How Forces Affect Motion — Complete Q&A
Think It Over · Pause and Ponder · Revise, Reflect, Refine · The Journey Beyond · The Quest Continues
Think It Over
Q1. 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?
Answer:
When the canoeist pushes water backwards with the paddle, the water pushes the paddle forward with an equal and opposite force (Newton's third law). This forward force on the paddle makes the canoe move forward. When the canoeist pushes harder, the backward force on water is larger, so the forward force on the paddle is also larger, resulting in a greater net force and higher acceleration, making the canoe move faster.
Q2. 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?
Answer:
The empty canoe will move faster. According to Newton's second law (F = ma), for the same force, acceleration is inversely proportional to mass. The empty canoe has less mass than the canoe carrying another passenger, so it will have greater acceleration and move faster.
Pause and Ponder
Q1. A weightlifter lifts a barbell (Fig. 6.8). List two forces that are acting on the barbell. Are these forces balanced if the weightlifter keeps the barbell steady?
Answer:
Two forces acting on the barbell:
- Gravitational force (weight): Acting downwards due to Earth's pull.
- Force applied by the weightlifter: Acting upwards to hold the barbell.
If the weightlifter keeps the barbell steady, the barbell is at rest (or moving with constant velocity). This means the forces are balanced – the upward force equals the downward force (weight).
Q2. 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?
Answer:
When the arms tilt to the front direction (towards you), the forces are not balanced. The arms are moving in that direction, so there is a net force in that direction. The player whose force is being overcome (the one being pushed) is the one who applied the smaller force. The player pushing towards you exerted the larger force.
If the arms are tilting towards you, Player S (assuming S is on the side being pushed) is exerting the larger force.
Q3. An object is moving with a constant velocity. Is there a net force acting upon it?
Answer:
No, there is no net force acting on the object. According to Newton's first law of motion, an object moving with constant velocity (both magnitude and direction constant) continues to do so unless acted upon by a net force. If a net force were acting, the object would accelerate (change its velocity).
Q4. 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.
Answer:
(i) Possible – An object at rest remains at rest when no net force acts (Newton's first law).
(ii) Possible – An object moving with constant velocity continues to do so when no net force acts.
(iii) Not possible – Constant acceleration means velocity is changing, which requires a net force (Newton's second law).
Q5. 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.
Answer:
In the real world, multiple forces act on an object. However, by applying additional forces, the net force can be made zero.
Example: A book resting on a table. The forces acting are:
- Gravitational force (weight) acting downwards.
- Normal force from the table acting upwards.
These two forces are equal in magnitude and opposite in direction, so the net force is zero. The book remains at rest.
Q6. A toy car of mass 100 g is moving with a constant velocity of 0.5 m s⁻¹. What is the net force acting on the toy car?
Answer:
Answer: 0 N
Since the toy car is moving with constant velocity, its acceleration is zero. According to Newton's second law (F = ma), if acceleration is zero, the net force is also zero.
Q7. 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.
Answer:
According to Newton's second law (F = ma), for the same acceleration, the force required is directly proportional to mass.
To impart identical initial acceleration, you would need to apply a larger force to the heavier child (the one with greater mass). This is because F = ma – more mass requires more force for the same acceleration.
Q8. How are glass items packed for transportation using a bubble wrap or hay protected from damage?
Answer:
Bubble wrap or hay increases the time duration over which the glass items come to rest during an impact. According to Newton's second law (F = ma), if the time of impact increases, the acceleration decreases (change in velocity over a longer time). This reduces the force exerted on the glass items, preventing them from breaking.
Q9. Why does a fireperson sometimes struggle when holding the pipe issuing water?
Answer:
When water rushes out of the pipe with high velocity, it exerts an equal and opposite force on the pipe (Newton's third law). This reaction force pushes the pipe backwards. The fireperson must apply a force to counteract this reaction and keep the pipe steady. If the water pressure is high, the reaction force is large, making it difficult to hold the pipe.
Q10. Suppose a spacecraft is moving in a region of space where the gravitational force acting upon it is negligible. Suggest how can it change its velocity.
Answer:
The spacecraft can change its velocity by firing its engines (expelling gas or exhaust). According to Newton's third law, when the spacecraft expels gas in one direction, an equal and opposite force acts on the spacecraft in the opposite direction, changing its velocity. This is how rockets maneuver in space.
Revise, Reflect, Refine
Q1. 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?
Answer:
Answer: The frictional force is equal to F.
Since the table is moving with constant velocity, the net force on the table is zero. The applied force F and the frictional force are equal in magnitude and opposite in direction. Therefore, frictional force = F.
Q2. 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.
Answer:
(i) remain the same – Newton's first law: no net force → constant velocity.
(ii) increase – Force in direction of motion → acceleration in same direction → velocity increases.
(iii) decrease – Force opposite to motion → acceleration opposite → velocity decreases (deceleration).
Q3. 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.
Answer:
The correct option is (i) P experiences a net force and Q does not experience a net force.
Explanation:
- Block P has two forces (4 N and 5 N) acting in opposite directions. They are unequal, so the net force on P is 1 N (non-zero).
- Block Q is moving with constant velocity, which means the net force on Q is zero (Newton's first law).
Q4. While practising for the snake boat race (Vallum kalli 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.)
Answer:
Given:
- Total oarsmen = 100
- Force by each oarsman = 200 N
- 95 oarsmen row backwards (propel boat forward)
- 5 oarsmen row forward (oppose boat motion)
Forward force = 95 × 200 N = 19,000 N
Backward force = 5 × 200 N = 1,000 N
Net force = 19,000 N − 1,000 N = 18,000 N forward
Q5. 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.
Answer:
The correct option is (iv) in the direction of force, with acceleration proportional to the force acting on the object.
According to Newton's second law (F = ma), acceleration is in the direction of the net force and is directly proportional to the force (for a given mass).
Q6. 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
Answer:
Answer: (iii) Object C
Explanation:
- Object A: Straight line with constant slope → constant velocity → zero net force.
- Object B: Horizontal line → at rest → zero net force.
- Object C: Curved line → changing slope → changing velocity → acceleration → net force acts.
- Object D: Straight line with constant slope → constant velocity → zero net force.
Only object C shows accelerated motion, so a net force acts on it.
Q7. 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.
Answer:
Answer: Yes, the boat will move backwards.
According to Newton's third law of motion, when the sailor jumps forward (applies a force on the boat in the backward direction), the boat applies an equal and opposite force on the sailor in the forward direction. The boat experiences a reaction force in the backward direction, causing it to move away from the shore.
Q8. 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.
Answer:
When the athlete falls, they have a certain velocity. The landing mat or sand bed increases the time duration over which the athlete's velocity reduces to zero. According to Newton's second law (F = ma), a longer time means smaller acceleration, which results in a smaller force on the athlete's body. This reduces the risk of injury.
Q9. A hand cart loaded with vegetables collides 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.
Answer:
The correct option is (iv) the loaded cart and the empty cart, both exert an equal magnitude of force on each other.
According to Newton's third law of motion, when two objects interact, they exert equal and opposite forces on each other. The masses of the carts do not affect the magnitude of the forces they exert on each other during the collision.
Q10. 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.
Answer:
Explanation:
From the acceleration-mass graph, acceleration is inversely proportional to mass (a ∝ 1/m) for a constant force. Since F = ma is constant, the force-mass graph will be a horizontal straight line (constant force) showing that force does not depend on mass.
Q11. The velocity-time graph of an object of mass 10 kg moving along a straight line is shown in Fig. 6.41. Calculate the force acting on the object by using the graph.
Answer:
Given: Mass (m) = 10 kg
From the graph (assuming data):
- At t = 0 s, v = 0 m/s
- At t = 4 s, v = 20 m/s
Acceleration: a = (20 − 0)/4 = 5 m/s²
Force: F = ma = 10 × 5 = 50 N
(If the graph shows different values, substitute accordingly.)
Q12. A bullet of mass 50 g moving with a speed of 100 m s⁻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).
Answer:
Given:
- Mass (m) = 50 g = 0.05 kg
- Initial velocity (u) = 100 m/s
- Final velocity (v) = 0 m/s
- Distance (s) = 50 cm = 0.5 m
Step 1: Find acceleration
Using v² = u² + 2as:
0 = (100)² + 2 × a × 0.5
0 = 10000 + a
a = −10,000 m/s² (negative sign indicates deceleration)
Step 2: Find force
F = ma = 0.05 × (−10000) = −500 N
Magnitude of stopping force = 500 N (opposite to direction of motion).
Q13. An ace footballer converted a penalty shot by kicking the football with a speed of 108 km h⁻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.
Answer:
Given:
- Final velocity (v) = 108 km/h = 108 × (5/18) = 30 m/s
- Initial velocity (u) = 0 m/s
- Force (F) = 800 N
- Mass (m) = 0.4 kg
Step 1: Find acceleration
F = ma → a = F/m = 800/0.4 = 2000 m/s²
Step 2: Find time
Using v = u + at:
30 = 0 + 2000 × t
t = 30/2000 = 0.015 s
Q14. An object of mass 2 kg moving with a constant velocity of 10 m s⁻¹ 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?
Answer:
Given:
- Mass (m) = 2 kg
- Initial velocity (u) = 10 m/s
- Final velocity (v) = 0 m/s
- Force of friction = 7 N (opposing motion)
- Additional opposing force = 3 N
Total opposing force = 7 + 3 = 10 N
Acceleration: F = ma → a = F/m = 10/2 = 5 m/s² (opposite to motion, so negative)
Distance: Using v² = u² + 2as:
0 = 100 + 2 × (−5) × s
0 = 100 − 10s
s = 10 m
Q15. 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.
Answer:
Given:
- F = m₁a₁ → m₁ = F/a₁
- F = m₂a₂ → m₂ = F/a₂
When both are pulled together:
Total mass = m₁ + m₂ = F/a₁ + F/a₂ = F(1/a₁ + 1/a₂)
Using F = (m₁ + m₂)a:
F = F(1/a₁ + 1/a₂) × a
1 = (1/a₁ + 1/a₂) × a
a = 1 / (1/a₁ + 1/a₂) = a₁a₂ / (a₁ + a₂)
Q16. 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.
Answer:
According to Newton's third law, the forces on the bar magnet and the compass needle are equal in magnitude but act on different objects.
The bar magnet does not move visibly because its mass is much larger than that of the compass needle. According to Newton's second law (a = F/m), for the same force, the acceleration is inversely proportional to mass. The compass needle has very small mass, so it experiences large acceleration and moves. The bar magnet has large mass, so its acceleration is negligible.
The Journey Beyond
Q1. You know that the force of friction depends on the nature of the surfaces in contact. Does it also depend on how hard the surfaces press each other? Is the friction acting on an object that is about to move larger than the friction after motion begins? Is the friction which acts on a rolling object less than that on a sliding object? Find answers to these questions and create an infographic. Such observations help explain why the invention of the wheel was a major milestone in human history.
Answer:
This is a project/exploration activity.
Key findings to explore:
- Friction depends on normal force: Friction is directly proportional to the normal force (how hard surfaces press against each other). F = μN.
- Static friction vs Kinetic friction: Static friction (friction when object is about to move) is greater than kinetic friction (friction during motion). This is why it's harder to start moving an object than to keep it moving.
- Rolling friction vs Sliding friction: Rolling friction is much less than sliding friction. This is why wheels were a major invention – they reduce friction significantly.
Infographic can include: Diagrams showing static, sliding, and rolling friction; comparison of friction values; real-life examples.
Q2. Take two toy cars of equal mass and stick a bar magnet on top of each. Fix a metre scale on a smooth surface. Place the cars near the midpoint of the metre scale with the like poles touching. Release the cars and record the time taken (using two stopwatches), and distance travelled by each before coming to a rest. Repeat the experiment after adding equal masses to both cars. Did the cars travel equal distances in opposite directions? Plot a graph of distance travelled versus mass. Analyse and discuss your findings.
Answer:
This is an experiential activity.
Expected observations:
- When like poles of magnets are placed together, they repel each other with equal and opposite forces (Newton's third law).
- The cars will move in opposite directions with equal acceleration (if masses are equal).
- They will travel equal distances in opposite directions.
- When equal masses are added to both cars, the acceleration decreases (F = ma), but the distances travelled remain equal in opposite directions.
- Graph of distance vs mass will show inverse relationship – as mass increases, distance decreases.
Analysis: The experiment demonstrates Newton's third law and the effect of mass on motion.
Q3. Wrap a rope once around a rough tree branch or post. Attach a heavy bucket to one end and try to hold it by the other end. Now, add one more turn of the rope and repeat. You will find that each extra turn increases the 'grip' between the rope and the branch, increasing the friction and reducing the force required, making it much easier to hold the same load. The reduction in effort is much larger than you might expect from just adding one turn. This shows that friction does not increase in a simple linear way, small changes in contact can lead to large changes in force. In the same way, friction between a rope and a post allows large ships to be held safely at a pier.
Answer:
This is an experiential activity.
Explanation:
When a rope is wrapped around a post, the friction between the rope and the post increases with each turn. This friction helps hold the load with less effort. The relationship is exponential – each additional turn significantly increases the friction force. This principle is used in:
- Docking ships (ropes wrapped around bollards)
- Climbing (belay devices)
- Tying knots
Q4. It is often instructive to examine how scientific ideas develop over time. If you are interested, explore how Newton formulated the laws of motion by reading excerpts from his original work, the Principia. Both the original text and commentaries are available online.
Answer:
This is a research activity.
Key points to explore:
- Newton's Principia Mathematica (1687) laid the foundation for classical mechanics.
- Newton built upon the work of Galileo and Kepler.
- He formulated the three laws of motion and the law of universal gravitation.
- The original text uses geometric reasoning rather than modern algebraic notation.
- Commentaries help understand the historical context and significance.
The Quest Continues
Q1. In the real world, friction is always present whenever surfaces are in contact. Scientists have been trying to find ways to reduce friction between surfaces by using lubricants, coatings or texturing of surfaces, streamlining shapes of objects, and by using magnetic levitation.
Answer:
This is a thought-provoking extension.
Ways to reduce friction:
- Lubricants: Oil, grease, graphite – reduce direct contact between surfaces.
- Coatings: Teflon, ceramic coatings – make surfaces smoother.
- Texturing: Creating patterns to trap lubricants or reduce contact area.
- Streamlining: Reducing air resistance (aerodynamic shapes).
- Magnetic levitation: Using magnetic forces to eliminate contact (Maglev trains).
Applications: Reducing friction improves efficiency, saves energy, and reduces wear and tear in machines.