Force and Laws of Motion
CBSE Class 9 · Science · Notes, formulas and practice questions
This chapter explains why unbalanced forces change the motion of an object, introduces inertia and momentum, and covers Newton's three laws of motion with applications such as recoil and collisions.
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This chapter begins with the idea of force as a push or a pull. The first important distinction is between balanced and unbalanced forces: balanced forces cancel out and produce no change in a body's state of rest or uniform motion, while an unbalanced force produces a net force that changes velocity. Force can alter speed, change the direction of motion, or deform a body. So the central question the chapter answers is not whether a force keeps a body moving, but what force changes its motion.
Newton's first law states that a body maintains its state of rest or uniform motion unless an external unbalanced force acts on it. This property of resisting a change in motion is called inertia. A larger mass has larger inertia, so it is harder to start moving, slow down, speed up, or change direction. Common examples, such as passengers lurching forward when a bus stops suddenly, are explained by inertia. Since balanced forces do not cause acceleration, no continuous forward push is needed to keep an object moving at constant velocity when friction is absent.
Newton's second law makes these ideas quantitative. Momentum is mass multiplied by velocity, and the law says that the rate of change of momentum of a body is directly proportional to, and in the direction of, the unbalanced force acting on it. For a body of constant mass, this gives the relation F = ma. The SI unit of force, the newton, is defined from this relation: 1 N is the force that gives a 1 kg mass an acceleration of 1 m/s². This law also explains why heavier objects need a larger force to produce the same acceleration.
Newton's third law reminds us that forces always occur in pairs but act on two different bodies. During a collision or recoil, the forces two bodies exert on each other are internal to the two-body system. If no external unbalanced force acts, the total momentum before the interaction equals the total momentum after it. This principle of conservation of momentum allows us to calculate the recoil velocity of a gun or the common velocity of objects that collide and stick together, which is the main problem-solving skill examined.
Key terms
- Force
- A push or a pull applied to an object. An unbalanced force can bring a stationary object into motion, increase or decrease its speed, change its direction, or deform it. Force is a vector quantity, and its SI unit is the newton (N).
- Balanced forces
- Forces acting on the same body whose resultant is zero. They do not change the state of motion of the body, so a body at rest stays at rest and a body moving uniformly continues at the same velocity. Balanced forces can still stretch, compress, or deform a body.
- Unbalanced forces
- Forces acting on a body whose resultant is not zero. The resultant, or net, force accelerates the body, changing its speed or direction. The net force is the vector sum of all the individual forces acting on the body.
- Newton's first law of motion
- A body remains at rest, or in uniform motion in a straight line, unless an external unbalanced force acts on it. This is also called the law of inertia because it describes the natural tendency of bodies to keep doing what they are doing.
- Inertia and mass
- Inertia is the tendency of a body to resist any change in its state of rest or uniform motion. Mass is the quantitative measure of inertia: the more massive a body is, the larger the force needed to change its velocity by a given amount.
- Momentum
- The amount of motion a body possesses, calculated as the product of its mass and velocity. Momentum is a vector quantity with the same direction as the velocity, and its SI unit is kg m/s. Faster or heavier objects have greater momentum.
- Newton's second law of motion
- The rate of change of momentum of a body is directly proportional to the applied unbalanced force and takes place in the direction of that force. For a body of constant mass, this reduces to F = ma, where F is the net force, m is the mass, and a is the acceleration produced.
- Newton's third law of motion
- When one body exerts a force on a second body, the second body simultaneously exerts an equal and opposite force on the first. The action and reaction always act on different bodies, so they do not act on the same object and cannot cancel each other out.
- Conservation of momentum
- If no external unbalanced force acts on a system of bodies, the total momentum of the system remains constant. This applies during collisions, explosions, and recoil, when the only forces involved are internal to the system.
Formula sheet
| What | Formula | Notes |
|---|---|---|
| Momentum | p = mv | p is momentum, m is the mass of the body, and v is its velocity. Momentum is a vector quantity and its SI unit is kg m/s. |
| Newton's second law for constant mass | F = ma | F is the net unbalanced force on the body, m is its mass, and a is its acceleration. This holds when the mass does not change, and 1 N = 1 kg m/s². |
| Newton's second law using momentum change | F = Δp/Δt | Δp is the change in momentum and Δt is the time interval in which the change takes place. Force acts in the direction of the change in momentum; for a fixed mass this is equivalent to F = ma. |
| Conservation of momentum for two bodies | m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ | m₁ and m₂ are the masses of the two bodies, u₁ and u₂ are their velocities before collision, and v₁ and v₂ are their velocities after collision. The equation applies when no external unbalanced force acts on the system; velocities must be taken with proper signs for direction. |
Practice questions with answers
1. Define one newton.
One newton is the force that gives a mass of 1 kg an acceleration of 1 m/s². From F = ma, 1 N is therefore equal to 1 kg m/s².
2. State Newton's first law of motion. What name is given to the property it describes?
A body remains at rest, or in uniform motion in a straight line, unless an external unbalanced force acts on it. The property of resisting any change in its state of motion is called inertia, so the law is also called the law of inertia.
3. Find the momentum of a cricket ball of mass 150 g bowled at 108 km/h.
Convert the mass to 0.15 kg and the speed to 108 × 1000/3600 = 30 m/s. Then p = mv = 0.15 × 30 = 4.5 kg m/s. The momentum is 4.5 kg m/s in the direction of the ball's motion.
4. An unbalanced force of 5 N acts on a body of mass 2.5 kg. What is the acceleration produced?
Using F = ma, a = F/m = 5/2.5 = 2 m/s². The acceleration is 2 m/s² in the direction of the applied force.
5. A passenger standing in a bus falls forward when the bus stops suddenly. Explain why.
The passenger and the bus are initially moving forward together. When the bus brakes, the lower part of the passenger slows down, but the upper body tends to keep moving forward because of inertia. This tendency of the body to continue its earlier motion makes the passenger lurch forward.
6. A car of mass 800 kg travelling at 54 km/h is uniformly stopped in 5 s. What is the average retarding force acting on it?
54 km/h converted to m/s is 54 × 1000/3600 = 15 m/s. The deceleration is 15/5 = 3 m/s², so the retarding force is F = ma = 800 × 3 = 2400 N. Thus the average force opposing the motion is 2400 N.
7. A bullet of mass 20 g is fired from a gun of mass 3 kg with a velocity of 150 m/s. Find the recoil velocity of the gun.
Before firing, the total momentum of gun and bullet is zero. After firing, conservation of momentum gives 0 = 0.02 × 150 + 3v. Since 0.02 × 150 = 3, we get v = −1 m/s. The gun recoils with a speed of 1 m/s in the direction opposite to the bullet.
8. State the law of conservation of momentum.
When no external unbalanced force acts on a system of bodies, the total momentum of the system remains unchanged before and after any interaction, such as a collision or explosion. This law is a direct consequence of Newton's laws of motion.
9. A trolley of mass 2 kg moving at 4 m/s collides with a stationary trolley of mass 2 kg, and the two get linked together. Find their common velocity.
Ignoring external horizontal forces, total momentum before the collision is 2 × 4 + 2 × 0 = 8 kg m/s. After they link, the combined mass is 4 kg, so 4v = 8, giving v = 2 m/s. The linked trolleys move together at 2 m/s in the original direction of motion.
10. Newton's third law says every action has an equal and opposite reaction. Why do these forces not cancel out when a horse pulls a cart?
Action and reaction always act on two different bodies, so they can never balance each other on the same body. The horse pulls the cart forward while the cart pulls the horse backward, but the horse also pushes the ground backward, and the ground pushes the horse forward. It is this forward reaction force from the ground that lets the horse move.
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