Force and Laws of Motion
Newton's Laws, Inertia & Momentum
In-Text Questions (Page 118)
Q1. Which of the following has more inertia: (a) a rubber ball and a stone of the same size? (b) a bicycle and a train? (c) a five-rupees coin and a one-rupee coin?
Inertia is the measure of the mass of an object. The object with more mass has more inertia.
- (a) Stone has more inertia (heavier).
- (b) Train has more inertia (heavier).
- (c) Five-rupees coin has more inertia (heavier).
Q2. In the following example, try to identify the number of times the velocity of the ball changes...
The velocity changes 4 times:
- When the player kicks the ball to another player.
- When the second player kicks the ball towards the goal.
- When the goalkeeper collects the ball (brings it to zero).
- When the goalkeeper kicks it towards his own team.
In-Text Questions (Page 126)
Q1. If action is always equal to the reaction, explain how a horse can pull a cart.
The horse pushes the ground backward with its feet (Action). The ground pushes the horse forward with an equal and opposite force (Reaction). This reaction force allows the horse to move forward and pull the cart. The cart moves when the force applied by the horse exceeds the frictional force of the cart wheels.
Q2. Explain, why is it difficult for a fireman to hold a hose, which ejects large amounts of water at a high velocity.
According to Newton's Third Law, when water is ejected forward at high velocity (Action), it exerts an equal and opposite backward force on the hose (Reaction). This backward force makes it difficult for the fireman to hold the hose stable.
Q3. From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m/s. Calculate the initial recoil velocity of the rifle.
Given: m1 (rifle) = 4 kg, m2 (bullet) = 0.05 kg, v2 = 35 m/s, v1 (recoil) = ?
Principle: Conservation of Momentum. Total initial momentum = Total final momentum = 0.
m1v1 + m2v2 = 0
4
× v1 + 0.05 × 35 = 0
4v1 = -1.75
v1 = -1.75 / 4 =
-0.4375 m/s (Negative sign indicates backward direction).
Main Textbook Exercises
Q5. A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration. Find the force acting on it if its mass is 7 tonnes (1 tonne = 1000 kg).
Given: u = 0, s = 400 m, t = 20 s, m = 7000 kg.
(i) Acceleration: s = ut + ½at²
400 =
0 + 0.5 × a × (20)²
400 = 200a
a = 2 m/s².
(ii) Force: F = ma
F = 7000 × 2 =
14000 N.
Q13. A hockey ball of mass 200 g travelling at 10 m/s is struck by a hockey stick so as to return it along its original path with a velocity at 5 m/s. Calculate the magnitude of change of momentum.
Given: m = 0.2 kg, u = 10 m/s (forward), v = -5 m/s (return path).
Change in Momentum: Δp = mv - mu = m(v - u)
Δp = 0.2 × (-5 - 10) = 0.2 × (-15) = -3 kg
m/s.
Magnitude = 3 kg m/s.
Q18. How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m/s².
Given: m = 10 kg, s = 0.8 m, a = 10 m/s², u = 0.
Find v: v² = u² + 2as
v² = 0 + 2 × 10
× 0.8 = 16
v = 4 m/s.
Momentum: p = mv = 10 × 4 = 40 kg m/s.
Force and Laws of Motion
Newton's Three Laws & Conservation of Momentum
1. Balanced and Unbalanced Forces
Resultant force is zero. State of object does not change (Rest remains Rest, Motion remains Motion).
Resultant force is non-zero. Causes acceleration (Change in speed or direction).
2. Newton's Laws of Motion
An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force.
Example: Passengers fall forward when a bus applies sudden brakes (Inertia of Motion).The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.
Force = 1 Newton (1 kg m/s²)
To every action, there is an equal and opposite reaction and they act on two different bodies.
Example: Recoil of a gun, Walking on ground, Rocket propulsion.3. Conservation of Momentum
The sum of momenta of the two objects before collision is equal to the sum of momenta after the collision provided there is no external unbalanced force acting on them.
Where m = mass, u = initial velocity, v = final velocity.
4. Numerical Examples
An object of mass 5 kg is accelerated by a constant force for 2 s. Velocity changes from 3 m/s to 7 m/s. Find the force.
Solution: a = (7 - 3)/2 = 2 m/s².
F = m ×
a = 5 × 2 = 10 N.
A bullet of 10g traveling at 150 m/s hits a wooden block and comes to rest in 0.03 s. Calculate distance of penetration.
Given: u=150 m/s, v=0, t=0.03s.
Step 1: a = (0 - 150)/0.03 = -5000 m/s².
Step 2: s = ut + ½at² = 150(0.03) + 0.5(-5000)(0.03)² = 4.5 - 2.25 = 2.25 m.
Key Facts & Definitions
50+ Important Points to Remember
A push or pull acting on an object.
Can change state of rest, motion, direction, or shape.
Two forces equal in magnitude but opposite in direction. Net force = 0.
Resultant force is not zero. Causes motion/acceleration.
Force that opposes the motion of an object over a surface.
Concluded that an object moves with constant speed if no external force acts on it.
Law of Inertia. Object maintains its state unless acted upon by unbalanced force.
Natural tendency of an object to resist a change in its state of motion or rest.
Mass is the measure of inertia. More mass = More inertia.
Tendency to remain at rest (e.g., dust falls when carpet is beaten).
Tendency to stay in motion (e.g., passenger falls forward when bus stops).
Tendency to maintain direction (e.g., thrown out when car turns sharply).
Product of mass and velocity. p = mv.
kg m/s.
Vector quantity (has direction same as velocity).
Rate of change of momentum is proportional to applied force.
F = ma (Force = Mass × Acceleration).
Newton (N).
Force that produces 1 m/s² acceleration in a body of 1 kg mass.
Force acted for a short time to produce large change in momentum (F × t).
Cricketer pulls hands back to increase time, reducing force (Newton's 2nd Law).
Prevent injury due to inertia of motion during sudden braking.
Action and Reaction are equal and opposite.
Act on two different bodies simultaneously.
Possible due to 3rd law (We push ground back, ground pushes us forward).
Gun moves backward when bullet moves forward (Conservation of Momentum).
Hot gases down (Action) -> Rocket moves up (Reaction).
Total momentum of an isolated system remains constant.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
Used to increase time of impact, reducing force (impact).
Mass is scalar (kg); Weight is vector (force due to gravity, N).
g = 9.8 m/s².
Means acceleration = 0 (Uniform Velocity).
Increases friction to help train stop or start.
Reduce friction.
Convert sliding friction to rolling friction (which is lesser).
Less than sliding friction.
Drag; friction exerted by fluids (liquids/gases).
Shape used to reduce fluid friction (e.g., Fish, Airplanes).
Device used to measure force/weight.
Forces acting when objects touch (Friction, Muscular).
Forces acting from distance (Magnetic, Gravitational, Electrostatic).
Attractive force between any two masses.
Force exerted by a charged body.
Diagram showing all forces acting on an object.
Force transmitted through a string/rope.
Perpendicular force exerted by a surface on an object.
Vector sum of all forces acting on an object.
Single force that has the same effect as multiple forces.
Based on Galileo's observations on inclined planes.