Class 9 › Science › Chapter 6
How Forces Affect Motion
Force and net force, balanced and unbalanced forces, friction, Newton's three laws of motion with applications, and forces on a system of objects.
1. The Concept of Force
- A force can make a stationary object move, change the speed or direction of a moving object, or change its shape (kicking a ball, a bat striking a ball, squeezing a lemon).
- Force is a quantity with magnitude and direction, like displacement, velocity and acceleration. If either magnitude or direction (or both) changes, the effect changes.
- SI unit: newton (full name starts with a small 'n'; symbol N is capital). The magnitude expresses the strength of the force.
- Measuring force: a spring balance measures the magnitude of a force in general; weight is the gravitational force with which the Earth pulls an object.
- Scale: the smallest forces we feel are about millinewtons ($10^{-3}$ N); specialised experiments measure down to yoctonewtons ($10^{-24}$ N). A 100 g mass in your palm presses with about 1 N.
2. Balanced and Unbalanced Forces; Net Force
- Usually more than one force acts on an object: pushing a box (applied force + friction opposite to motion), a ball floating on water (gravity down + buoyant force up).
- Balanced forces: equal in magnitude, opposite in direction (tug of war with a stationary rope): net force is zero. Unbalanced: a non-zero net force acts and the object's motion changes.
- Motion depends only on the net force.
| Situation | Net force magnitude | Direction |
|---|---|---|
| Two forces in the same direction | Sum of the two | Same as the forces |
| Two forces in opposite directions | Difference of the two | Along the larger force |
| Equal and opposite | Zero (balanced) | None |
Example 6.1: forces of 10 N and 6 N acting on a block in three different ways.
- Beyond: forces at an angle, and equal-opposite forces on the two ends of an extended object (turning a tap or handlebar) are handled in higher grades. A pushed object also has weight (down) balanced by the normal force (up, perpendicular to the surface); air friction is often negligible.
3. The Force of Friction
- Friction acts between the surfaces in contact, in the direction opposite to (attempted or actual) motion.
- A box does not move until the applied force becomes larger than friction, so that a net force acts in its direction of motion.
- A moving object slows and stops (bicycle, ball) because friction acts against its motion. A force is needed to counter friction, not to keep an object moving in the absence of friction.
Activity 6.1: stack of four coins released by a rubber band
Same stretch (A, B, C marks) on different surfaces: wood, laminated top, polished marble or tile.
Observation: velocity decreases gradually on release; the coins travel farther on smoother surfaces.
Inference: smoother surface means less friction, so velocity falls more slowly and the stack goes farther before stopping.
Activity 6.2: measuring friction with a spring balance
Pull a wooden block with a spring balance and note the reading when the block just starts moving (steady velocity means net force is zero, so the reading $\approx$ the force of friction).
Smaller reading = smaller friction; the surface on which coins went farthest has the smallest reading.
Thought experiment (Galileo, 17th century): if all impediments are removed (zero friction on a horizontal plane), a moving object would continue to move indefinitely. It was long wrongly believed that a force is needed to keep an object moving at constant velocity.
- Friction helps too: walking, running and driving rely on friction (see third law). Grooves on shoe soles and treads on tyres increase friction; wet polished floors, ice, water or snow on roads are risky because friction is small.
- Activity to explore: friction depends on the nature of surfaces; also on how hard they press, and rolling friction is less than sliding (why the wheel mattered). Extra turns of a rope on a post greatly reduce the effort needed to hold a load.
4. Newton's First Law of Motion
First law
An object at rest remains at rest, and an object in motion continues to move with a constant velocity, unless a net force acts upon it.
- If net force is zero, acceleration is zero: the object cannot start moving or change its velocity.
- Constant velocity means no change in magnitude or direction; a non-zero constant velocity means straight-line motion at steady speed.
- Inertia: Newton's word for the tendency of objects to resist change in their state of rest or uniform motion; the first law is built on it.
- Net force is needed to change velocity (start, stop, speed up, slow down or turn), but not to keep an object moving at constant velocity.
- Example 6.2: a person pushes a moving box with a force equal to friction. The two are equal and opposite, net force is zero, so the box continues at constant velocity.
- If a table moves at constant velocity under a force $F$, friction $= F$ (opposite).
| State (net force zero) | Position-time graph | Velocity-time graph |
|---|---|---|
| At rest | Horizontal line | Horizontal line at zero (on the time axis) |
| Constant velocity | Straight sloping line | Horizontal line at the constant value |
5. Newton's Second Law of Motion
Second law
When a net force acts on an object, it accelerates in the direction of the net force. The acceleration is directly proportional to the net force and inversely proportional to the mass.
$$a = \dfrac{F}{m} \quad\Longleftrightarrow\quad F = ma$$
$$F = mg \quad (\text{weight; } g = 9.8\ \text{m s}^{-2}\approx 10\ \text{m s}^{-2})$$
- 1 newton: the force that produces an acceleration of $1\ \text{m s}^{-2}$ in an object of mass $1$ kg, so $1\ \text{N} = 1\ \text{kg m s}^{-2}$.
- $g$ does not depend on the mass of the object; it is nearly constant near the Earth's surface.
- Direction of acceleration = direction of net force. Use signs for direction.
Activities 6.3 and 6.4 (cart pulled by a falling cup)
Same cart, double the force (cup mass): acceleration increases (from $s=\tfrac12 aT^2$, $a_1/a_2 = T_2^2/T_1^2$).
Same force, double the cart mass: acceleration decreases. So $a \propto F$ and $a \propto 1/m$.
Measured values differ slightly from the ideal ratios because of friction in the wheels and measurement errors.
Solved examples
6.4 (weightlifter): total mass $=30$ kg; $F = mg = 30\times9.8 = 294$ N upward to hold the barbell steady.
6.5 (block 25 kg, max friction 50 N): (i) push of 50 N: balanced, block stays at rest. (ii) 55 N: net $=5$ N, $a = 5/25 = 0.2$ m s−2, $s = \tfrac12(0.2)(2)^2 = 0.4$ m forward in 2 s.
6.6 (car 1500 kg, from velocity-time graph): 0–5 s: $a = 10/5 = 2$ m s−2, $F = 3000$ N east. 5–10 s: constant velocity, $F = 0$. 10–15 s: $a = -2$, $F = -3000$ N (towards west).
- Method for graph problems: slope of the velocity-time graph gives $a$; then $F = ma$.
- Longer stopping time means smaller force: a force $F = ma$ falls when the same velocity change takes longer. Examples: a fielder pulls the hands back while catching a cricket ball; an airbag increases the time of impact; landing mats in high jump; bubble wrap or hay for glass. A coconut breaks when it stops in a very short time (huge force).
- Momentum form (beyond): momentum $=$ mass $\times$ velocity (direction as velocity). Net force is proportional to the rate of change of momentum; this form also works when mass changes.
6. Newton's Third Law of Motion
Third law
Whenever one object exerts a force on a second object, the second object simultaneously exerts an equal and opposite force on the first.
- Forces always occur in pairs, and the two forces act on two different objects. They never cancel each other (balanced forces act on the same object).
- Applies to all forces, contact and non-contact: magnetic (two bar magnets), electrostatic (two charged balloons), gravitational (Earth and fruit).
- Activity 6.5: push a table while sitting on a wheeled chair: you move the opposite way. Activity 6.6: two connected spring balances show equal readings.
- Equal forces do not give equal accelerations when masses differ, since $a = F/m$.
| Everyday example | Action force | Reaction force |
|---|---|---|
| Walking / running | Foot pushes ground backwards | Ground (friction) pushes foot forward |
| Cycling without pedalling | Feet push ground back | Ground pushes rider and bicycle forward |
| Climbing a coconut tree | Legs push down on trunk | Friction pushes person up (harder on smooth trunk) |
| Rowing a canoe | Paddle pushes water backwards | Water pushes paddle and canoe forward |
| Balloon with straw (Activity 6.7) | Balloon pushes air out | Air pushes balloon the opposite way |
| Rocket launch | Engine expels gas downwards | Gas pushes rocket up; lifts off when this exceeds the rocket's weight |
| Sailor jumping from a boat | Sailor pushes boat backwards | Boat pushes sailor forward (boat moves back) |
- Chandrayaan-3: the Vikram lander fired its engine in the direction of motion; exhaust gas pushed it backwards and slowed it for a soft landing near the Moon's south pole.
- Friction helps movement: without friction your foot would slip backwards while pushing the ground.
Examples 6.7 and 6.8
6.7: Earth and fruit pull each other with equal force, but the Earth's mass is enormous, so $a = F/m$ for the Earth is too small to notice.
6.8: 0.1 kg bullet, 5 kg gun, force 2 N on each. Gun: $a = 2/5 = 0.4$ m s−2. Bullet: $a = 2/0.1 = 20$ m s−2. Equal forces, unequal accelerations because the masses differ.
7. Forces Acting on a System of Objects
- Two boxes $m_1$ and $m_2$ on a frictionless surface joined by a string; a force $F$ pulls box 1. The string's pull is the tension $T$: box 1 pulls box 2 forward with $T$, and box 2 pulls box 1 back with $T$ (third law).
- Internal forces (tension, between parts of the system) can be ignored; only external forces (like $F$) matter when treating the boxes and string as one system.
Acceleration of the system
$$a = \dfrac{F}{m_1 + m_2}$$
The system accelerates like a single object of mass $m_1 + m_2$. (Gravity $(m_1+m_2)g$ is balanced by the normal force from the ground.)
- Treating connected objects as one system simplifies the analysis, as when we study a walking person's overall motion as a single object.
- Limits: Newton's laws need modification only near very massive objects, at speeds close to the speed of light, and at atomic scales.
- Reducing friction: lubricants, coatings, surface texturing, streamlined shapes, magnetic levitation.
8. Quick Revision
| Law | Statement in short | Key idea |
|---|---|---|
| First | No net force: rest stays rest, motion continues with constant velocity | Inertia; force changes velocity, not needed to maintain it |
| Second | $F = ma$; acceleration along net force | $a \propto F$, $a \propto 1/m$; $1\ \text{N} = 1\ \text{kg m s}^{-2}$ |
| Third | Equal and opposite forces on two different objects | Forces in pairs; they never cancel |
Formulas
Key equations
$F = ma$
Weight $= mg$
System: $a = F/(m_1+m_2)$
Plus $v = u+at$, $s = ut+\tfrac12at^2$, $v^2=u^2+2as$.
Tip
Net force problems
1. Find net force (add if same direction, subtract if opposite). 2. Use $a = F/m$. 3. Use kinematic equations for distance or time.
Tip
Impact time
Same change in velocity over a longer time means smaller acceleration and force (airbag, fielder, mats).
Common mistakes:
• Saying a force is needed to keep an object moving at constant velocity.
• Saying the action-reaction pair cancels (they act on different objects).
• Using the sum of forces when they are opposite (use the difference).
• Using mass in grams in $F = ma$ (convert to kg).
• Saying equal and opposite forces mean equal accelerations.
• Writing 'Newton' or 'n' for the unit (newton, N).
• Forgetting friction can help (walking) as well as oppose motion.
• Using $F = ma$ with only one of several forces instead of the net force.
• Saying a force is needed to keep an object moving at constant velocity.
• Saying the action-reaction pair cancels (they act on different objects).
• Using the sum of forces when they are opposite (use the difference).
• Using mass in grams in $F = ma$ (convert to kg).
• Saying equal and opposite forces mean equal accelerations.
• Writing 'Newton' or 'n' for the unit (newton, N).
• Forgetting friction can help (walking) as well as oppose motion.
• Using $F = ma$ with only one of several forces instead of the net force.