between balanced and unbalanced forces. Give one example of each from daily life.

Ans: Balanced forces are two forces that are equal in magnitude but opposite in direction, acting on the same object. The net force on the object is zero, and the object does not accelerate – it either remains at rest or continues moving with constant velocity.
Example: In a tug-of-war where both teams pull with equal force, the rope does not move – the forces are balanced.

Unbalanced forces occur when the forces acting on an object are not equal, producing a non-zero net force. This net force causes the object to accelerate in the direction of the larger force.
Example: When one team in a tug-of-war pulls harder, the rope moves in the direction of the larger force – the forces are unbalanced.

Ques 3: Two forces of 15 N and 9 N act on a block. Find the magnitude and direction of the net force when (i) both forces act in the same direction, (ii) both forces act in opposite directions.

Ans: (i) Both forces in the same direction:

Net force $=15\text{ N}+9\text{ N}=24\text{ N}$

Direction: along the direction of both forces.

(ii) Both forces in opposite directions:

Net force $=15\text{ N}-9\text{ N}=6\text{ N}$

Direction: along the direction of the larger force, i.e., in the direction of the 15 N force.

Note: When forces act in opposite directions, the net force equals the difference of the two magnitudes and acts in the direction of the larger force.

Ques 4: What is the force of friction? In which direction does it act on a moving object? How does the nature of the surface affect the force of friction?

Ans: The force of friction is a force that arises between two surfaces in contact when one object moves or tends to move over another. It opposes relative motion between the surfaces.

Direction: The force of friction always acts in the direction opposite to the direction of motion of the object. For example, when a box is pushed forward on the floor, friction acts backward on the box.

Effect of surface nature: The force of friction depends on the nature of the surfaces in contact. A rougher surface (like a cemented floor) exerts a larger force of friction than a smoother surface (like a polished marble floor). This is why an object travels a larger distance on a smooth surface and a shorter distance on a rough surface before coming to rest, when given the same initial push.

Ques 5: State Newton’s first law of motion. What does it tell us about the motion of an object when the net force acting on it is zero? Give one example.

Ans: Newton’s First Law of Motion: An object at rest remains at rest and an object in motion continues to move with a constant velocity, unless a net force acts upon the object.

When net force is zero: If the net force acting on an object is zero, the object cannot begin to move (if at rest) and cannot change its velocity (if already moving). Its acceleration is zero. Constant velocity means there is no change in either the magnitude or the direction of velocity.

Example: A person pushes a box on a floor with a force exactly equal to the force of friction opposing the motion. The two forces are equal and opposite, so the net force is zero, and the box moves with constant velocity – it neither speeds up nor slows down.

Ques 6: What is inertia? Who introduced this concept? Explain how Newton’s first law of motion is also called the law of inertia.

Ans: Inertia is the tendency of an object to resist any change in its state of rest or uniform motion. In other words, an object at rest tends to stay at rest and an object in motion tends to remain in motion with the same velocity, unless acted upon by an external net force.

The word ‘inertia’ was introduced by Isaac Newton to describe this property of objects. Galileo Galilei had earlier argued through thought experiments that a body moving on a frictionless horizontal surface would continue to move indefinitely, foreshadowing this idea.

Newton’s first law is called the law of inertia because it describes the natural behaviour of objects in the absence of a net force – they continue in their existing state (rest or uniform motion) due to their inertia. A net force is required to overcome inertia and change the state of motion of an object.

Ques 7: State Newton’s second law of motion. Write the mathematical expression relating force, mass, and acceleration. Define one newton using this expression.

Ans: Newton’s Second Law of Motion: When a net force acts on an object, the object accelerates in the direction of the net force. The magnitude of the acceleration is proportional to the magnitude of the net force and is inversely proportional to the mass of the object.

Mathematical expression:

$$a=\frac{F}{m}\text{or}F=ma$$

where $F$ = net force (in N), $m$ = mass of the object (in kg), and $a$ = acceleration ${\text{(in m s}}^{-2}\text{)}$. The direction of acceleration is the same as the direction of the net force.

Definition of one newton: One newton is the force that produces an acceleration of $1{\text{ m s}}^{-2}$ in an object of mass $1\text{ kg}$.

$$1\text{ N}=1\text{ kg}\times 1{\text{ m s}}^{-2}=1{\text{ kg m s}}^{-2}$$

Ques 8: A student pushes a stationary block of mass 20 kg on a horizontal floor. The maximum force of friction is 40 N. Find the acceleration of the block if the student applies a force of (i) 40 N and (ii) 50 N in the forward direction.

Ans: (i) Applied force = 40 N:

Net force $=40\text{ N}-40\text{ N}=0\text{ N}$

The forces are balanced, so acceleration $=0{\text{ m s}}^{-2}$.

The block remains stationary.

(ii) Applied force = 50 N:

Net force $=50\text{ N}-40\text{ N}=10\text{ N}$

Using Newton’s second law: $a={\displaystyle \frac{F}{m}}={\displaystyle \frac{10\text{ N}}{20\text{ kg}}}=0.5{\text{ m s}}^{-2}$

The block accelerates at $0.5{\text{ m s}}^{-2}$ in the forward direction.

Ques 9: What is the gravitational force? Write the expression for the gravitational force acting on an object of mass m. What is the value of g near the surface of the Earth?

Ans: The gravitational force is the force with which the Earth attracts every object towards itself. When an object falls freely under the influence of this force, the acceleration involved is called the acceleration due to gravitational force by the Earth, denoted by $g$.

Using Newton’s second law $(F=ma)$, the gravitational force acting on an object of mass $m$ is:

$$F=mg$$

The value of $g$ near the surface of the Earth is $g=9.8{\text{ m s}}^{-2}$. For quick estimations, $g$ is taken as $10{\text{ m s}}^{-2}$.

Unlike force, the acceleration due to gravity does not depend on the mass of the object – all objects, regardless of their mass, experience the same gravitational acceleration near the Earth’s surface.

Ques 10: State Newton’s third law of motion. Explain with the help of the example of a canoeist rowing a boat why the two forces in Newton’s third law do not cancel each other.

Ans: Newton’s Third Law of Motion: Whenever one object is exerting a force on a second object, the second object is simultaneously exerting an equal and opposite force on the first object.

Example – Canoeist rowing a boat: When the canoeist pushes the water backwards with the paddle, the water pushes the paddle (and canoe) forward with an equal force. These two forces are equal in magnitude but act on two different objects – one force acts on the water and the other acts on the paddle and canoe.

Why they do not cancel: Forces can cancel each other only if they act on the same object. Since the action-reaction forces in Newton’s third law always act on two different objects, they cannot cancel each other. The net force on the canoe is the forward force from the water, which accelerates the canoe forward.

Ques 11: Explain how Newton’s second law of motion is used to explain why a fielder in cricket pulls their hands backwards while catching a fast-moving ball.

Ans: When a fielder catches a fast-moving cricket ball, the ball has a high velocity that must be reduced to zero. The change in velocity of the ball produces acceleration (deceleration in this case).

By pulling the hands backwards with the ball just after catching it, the fielder increases the time duration over which the ball’s velocity changes from a high value to zero. From Newton’s second law:

$$F=ma=m\times \frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}$$

Since the change in velocity $(\mathrm{\Delta }v)$ is fixed, increasing the time $(\mathrm{\Delta }t)$ reduces the magnitude of the acceleration $(a)$. A smaller acceleration means a smaller force is required to stop the ball. Applying a smaller force on the moving ball also minimises injury to the fielder’s hands.

The same principle explains why airbags in vehicles and landing mats in high-jump events protect against injury – they increase the time of impact and thereby reduce the force experienced.

Ques 12: What are internal forces and external forces in a system of objects? Two boxes of masses m1 and m2 are connected by a string and pulled by a force F on a frictionless surface. Write the expression for the acceleration of the system.

Ans: When two or more objects are considered together as a system, forces that act between objects within the system are called internal forces, and forces that act on the system from outside are called external forces. Only external forces can change the motion of the system as a whole.

Example: Consider two boxes of masses $m_1$ and $m_2$ connected by a string on a frictionless surface, pulled by an external force $F$. The tension $T$ in the string is the internal force between the two boxes, while $F$ is the external force on the system.

Treating the two boxes and the string as a single system and applying Newton’s second law:

$$a=\frac{F}{\text{mass of the system}}=\frac{F}{m_1+m_2}$$

The system accelerates just like a single object of mass $(m_1+m_2)$. Treating connected objects as a system often simplifies the analysis, highlighting the power of Newton’s laws.

Long Answer Type Questions

Ques 1: State Newton’s second law of motion and derive the mathematical relation F=ma. Using this relation, explain with a solved example how force, mass, and acceleration are related. (Take g=9.8 m s−2.)

Ans: Newton’s Second Law of Motion: When a net force acts on an object, the object accelerates in the direction of the net force. The magnitude of the acceleration is proportional to the magnitude of the net force and is inversely proportional to the mass of the object.

Derivation of F=ma:

1. For an object of fixed mass $m$, experiments show that if the net force is increased, the acceleration increases proportionally:$$a\propto F\text{(for constant }m\text{)}$$
2. For the same net force $F$, if the mass is increased, the acceleration decreases:$$a\propto \frac{1}{m}\text{(for constant }F\text{)}$$
3. Combining these two proportionalities:$$a\propto \frac{F}{m}$$
4. Introducing a proportionality constant $k$: $a=k{\displaystyle \frac{F}{m}}$. In SI units, $k=1$, giving:$$F=ma$$

The direction of acceleration is always the same as the direction of the net force $F$. The SI unit of force is the newton (N), where $1\text{ N}=1{\text{ kg m s}}^{-2}$.

Solved Example: A weightlifter holds a barbell steady. The bar has a mass of 10 kg and there are 10 kg weights fixed on each side. How much force is she applying?

Total mass of barbell $=10+10+10=30\text{ kg}$

Gravitational force (downward) $=mg=30\text{ kg}\times 9.8{\text{ m s}}^{-2}=294\text{ N}$

Since the barbell is held steady, net force $=0$.

Therefore, the weightlifter applies $294\text{ N}$ in the upward direction.

Note: The acceleration due to gravity $g$ does not depend on the mass of the object.
Ques 2: State Newton’s third law of motion. Explain with four different examples from daily life how this law operates. Also explain why the Earth does not appear to move when a fruit falls towards it, even though the fruit exerts an equal and opposite force on the Earth.

Ans: Newton’s Third Law of Motion: Whenever one object is exerting a force on a second object, the second object is simultaneously exerting an equal and opposite force on the first object. These forces always occur in pairs and act on two different objects.

Four examples from daily life:

1. Walking: When a person walks, their foot pushes the ground backwards (action). The ground exerts an equal and opposite friction force on the foot in the forward direction (reaction). This reaction force propels the person forward. This is why it is difficult to walk on wet polished floors or ice – the friction (reaction) is very small.
2. Rowing a canoe: The canoeist pushes the water backwards with the paddle (action). The water pushes the paddle and canoe forward with an equal force (reaction). When the canoeist pushes harder, the forward force increases and the canoe moves faster.
3. Rocket propulsion: The rocket engine expels gases downward with a large force (action). The gases exert an equal and opposite force on the rocket in the upward direction (reaction). This upward force accelerates the rocket upward. The same principle explains how an inflated balloon moves forward when air rushes out backward.
4. Kicking a ball: When a player kicks a football, the foot applies a force on the ball (action). The ball simultaneously applies an equal and opposite force on the player’s foot (reaction). This is why the foot may feel an impact upon kicking.

Why does the Earth not appear to move?
The Earth and the fruit apply equal and opposite gravitational forces on each other (Newton’s third law). The force on the fruit causes it to accelerate towards the Earth. However, the Earth has an enormously large mass compared to the fruit. Using Newton’s second law $(a={\displaystyle \frac{F}{m}})$, the acceleration of the Earth caused by the same force is:

$$a_{\text{Earth}}=\frac{F}{m_{\text{Earth}}}$$

Since $m_{\text{Earth}}$ is extremely large (about $6\times 10^{24}\text{ kg}$), $a_{\text{Earth}}$ is so tiny that it is completely undetectable. Thus, the Earth does not seem to move towards the fruit, even though an equal force acts on it.

Ques 3: A sports car of mass 1500 kg is moving towards the east. Its velocity-time graph shows: velocity increases uniformly from 0 m s−1 to 10 m s−1 in the first 5 s, remains constant at 10 m s−1 from 5 s to 10 s, and then decreases uniformly to 0 m s−1 from 10 s to 15 s. Calculate the force acting on the car during each time interval.

Ans: (i) During 0 s to 5 s:

Initial velocity $u=0{\text{ m s}}^{-1}$, final velocity $v=10{\text{ m s}}^{-1}$, time $t=5\text{ s}$

Using $v=u+at$: $10=0+a\times 5$

$a=2{\text{ m s}}^{-2}$ (towards the east)

$F=ma=1500\text{ kg}\times 2{\text{ m s}}^{-2}=3000\text{ N}$ towards the east.

(ii) During 5 s to 10 s:

Velocity is constant, so acceleration $a=0{\text{ m s}}^{-2}$.

$F=ma=1500\times 0=0\text{ N}$

No net force is acting on the car.

(iii) During 10 s to 15 s:

Initial velocity $u=10{\text{ m s}}^{-1}$, final velocity $v=0{\text{ m s}}^{-1}$, time $t=5\text{ s}$

Using $v=u+at$: $0=10+a\times 5$

$a=-2{\text{ m s}}^{-2}$ (i.e., deceleration of $2{\text{ m s}}^{-2}$)

$F=ma=1500\times (-2)=-3000\text{ N}$

The negative sign shows the force acts towards the west (opposite to direction of motion).

Ques 4: Describe in detail the thought experiment suggested by Galileo Galilei that led to the concept of inertia. How did Isaac Newton extend this idea to formulate Newton’s first law of motion? Also explain, with two real-life examples, how continuous application of force is sometimes needed to keep an object moving.

Ans: Galileo’s Thought Experiment:
For many centuries, it was mistakenly believed that a force was required to keep an object moving with a constant velocity. Galileo challenged this view in the 17th century through thought experiments.

Galileo argued: suppose a body moves along a horizontal plane with all impediments to its motion removed (i.e., no friction). In such a case, there is no force opposing the motion. Will the body slow down and stop, or will it continue moving?

Galileo concluded that if all friction and other resistive forces were removed, a body moving on a horizontal surface would continue to move indefinitely with the same velocity – it would never stop on its own. This was a radical departure from the earlier belief.

Newton’s Extension – First Law of Motion:
Isaac Newton used the word inertia to describe this tendency of objects to resist any change in their state of rest or uniform motion. He framed Galileo’s idea into his first law of motion:

An object at rest remains at rest and an object in motion continues to move with a constant velocity, unless a net force acts upon the object.

This law tells us that force is not needed to maintain constant velocity – it is only needed to change the state of motion (i.e., to cause acceleration).

Why continuous force is sometimes needed:
In the real world, friction is always present. When a moving object has friction acting on it in the direction opposite to its motion, the object decelerates and eventually stops. To keep it moving at a constant velocity, we must continuously apply a force just to counteract the friction – not to accelerate the object, but to balance friction so the net force remains zero.

1. Cycling: When you stop pedalling a bicycle, it slows down and comes to rest after travelling some distance. This is because friction (between the tyres and the road) and air resistance act on the cycle. To keep moving at constant speed, you must keep pedalling to balance the friction force.
2. Pushing a box: Once you stop pushing a box on the floor, it stops due to friction. To keep it moving, you must continuously apply a force equal to the friction force so that the net force is zero and the velocity remains constant.

Ques 5: A bullet of mass 50 g is moving with a speed of 100 m s−1 and enters a heavy stationary wooden block. It stops after penetrating a distance of 50 cm. Estimate the stopping force acting on the bullet (assume constant acceleration). Also explain, using Newton’s third law, what force the bullet exerts on the wooden block, and why the block moves but the bullet does not come back out.

Ans: Step 1 – Find the deceleration of the bullet:

Mass of bullet $m=50\text{ g}=0.05\text{ kg}$

Initial velocity $u=100{\text{ m s}}^{-1}$, final velocity $v=0{\text{ m s}}^{-1}$

Distance $s=50\text{ cm}=0.5\text{ m}$

Using $v^2=u^2+2as$:

$0=(100{)}^2+2\times a\times 0.5$

$0=10000+a$

$a=-10000{\text{ m s}}^{-2}$ (deceleration)

Step 2 – Find the stopping force on the bullet:

Using $F=ma$:

$$F=0.05\text{ kg}\times 10000{\text{ m s}}^{-2}=500\text{ N}$$

The wooden block exerts a stopping force of 500 N on the bullet in the backward direction.

Newton’s Third Law – Force on the wooden block:
By Newton’s third law, the bullet exerts an equal and opposite force of 500 N on the wooden block in the forward direction. Since the wooden block is heavy (large mass), the acceleration produced in the block $(a={\displaystyle \frac{F}{m_{\text{block}}}})$ is very small – the block may move only slightly or not at all if fixed.

Why the bullet does not come back out:
The stopping force acts on the bullet only while it is moving forward inside the block. Once the bullet’s velocity reaches zero, there is no longer any net forward force on the bullet. The friction between the bullet and the wood on all sides holds the bullet in place. There is no force to reverse the bullet’s direction, so it remains embedded in the block