How Forces Affect Motion – Notes, MCQs, Quiz & Worksheet

(c) there is a force on the ball opposing the motion.

Explanation:  The ball comes to rest because of friction between the ball and the ground. This frictional force opposes the motion of the ball and slows it down until it stops.

When a carpet is beaten with a stick, the carpet moves suddenly, but the dust particles tend to stay in their original position due to inertia. Because of this, the dust gets separated from the carpet and comes out.

This happens due to Newton’s First Law of Motion, which says that an object at rest will stay at rest unless an external force acts on it. The dust remains at rest while the carpet moves, so it gets left behind.

Mass (m) = 100 kg
Initial velocity (u) = 5 m/s
Final velocity (v) = 8 m/s
Time (t) = 6 s

1.Initial momentum = mass × initial velocity
                                         = 100 × 5 = 500 kg·m/s

2. Final momentum = mass × final velocity
                                       = 100 × 8 = 800 kg·m/s

3. Force = rate of change of momentum
     Force = (Final momentum – Initial momentum) ÷ time
                 = (800 – 500) ÷ 6
                 = 300 ÷ 6 = 50 N

Mass = 10 kg
Height = 80 cm = 0.8 m
Acceleration due to gravity (g) = 10 m/s²
Initial velocity = 0 (since it falls from rest)

Step 1: Find final velocity before hitting the floor
Use the formula:
v² = u² + 2gh
v² = 0 + 2 × 10 × 0.8 = 16
v = √16 = 4 m/s

Step 2: Find momentum
Momentum = mass × velocity
= 10 × 4 = 40 kg·m/s

Hence the dumb-bell transfers 40 kg·m/s of momentum to the floor.

Rahul is correct.

According to Newton's Third Law of Motion, every action has an equal and opposite reaction. This means that the force the motorcar exerts on the insect is equal in magnitude and opposite in direction to the force the insect exerts on the motorcar.
Both the insect and the car experience the same force and the same change in momentum (but in opposite directions).
However, since the insect has a much smaller mass, it undergoes a large change in velocity and gets damaged. The car, being much heavier, shows no noticeable change in motion.

Kiran is wrong because change in momentum depends on both mass and velocity. Even though the insect’s velocity changes more, its small mass results in a smaller change in  momentum.

Akhtar is also wrong because the force is not greater on the insect alone. Both the insect and the car experience the same force.

When a moving bus stops suddenly, your body keeps moving forward due to inertia, so you fall forward. When the bus starts moving from rest, your body tries to stay in the same place due to inertia, so you fall backward.
Inertia is the tendency of the body to resist any change in its state of rest or motion.

(d) mv
Momentum is the product of mass and velocity.
Formula: momentum (p) = m × v

Yes, it is possible for the object to travel with a non-zero velocity even when the net external unbalanced force is zero.

Condition:
The object must be moving with a constant speed in a straight line. This means its velocity should not change.
According to Newton's First Law of Motion, an object will keep moving with the same velocity unless an unbalanced force acts on it. So, if the net force is zero, the object can keep moving at a steady speed.

When we vigorously shake the branch of a tree, the branch moves suddenly, but the leaves tend to stay in their original position due to inertia. Inertia is the tendency of an object to resist any change in its state of rest or motion.

As a result, the leaves cannot follow the motion of the branch and may get detached. This is explained by Newton’s First Law of Motion, which states that an object at rest stays at rest unless acted upon by an external force.

Mass = 10 g = 0.01 kg
Initial velocity (u) = 150 m/s
Final velocity (v) = 0 m/s
Time (t) = 0.03 s

Step 1: Find acceleration (a)
Use the formula:
v = u + at
0 = 150 + a × 0.03
a = -150 ÷ 0.03 = -5000 m/s²

Step 2: Find distance (s)
Use the formula:
s = ut + (1/2)at²
s = 150 × 0.03 + (1/2) × (-5000) × (0.03)²
s = 4.5 - 2.25 = 2.25 m

Step 3: Find force (F)
Use the formula:
F = m × a
F = 0.01 × (-5000) = -50 N
(Magnitude of force = 50 N)

Hence the distance of penetration = 2.25 m and magnitude of force = 50 N

Mass (m) = 1500 kg
Acceleration (a) = –1.7 m/s² 

Use the formula:
Force (F) = mass × acceleration
F = 1500 × (–1.7)
F = –2550 N

Hence the force between the vehicle and the road must be 2550 N opposite to the direction of motion.

The student's logic is incorrect.

According to Newton’s Third Law of Motion, the action and reaction forces are equal and opposite, but they act on different objects, not on the same object. So, they do not cancel each other.
When you push the truck, the force you apply is on the truck, and the truck applies an equal and opposite force on you. These forces act on different bodies.
The truck does not move because the force you apply is not enough to overcome the friction between the truck’s tires and the ground, and the inertia of its large mass. If a much greater force is applied, the truck can move.

When an object moves with constant velocity, the applied force is balanced by the friction force.
So, the friction force = applied force = 200 N

Mass of the ball = 200 g = 0.2 kg
Initial velocity = 10 m/s
Final velocity = -5 m/s (negative because it moves in the opposite direction)

Initial momentum = 0.2 × 10 = 2 kg·m/s
Final momentum = 0.2 × (-5) = -1 kg·m/s

Change in momentum = Final momentum - Initial momentum
= -1 - 2 = -3 kg·m/s

Magnitude of change in momentum = 3 kg·m/s

Mass (m) = 1 kg
Initial velocity (u) = 20 m/s
Final velocity (v) = 0 m/s (comes to rest)
Distance (s) = 50 m

Step 1: Find acceleration (a)
Use the formula:
v² = u² + 2as
=> 0 = (20)² + 2 × a × 50
=> 0 = 400 + 100a
=> 100a = -400
=> a = -400 ÷ 100 = -4 m/s²

Step 2: Find the force (F)
Use the formula:
F = m × a
F = 1 × (-4) = -4 N

Hence force of friction = 4 N (opposite to direction of motion)

Given:
Mass of engine = 8000 kg
Mass of each wagon = 2000 kg
Number of wagons = 5
Total mass of wagons = 5 × 2000 = 10000 kg
Total mass of train = 8000 + 10000 = 18000 kg
Force by engine = 40000 N
Friction force = 5000 N

(a) Net accelerating force = Force by engine − Friction force
Net force = 40000 − 5000 = 35000 N

(b) Acceleration of the train = Net force ÷ Total mass
a = 35000 ÷ 18000 = 1.94 m/s² (approximately)

Hence:-
(a) Net accelerating force = 35000 N
(b) Acceleration of the train = 1.94 m/s²

It is advised to tie the luggage on the roof of a bus with a rope to stop it from falling off when the bus moves suddenly, stops, or turns.
Because of inertia, the luggage tries to stay in the same position.

1. If the bus starts quickly, the luggage may fall backward.
2. If the bus stops suddenly, the luggage may fall forward.
3. If the bus turns, the luggage may slide to the side.

(a) A rubber ball and a stone of the same size

        Answer: The stone has more inertia.
        Reason: Inertia depends on mass. Since the stone is heavier than the rubber ball, it has more inertia.

(b) A bicycle and a train

        Answer: The train has more inertia.
        Reason: The train has much more mass than the bicycle, so it resists changes in motion more and has more inertia.

(c) A five-rupees coin and a one-rupee coin

        Answer: The five-rupees coin has more inertia.
        Reason: It has more mass than the one-rupee coin, so it has greater inertia.

initial velocity (u) = 0 m/s
Distance (s) = 400 m
Time (t) = 20 s
Mass (m) = 7 tonnes = 7000 kg

Step 1: Find acceleration (a)
Use the formula:
s = ut + (1/2)at²
=> 400 = 0 × 20 + (1/2) × a × (20)²
=> 400 = (1/2) × a × 400
=> 400 = 200a
=> a = 400 ÷ 200 = 2 m/s²

Step 2: Find the force (F)
Use the formula:
F = m × a
F = 7000 × 2 = 14000 N

Hence  Acceleration = 2 m/s²  &  Force = 14000 N

Mass of moving object = 1 kg
Velocity of moving object = 10 m/s
Mass of wooden block = 5 kg
Velocity of wooden block = 0 m/s

Total momentum before impact = (1 × 10) + (5 × 0) = 10 kg·m/s

Let the combined velocity after impact be v
Total mass after impact = 1 + 5 = 6 kg
Using conservation of momentum:
Total momentum after impact = 6 × v
So, 10 = 6 × v
v = 10 ÷ 6 = 1.67 m/s (approximately)

Total momentum after impact = 6 × 1.67 = 10 kg·m/s

Hence -
Total momentum before impact = 10 kg·m/s
Total momentum after impact = 10 kg·m/s
Velocity of the combined object = 1.67 m/s

The velocity of the ball changes three times.

1. First player kicks the football to another player – velocity changes
2. Second player kicks it towards the goal – velocity changes again
3. Goalkeeper kicks it towards his teammate – velocity changes once more

So, velocity changes 3 times.