Question 1

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.

Accepted Answer

Yes, the boat will move backward. When the sailor jumps forward, he exerts a force on the boat in the backward direction. According to Newton's third law, the boat exerts an equal and opposite force on the sailor. As a result, the boat moves backward while the sailor moves forward. — Newton's third law states that for every action, there is an equal and opposite reaction. The sailor pushes the boat backward to jump forward, causing the boat to move backward.

Question 2

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.

Accepted Answer

The landing mat or sand bed is used to increase the time over which the athlete comes to rest after the jump. This reduces the force experienced by the athlete on landing, preventing injury. According to the impulse-momentum principle, increasing the time of impact decreases the force. — Force experienced is inversely proportional to the time over which the change in momentum occurs. A soft mat increases the stopping time, thereby reducing the impact force.

Question 3

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.

Accepted Answer

Option (iv) is correct. According to Newton's third law of motion, the forces exerted by the two carts on each other are equal in magnitude and opposite in direction, regardless of their masses or velocities. — Newton's third law states that forces between two interacting bodies are equal and opposite. Hence, both carts exert equal magnitude forces on each other during collision.

Question 4

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.

Accepted Answer

From the graph of acceleration (a) versus mass (m), since force F = m × a, the force is constant if the product of m and a is constant. The force-mass graph will be a horizontal line indicating constant force irrespective of mass. — Given that acceleration decreases as mass increases such that the product m × a remains constant (force), plotting force versus mass yields a constant force line. This is consistent with Newton's second law.

Question 5

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.

Accepted Answer

First, find the acceleration from the velocity-time graph by calculating the slope (change in velocity/change in time). Then use Newton's second law F = m × a.

Assuming from the graph (Fig. 6.41) that velocity decreases from 20 m/s to 0 m/s in 4 seconds:

Acceleration, a = (0 - 20) / 4 = -5 m/s²

Mass, m = 10 kg

Force, F = m × a = 10 × (-5) = -50 N

The negative sign indicates the force is opposite to the direction of motion. — Calculate acceleration from the slope of the velocity-time graph. Then apply F = m × a to find the force. The force is negative indicating it acts opposite to motion, likely a retarding force.

Question 6

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).

Accepted Answer

Given:
Mass, m = 50 g = 0.05 kg
Initial velocity, u = 100 m/s
Final velocity, v = 0 m/s (stops)
Distance, s = 50 cm = 0.5 m

Using the equation v² = u² + 2as to find acceleration a:
0 = (100)² + 2 × a × 0.5
=> 0 = 10000 + a
=> a = -10000 / 1 = -10000 m/s²

Force, F = m × a = 0.05 × (-10000) = -500 N

The negative sign indicates the force acts opposite to the bullet's motion, i.e., a stopping force of 500 N. — Use kinematic equation to find acceleration, then apply Newton's second law to find force. The large deceleration results in a large stopping force.

Question 7

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.

Accepted Answer

Given:
Initial velocity, u = 0 (ball initially at rest)
Final velocity, v = 108 km/h = (108 × 1000) / 3600 = 30 m/s
Force, F = 800 N
Mass, m = 0.4 kg

Using impulse-momentum theorem:
Impulse = Change in momentum = F × t = m × (v - u)

=> 800 × t = 0.4 × 30
=> 800 × t = 12
=> t = 12 / 800 = 0.015 s

Time of contact = 0.015 seconds. — Impulse equals change in momentum. Rearranging impulse formula gives contact time. The short contact time corresponds to a large force.

Question 8

An object of mass 2 kg moving with a constant velocity of 10 ms⁻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?

Accepted Answer

Given:
Mass, m = 2 kg
Initial velocity, u = 10 m/s
Friction force, f₁ = 7 N (opposing motion)
Additional opposing force, f₂ = 3 N
Total opposing force, F = 7 + 3 = 10 N

Acceleration, a = F / m = 10 / 2 = 5 m/s² (deceleration)

Using equation v² = u² + 2as, with final velocity v = 0:
0 = (10)² + 2 × (-5) × s
=> 0 = 100 - 10s
=> 10s = 100
=> s = 10 m

The object travels 10 meters before coming to rest. — Calculate total opposing force and resulting deceleration. Use kinematic equation to find stopping distance.

Question 9

A tractor pulls a harrow (a ploughing tool) of mass m₁ with a net force F resulting in an acceleration of α₁. The same tractor pulls a trolley of mass m₂ with a force F producing an acceleration of α₂. 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 α₁ and α₂. Ignore friction.

Accepted Answer

Given:
Force F produces acceleration α₁ on mass m₁:
F = m₁ × α₁
Force F produces acceleration α₂ on mass m₂:
F = m₂ × α₂

When the tractor pulls both together (mass m₁ + m₂) with force F, acceleration α is:
α = F / (m₁ + m₂)

Substitute F from above:
F = m₁ × α₁ = m₂ × α₂

Therefore,
α = F / (m₁ + m₂) = (m₁ × α₁) / (m₁ + m₂) = (m₂ × α₂) / (m₁ + m₂)

Hence, the resulting acceleration is:
α = (m₁ α₁) / (m₁ + m₂) = (m₂ α₂) / (m₁ + m₂) — Use Newton's second law for each case to express force. Then for combined mass, acceleration is force divided by total mass. Express acceleration in terms of given accelerations.

Question 10

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.

Accepted Answer

The compass needle moves because it is free to rotate and is small in mass, so the magnetic force causes it to move. The bar magnet does not move because it is held firmly or has a much larger mass and inertia, making it difficult to move. Although forces are equal and opposite, the resulting motion depends on the masses and constraints of the objects. — Newton's third law states forces are equal and opposite, but acceleration depends on mass and constraints. The compass needle, being light and free, moves; the bar magnet, being heavy or fixed, does not.

Question 11

A canoe moves forward when the canoeist pushes water backwards with a paddle. Why does the canoe move faster when the canoeist pushes harder?

Accepted Answer

Because pushing harder increases the force on water, resulting in a greater reaction force propelling the canoe forward — According to Newton's third law, when the canoeist pushes water backwards with greater force, the water pushes the canoe forward with an equal and opposite force. This increased reaction force causes the canoe to move faster.

Question 12

Suppose a canoeist uses the same paddle force in two canoes, one empty and one carrying a passenger. In which canoe will the canoe move faster and why?

Accepted Answer

The empty canoe will move faster because it has less mass, so the same force produces greater acceleration — According to Newton's second law, acceleration is inversely proportional to mass (a = F/m). With the same force applied, the canoe with less mass (empty) accelerates more and thus moves faster.

Question 13

Which of the following is NOT an effect of force on an object?

Accepted Answer

Changing the color of the object — Force can cause motion or deformation (change in shape) but it does not affect the color of an object.

Question 14

Identify the SI unit of force and its correct symbol.

Accepted Answer

newton / N — The SI unit of force is the newton, symbolized by 'N'. It is named after Sir Isaac Newton.

Question 15

Which instrument is commonly used to measure the magnitude of a force?

Accepted Answer

Spring balance — A spring balance measures force by the extension of a spring when a force is applied. It is commonly used to measure weight and other forces.

How Forces Affect

How Forces Affect — Study Notes

How Forces Affect Motion

6.1 The Concept of Force

6.1.1 Measuring the magnitude of a force

Practice Questions — How Forces Affect

All 13 Chapters in Exploration