NCERT Solutions for Chapter 6: How Forces Affect Motion
Here are the NCERT solutions for Chapter 6: How Forces Affect Motion, with the questions given in the NCERT book and the answers provided in simplified English language.
Revise, Reflect, Refine (Exercise Questions - Page 112)
Question 1. Using a horizontal force F, a table is moved across the floor at a constant velocity. How much is the frictional force exerted by the floor on the table?
Since the table moves at a constant speed, it is not accelerating. This means the net force is zero. Therefore, the frictional force must be exactly equal to the applied force F, but acting in the opposite direction.
Question 2. For a ball moving on a smooth, frictionless surface, choose the appropriate option that will make the following statements physically correct.
(i) If no net force is applied on the ball, the velocity of the ball will remain the same/increase/decrease.
(ii) If a net force is applied on the ball in the direction of its motion, the magnitude of the velocity of the ball will remain the same increase/decrease.
(iii) If a net force is applied on the ball in a direction opposite to the direction of its motion, the magnitude of the velocity of the ball will remain the same/increase/decrease.
• (i) The velocity will remain the same (objects keep doing what they are doing if no force stops them).
• (ii) The velocity will increase (pushing in the same direction makes it faster).
• (iii) The velocity will decrease (pushing in the opposite direction slows it down).
Question 3. Two blocks P and Q on a smooth horizontal surface are shown in Fig. 6.36a and Fig. 6.36b. Two forces of magnitudes 4 N and 5 N are acting in opposite directions on block P, while block Q is moving with a constant velocity. Which of the following statement is correct?
(i) P experiences a net force, and Q does not experience a net force.
(ii) P does not experience a net force, and Q experiences a net force.
(iii) Both P and Q experience a net force.
(iv) Neither P nor Q experiences a net force.
The correct option is (i). Block P has two different forces (4 N and 5 N) pulling against each other, leaving a leftover (net) force of 1 N. Block Q is moving at a constant speed, which means all forces on it are balanced and there is no net force.
Question 4. While practising for the snake boat race (Valium kaili in Kerala), 100 oarsmen are rowing a boat together. Out of these, 95 row backwards to propel the boat forward. But by mistake, 5 oarsmen row in the opposite direction. If each oarsman applies a horizontal force of 200 N, what is the net force on the snake boat? (Ignore drag forces, air friction, etc.)
Each person pulls with 200 N.
• 95 rowers pushing forward: 95 × 200 = 19,000 N.
• 5 rowers pushing backward: 5 × 200 = 1,000 N.
• Net force: 19,000 - 1,000 = 18,000 N forward.
Question 5. When a net force acts on an object, we observe that the object accelerates:
(i) opposite to the direction of force, with acceleration proportional to the force acting on the object.
(ii) opposite to the direction of force, with acceleration proportional to the mass of the object.
(iii) in the direction of force, with acceleration inversely proportional to the force acting on the object.
(iv) in the direction of force, with acceleration proportional to the force acting on the object.
The correct option is (iv). According to Newton’s second law, an object always speeds up in the same direction you push it, and the harder you push, the more it accelerates.
Question 6. The position-time graph for four objects A, B, C and D moving along a straight line are given in Fig. 6.37. A net force acts on:
(i) Object A
(ii) Object B
(iii) Object C
(iv) Object D
The correct option is (iii) Object C. On this graph, Object C's line is curved, which means its speed is constantly changing. Changing speed requires a net force.
Question 7. A sailor jumps out from a small boat to the shore (Fig. 6.38). As the sailor jumps forward, will the boat move? If yes, in which direction and why?
Yes, the boat will move backward. When the sailor jumps forward, they push the boat away with their feet. Because every action has an equal and opposite reaction (Newton’s third law), the boat is pushed away from the shore.
Question 8. During a high jump event, a landing mat or sand bed is placed for the athlete to fall upon (Fig. 6.39). Explain the reason behind it.
The mat or sand is soft, so it takes more time for the athlete to come to a stop. When you increase the stopping time, the force of the impact becomes smaller and safer, which prevents injuries.
Question 9. A hand cart loaded with vegetables coffides with an identical but empty hand cart. During the collision:
(i) the loaded cart exerts a force of larger magnitude on the empty cart.
(ii) the empty cart exerts a force of larger magnitude on the loaded cart.
(iii) neither cart exerts a force on the other.
(iv) the loaded cart and the empty cart, both exert an equal magnitude of force on each other.
The correct option is (iv). Newton’s third law says that during any collision, both objects hit each other with the exact same amount of force, regardless of their weight.
Question 10. The acceleration-mass graph for the acceleration produced by a force on objects of different masses is plotted in Fig. 6.40. Plot the force-mass graph for this case.
By checking the points on the provided graph (like 1 kg at 10 m/s² or 2 kg at 5 m/s²), and using the formula Force = mass × acceleration, we see that the force is always 10 N. Therefore, the force-mass graph would be a flat, horizontal line at 10 N.
Question 11. The velocity-time graph of an object of mass 10 kg moving along a straight line is shown m Fig. 6.41. Calculate the force acting on the object by using the graph.
• Initial speed (u) = 10, Final speed (v) = 30, Time (t) = 8 seconds.
• Acceleration = (30 - 10) / 8 = 2.5 m/s².
• Force = 10 kg × 2.5 m/s² = 25 N.
Question 12. A bullet of mass 50 g moving with a speed of 100 ms⁻¹ enters a heavy, stationary wooden block and stops after penetrating a distance of 50 cm. Estimate the stopping force acting on the bullet (assume that the bullet undergoes constant acceleration within the block).
• Convert units: mass = 0.05 kg, distance = 0.5 m.
• Using the formula v² = u² + 2as: 0 = 100² + 2 × a × 0.5, which gives an acceleration of -10,000 m/s².
• Force = 0.05 kg × -10,000 = -500 N. The minus sign means it's a stopping force.
Question 13. An ace footballer converted a penalty shot by kicking the football with a speed of 108 kmh⁻¹. The estimated force they imparted was 800 N. The mass of the football was 0.4 kg. Calculate the time of contact between their foot and the ball.
• Convert speed: 108 km/h = 30 m/s.
• Acceleration = Force / Mass = 800 / 0.4 = 2,000 m/s².
• Using v = u + at: 30 = 0 + 2000 × t.
• Time = 30 / 2000 = 0.015 seconds.
Question 14. An object of mass 2 kg moving with a constant velocity of 10 m encounters a rough patch where the force of friction on the object is 7 N. At the same time, an additional constant force of 3 N opposing the motion is applied on the object. After entering the rough patch, how much distance does the object travel before coming to rest?
• Total stopping force = 7 N + 3 N = 10 N.
• Deceleration = 10 N / 2 kg = 5 m/s².
• Using v² = u² + 2as: 0 = 10² + 2 × (-5) × s.
• 10s = 100, so distance (s) = 10 m.
Question 15. A tractor pulls a harrow (a ploughing tool) of mass m₁ with a net force F, resulting in an acceleration of a₁. The same tractor pulls a trolley of mass m₂ with a force F producing an acceleration of a₂. If the tractor now pulls the trolley with the harrow placed on it (with the same force F), then obtain an expression for the resulting acceleration in terms of a₁ and a₂. Ignore friction.
The combined acceleration is found by adding the individual masses. The simplified final formula for the new acceleration is: a = (a₁ × a₂) / (a₁ + a₂).
Question 16. When the pole of a bar magnet is brought close to a magnetic compass, the bar magnet and the compass needle (which is also a magnet) exert a magnetic force on each other. As per Newton’s third law of motion, both the forces are equal in magnitude and opposite in direction. However, the compass needle moves, whereas the bar magnet does not move (Fig. 6.42). Explain why.
Even though the forces are equal, the compass needle has a very tiny mass, so the force is strong enough to make it move easily. The bar magnet is much heavier, so the same force causes such a tiny bit of movement that you can't even see it.
In-Text Questions (Think It Over & Pause and Ponder)
Question 1. Why does a canoe move forward when the canoeist pushes water backwards with their paddle, and why does it move faster when they push harder?
It moves forward because when you push the water back, the water pushes you forward with the same amount of force. If you push harder, you create a bigger force, which makes the boat speed up (accelerate) more.
Question 2. Suppose the same canoeist uses the same paddle force in two different canoes, one empty and one carrying another passenger. In which case will the canoe move faster?
The empty canoe will move faster. Because it has less mass, the same amount of force will make it accelerate much more than the heavy canoe.
Question 3. Is there an underlying cause for a change in position and velocity of an object? What is the nature of this cause? Do all motions require a cause?
Yes, the cause for any change in motion is force (a push or a pull). However, once an object is already moving, it doesn't need a force to keep moving—only to change how it's moving.
Question 4. How can we measure the magnitude of a force? Do you remember using a spring balance earlier to measure the weight of objects? Do you also remember the weight of an object is the gravitational force with which the Earth pulls the object?
We measure force using a spring balance, which tells us the magnitude based on how much the internal spring stretches. Weight is just a specific type of force—the pull of Earth's gravity on an object.
Question 5. In such cases, what is the effect of forces when more than one force is acting on an object at rest or in motion?
The result depends on the net force. If the forces balance each other out, nothing changes. If they don't balance, the object will start moving, stop, or change speed.
Question 6. A weightlifter lifts a barbell (Fig. 6.8). List two forces that are acting on the barbell. Are these forces balanced if the weight lifter keeps the barbell steady?
The two forces are the upward push from the lifter and the downward pull of gravity. If the barbell is staying perfectly still, these two forces are balanced (equal and opposite).
Question 7. Two players, R and S, are participating in an arm-wrestling match (Fig. 6.9). At the instant, when the arms tilt to the front direction (out of the page towards you), are the forces exerted by the players balanced? If not, which player exerted the larger force?
No, they are not balanced. If the arms are tilting, player 'S' is pushing harder (exerting more force) than player 'R'.
Question 8. If the velocity of the block is neither increasing nor decreasing, what can you say about the net force acting on the block? Does the reading of the spring balance indicate the magnitude of the force of friction acting on the wooden block?
If the speed is constant, the net force is zero. In this case, the spring balance reading is exactly the same as the amount of friction, because the two are perfectly balanced.
Question 9. Are the readings different? Is the reading smallest for the surface on which the stack of coins travelled the largest distance? Is the reading largest for which the distance travelled was the smallest?
Yes to all. Friction is different on every surface. The surface with the least friction (smallest reading) allows the coins to travel the farthest. The surface with the most friction (largest reading) stops them the quickest.
Question 10. An object is moving with a constant velocity. Is there a net force acting upon it?
No. If the speed and direction aren't changing, the forces must be perfectly balanced, meaning the net force is zero.
Question 11. Suppose no net force is acting on an object. Which of the following situations are possible? (i) Object remains at rest if at rest. (ii) Object keeps moving with a constant velocity if already moving. (iii) Object is moving with a constant acceleration.
Only (i) and (ii) are possible. Acceleration always requires a net force, so (iii) cannot happen if there is no force.
Question 12. In the real world, it is difficult to find a situation where no forces are acting on an object. But by applying additional forces, a condition can be achieved where the net force on the object is zero. Explain with the help of an example.
In the real world, things like friction are always pushing back. However, if you push a box with the exact same amount of force that friction is using to hold it back, the forces cancel out. The net force becomes zero, and the box moves at a steady, constant speed.
Question 13. But what is the relationship between the net force acting on an object and its acceleration?
The relationship is the formula F = ma (Force = mass × acceleration).
Question 14. A toy car of mass 100 g is moving with a constant velocity of 0.5 ms⁻¹. What is the net force acting on the toy car?
The net force is 0 N because the car is moving at a constant speed and not accelerating.
Question 15. Two children of different masses are sitting on identical swings. To impart identical initial acceleration, for which child would you require to apply a larger force? Explain why.
You need a larger force for the heavier child. Newton’s law says that for the same acceleration, more mass requires more force (F = ma).
Question 16. How are glass items packed for transportation using a bubble wrap or hay protected from damage?
These soft materials increase the time it takes for an impact to happen. By slowing down the impact, the actual force hitting the glass is reduced, which prevents it from breaking.
Question 17. Why is it difficult to walk on wet polished floors or ice, or why it is risky to drive on roads covered with water or snow?
These surfaces are very slippery, meaning there is very little friction to provide a grip for your feet or tires.
Question 18. Why does a firefighter sometimes struggle when holding the pipe issuing water?
When the water shoots forward with great force, it creates an equal and opposite reaction that pushes the pipe backward (recoil). This makes the pipe very hard to keep steady.
Question 19. Suppose a spacecraft is moving in a region of space where the gravitational force acting upon it is negligible. Suggest how it can change its velocity.
The spacecraft can use its engines to shoot gas out of the back. Even in empty space, this action creates a reaction force that pushes the spacecraft forward, allowing it to change speed or direction.
Question 20. How much does a force of 1 N feel?
It feels like holding a 100 g object (like a small apple) in the palm of your hand.