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9th Physics Federal Board Notes: Unit 3 Dynamics – I
📋 Table of Contents
- 1. Multiple Choice Questions
- 2. Short Response Questions
- 3. Long Response Questions
- 3.1 Newton's First Law of Motion
- 3.2 Inertia in Daily Life
- 3.3 Newton's Second Law of Motion
- 3.4 Newton's Third Law of Motion
- 3.5 Limitations of Newton's Laws
- 3.6 Contact and Non-Contact Forces
- 3.7 Free Body Diagrams
- 3.8 Momentum
- 3.9 Mass vs Weight
- 3.10 Gravitational Field and Strength
- 3.11 Electronic Balances
- 3.12 Newton's Second Law in Terms of Momentum
- 3.13 Isolated System and Conservation of Momentum
🔬 Introduction to Unit 3: Dynamics – I
Unit 3: Dynamics – I explores the fundamental principles that govern motion and the forces that cause changes in motion. This unit introduces Newton's Laws of Motion, which form the foundation of classical mechanics. You'll learn about inertia, momentum, force, and how these concepts explain everyday phenomena from walking to rocket launches.
Multiple Choice Questions
Inertia is the property of matter that resists changes in motion, and it is directly proportional to mass. The greater the mass of an object, the greater its inertia.
Weight = mg = 10 N, so mass m = 10/9.8 ≈ 1.02 kg
Using F = ma: 5 = 1.02 × a
a ≈ 5/1.02 ≈ 4.9 m/s² ≈ 5 m/s²
Momentum = mass × velocity = kg × m/s = kg m s⁻¹
According to Newton's second law, F = dp/dt, where F is force. For a free-falling body, the only force acting is weight (mg), so the rate of change of momentum equals weight.
From Newton's second law: F = Δp/Δt, so Δp = F × Î”t
The book is at rest, so the net force is zero. The weight (50 N) is balanced by the normal force from the table.
Thrust is a reaction force described by Newton's third law. When a rocket expels gases backward, the gases push the rocket forward with an equal force.
Using F = Δp/Δt = 50 kgm/s ÷ 2 s = 25 N
On rides like roller coasters or spinning attractions, friction between you and the seat provides the upward force that balances your weight.
The dust particles tend to remain at rest due to inertia when the carpet is suddenly moved, causing them to separate from the carpet.
The centrifugal force acting outward on the water when the bucket is swung fast enough provides the necessary force to keep the water in the bucket even when upside down.
The engine provides torque to the wheels, but it's the friction between the tires and the road that actually propels the car forward.
N/kg = (kg m/s²)/kg = m/s², which is the unit of acceleration.
Weight = mg = 1 kg × 9.8 m/s² = 9.8 N
When a body falls with uniform velocity, acceleration is zero, so net force must be zero according to Newton's second law.
Short Response Questions
1. When a motorcyclist hits a stationary car, he may fly off the motorcycle and the driver in the car may get a neck injury. Explain.
When a motorcyclist collides with a stationary car, two different injury mechanisms occur due to inertia:
- Motorcyclist flying off: The motorcyclist continues moving forward due to inertia when the motorcycle suddenly stops. This is an example of Newton's first law - an object in motion stays in motion unless acted upon by an external force.
- Driver's neck injury: The car driver's body is initially at rest. When the car is hit from behind, the seat pushes the driver's lower body forward, but the head tends to remain at rest due to inertia. This creates a whiplash effect that can injure the neck.
2. In autumn, when you shake a branch, the leaves are detached. Why?
This phenomenon demonstrates the principle of inertia:
- When you shake a branch, you apply force to the branch, causing it to move.
- The leaves, due to their inertia, tend to remain at rest while the branch moves away from them.
- This relative motion between the branch and leaves breaks the weak connections (petioles) holding the leaves to the branch.
- In autumn, these connections are already weakened as part of the tree's natural cycle, making detachment easier.
3. Why it is not safe to apply brakes only on the front wheel of a bicycle?
Applying brakes only on the front wheel creates a dangerous situation due to inertia:
- When the front wheel stops suddenly, the bicycle's forward motion is interrupted.
- The rear part of the bicycle and the rider continue moving forward due to inertia.
- This creates a rotational force that can cause the bicycle to flip over forward.
- The rider may be thrown over the handlebars, potentially causing serious injury.
- Proper braking involves applying both front and rear brakes simultaneously or using the rear brake first to maintain stability.
4. Deduce Newton's first law of motion from Newton's second law of motion.
Newton's second law states: F = ma
If no net external force acts on an object (F = 0), then:
Zero acceleration means:
- If the object was at rest, it remains at rest (velocity = 0)
- If the object was moving, it continues moving with constant velocity (no change in speed or direction)
This is exactly the statement of Newton's first law of motion, which we have derived from the second law.
5. Action and reaction are equal but opposite in direction. These forces always act in pair. Do they balance each other? Can bodies move under action – reaction pair?
Do action-reaction forces balance each other?
No, action and reaction forces do not balance each other because they act on different objects. For forces to balance, they must act on the same object.
Can bodies move under action-reaction pair?
Yes, bodies can and do move under action-reaction pairs. Examples include:
- Walking: You push backward on the ground (action), and the ground pushes you forward (reaction).
- Rocket propulsion: The rocket pushes exhaust gases downward (action), and the gases push the rocket upward (reaction).
- Swimming: You push water backward (action), and the water pushes you forward (reaction).
In each case, the action and reaction forces act on different objects, allowing motion to occur.
6. A man slips on the oily floor; he wants to move out of this area. He is alone. He throws his bag to move out of this slippery area. Why is it so?
This situation demonstrates Newton's third law of motion:
- When the man throws his bag in one direction, he applies a force to the bag (action).
- According to Newton's third law, the bag exerts an equal and opposite force on the man (reaction).
- This reaction force pushes the man in the direction opposite to the thrown bag.
- On a slippery surface with low friction, this reaction force is sufficient to move the man away from the dangerous area.
- This is the same principle that allows astronauts to maneuver in space by throwing objects.
7. How does a rocket move in space where there is no air?
Rocket motion in space is explained by Newton's third law and conservation of momentum:
- Rockets carry their own fuel and oxidizer, so they don't need air for combustion.
- When fuel burns in the combustion chamber, hot gases are expelled downward at high velocity through the nozzle.
- This expulsion of gases is the "action" force.
- According to Newton's third law, an equal "reaction" force pushes the rocket upward.
- In the vacuum of space, there's no air resistance, so rockets can achieve very high speeds efficiently.
- The rocket's acceleration increases as fuel is consumed because the mass decreases while thrust remains constant (from F = ma).
8. Why does a cricket batter wear gloves?
Cricket batters wear gloves primarily to protect their hands and reduce the impact force:
- When a fast-moving cricket ball hits the bat, it transfers momentum to the bat.
- This momentum transfer creates a large force over a short time interval.
- From the impulse-momentum theorem: F × Î”t = Δp
- Gloves increase the time interval (Δt) over which the force acts.
- Since the change in momentum (Δp) is fixed, increasing Δt decreases the average force (F) experienced by the hands.
- This reduced force minimizes the risk of injury to the batter's hands.
- Additionally, gloves provide padding that absorbs some of the impact energy.
9. Why is the weight of an object on the Moon 1/6th of that on the Earth?
The weight difference between Earth and Moon is due to their different gravitational field strengths:
- Weight = mass × gravitational field strength (W = mg)
- The mass of an object remains constant everywhere.
- Earth's gravitational field strength: gEarth ≈ 9.8 N/kg
- Moon's gravitational field strength: gMoon ≈ 1.6 N/kg
- gMoon / gEarth ≈ 1.6 / 9.8 ≈ 1/6
- Therefore, WMoon = (1/6) × WEarth
- This difference occurs because the Moon has less mass and smaller radius than Earth, resulting in weaker gravity.
10. A ball is falling freely. Does the ball attract the Earth? If yes, why does the Earth not move towards the ball?
Does the ball attract the Earth?
Yes, according to Newton's law of universal gravitation, every object with mass attracts every other object with mass. The falling ball does attract the Earth with the same force that the Earth attracts the ball.
Why does the Earth not move toward the ball?
Although both objects experience equal gravitational forces, their accelerations are dramatically different due to their vastly different masses:
- From Newton's second law: F = ma, so a = F/m
- The force F is the same for both ball and Earth
- For the ball: aball = F/mball ≈ 9.8 m/s²
- For the Earth: aEarth = F/mEarth
- Since mEarth is enormous (≈ 6 × 10²⁴ kg), aEarth is extremely small (≈ 10⁻²⁵ m/s²)
- This tiny acceleration of Earth is undetectable in everyday situations.
Long Response Questions
1. State and explain Newton's first law of motion. Give examples from daily life.
Newton's First Law of Motion (Law of Inertia):
"An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force."
Explanation:
This law introduces the concept of inertia - the natural tendency of objects to resist changes in their state of motion. Inertia is directly proportional to mass.
Daily Life Examples:
- Passengers lurching forward when a bus stops suddenly: Their bodies continue moving forward due to inertia when the bus decelerates.
- Dust falling off a beaten carpet: Dust particles tend to remain at rest when the carpet is shaken.
- Coin drop trick: A coin placed on a card over a glass falls into the glass when the card is quickly flicked away.
- Seat belts in cars: They prevent passengers from continuing forward motion during sudden stops.
- Tablecloth trick: Pulling a tablecloth quickly from under dishes without disturbing them.
2. Define inertia. Give examples from daily life where inertia plays an important role.
Definition of Inertia:
Inertia is the property of matter that resists changes in its state of motion. It is the natural tendency of objects to maintain their current velocity (which includes both speed and direction).
Daily Life Examples of Inertia:
- Shaking a ketchup bottle: The ketchup tends to remain at rest when the bottle stops moving suddenly.
- Removing water from wet clothes by shaking: Water droplets tend to continue moving when the clothes change direction.
- Hammer head tightening: The heavy hammer head continues moving when the handle stops, tightening the connection.
- Car turning: Passengers feel pushed outward because their bodies tend to continue moving in a straight line.
- Athletes in races: Runners find it difficult to stop quickly after crossing the finish line.
- Spacecraft in orbit: They continue moving without engine power due to inertia.
3. State and explain Newton's second law of motion. Show that F = ma.
Newton's Second Law of Motion:
"The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of acceleration is the same as the direction of the net force."
Mathematical Expression:
Derivation from Momentum:
Newton originally expressed his second law in terms of momentum:
For constant mass (dm/dt = 0):
Explanation:
- The same force applied to objects of different masses produces different accelerations.
- Larger mass requires more force to achieve the same acceleration.
- The net force determines the acceleration, not individual forces.
4. State and explain Newton's third law of motion. Give examples from daily life.
Newton's Third Law of Motion:
"For every action, there is an equal and opposite reaction."
Explanation:
When one object exerts a force on a second object, the second object simultaneously exerts a force equal in magnitude and opposite in direction on the first object.
Important Points:
- Action and reaction forces always occur in pairs.
- They act on different objects, so they don't cancel each other.
- They are equal in magnitude but opposite in direction.
- They occur simultaneously.
Daily Life Examples:
- Walking: You push backward on the ground, ground pushes you forward.
- Swimming: You push water backward, water pushes you forward.
- Rocket propulsion: Rocket pushes exhaust gases downward, gases push rocket upward.
- Gun recoil: Gun pushes bullet forward, bullet pushes gun backward.
- Balloon rocket: Air escapes backward, balloon moves forward.
- Bouncing ball: Ball pushes ground downward, ground pushes ball upward.
5. Discuss the limitations of Newton's laws of motion.
While Newton's laws are extremely successful in explaining everyday phenomena, they have limitations in certain situations:
| Limitation | Description | Applicable Theory |
|---|---|---|
| Very High Speeds | At speeds approaching the speed of light, Newton's laws become inaccurate. Time dilation and length contraction occur. | Einstein's Theory of Relativity |
| Very Small Scales | At atomic and subatomic levels, Newtonian mechanics fails to explain phenomena like electron behavior. | Quantum Mechanics |
| Strong Gravitational Fields | Near extremely massive objects like black holes, gravity behaves differently than predicted by Newton. | General Relativity |
| Non-Inertial Reference Frames | Newton's laws only hold in inertial (non-accelerating) frames. In accelerating frames, fictitious forces appear. | Advanced Mechanics |
| Complex Systems | For systems with many interacting particles, Newtonian calculations become extremely complex. | Statistical Mechanics |
Despite these limitations, Newton's laws remain highly accurate and useful for most engineering applications and everyday situations involving macroscopic objects at moderate speeds.
6. Differentiate between contact and non-contact forces with examples.
| Aspect | Contact Forces | Non-Contact Forces |
|---|---|---|
| Definition | Forces that require physical contact between objects | Forces that act at a distance without physical contact |
| Mechanism | Direct physical interaction | Fields (gravitational, electric, magnetic) |
| Examples |
|
|
| Range | Short range (direct contact only) | Can act over large distances |
| Medium Dependence | Often depends on surface properties | Can act through vacuum |
Important Notes:
- All contact forces are fundamentally electromagnetic in nature at the atomic level.
- Non-contact forces are field forces that can act through empty space.
- Gravity is the weakest non-contact force but has infinite range.
- Nuclear forces are the strongest but have very short range.
7. What is a free body diagram? Draw free body diagrams for a book placed on a table, a hanging picture frame, and a ladder leaning against a wall.
Free Body Diagram (FBD):
A free body diagram is a graphical representation that shows all the forces acting on a single object. It helps in analyzing the net force and predicting the object's motion.
Steps to Draw FBD:
- Isolate the object of interest
- Represent the object as a point or simple shape
- Draw and label all forces acting on the object
- Show force directions with arrows
- Indicate magnitudes if known
Example FBDs:
Book on Table
Forces:
- Weight (W) downward
- Normal force (N) upward from table
Since the book is at rest: W = N
Hanging Picture Frame
Forces:
- Weight (W) downward
- Tension (T) upward in the string
For equilibrium: T = W
Ladder Against Wall
Forces:
- Weight (W) downward at center
- Normal force from wall (N₁) horizontal
- Normal force from floor (N₂) vertical
- Friction from floor (f) horizontal
For equilibrium: N₁ = f and N₂ = W
8. Define momentum. Prove that the rate of change of momentum is equal to the applied force.
Definition of Momentum:
Momentum is the product of an object's mass and velocity. It is a vector quantity with both magnitude and direction.
where p = momentum, m = mass, v = velocity
Proof that F = dp/dt:
Newton originally stated his second law as:
Where dp/dt is the rate of change of momentum.
Derivation:
For constant mass:
For variable mass (like rockets):
Significance:
- This form is more general than F = ma
- It applies to systems with changing mass
- It's the fundamental form used in advanced physics
9. Differentiate between mass and weight.
| Aspect | Mass | Weight |
|---|---|---|
| Definition | Amount of matter in an object | Force of gravity on an object |
| Nature | Scalar quantity | Vector quantity |
| SI Unit | Kilogram (kg) | Newton (N) |
| Measuring Instrument | Beam balance, electronic balance | Spring balance |
| Location Dependence | Constant everywhere | Varies with location (gravity changes) |
| Zero Condition | Never zero | Zero in absence of gravity |
| Formula | Fundamental property | W = mg |
Key Relationship:
Where g ≈ 9.8 N/kg on Earth's surface
Example:
An object with mass 10 kg:
- On Earth: Weight = 10 × 9.8 = 98 N
- On Moon: Weight = 10 × 1.6 = 16 N
- Mass remains 10 kg in both locations
10. Define gravitational field and gravitational field strength. Write its mathematical form and unit.
Gravitational Field:
A gravitational field is the region of space surrounding a massive body in which another massive body experiences a force of gravitational attraction.
Gravitational Field Strength (g):
Gravitational field strength at a point is defined as the gravitational force per unit mass experienced by a small test mass placed at that point.
Mathematical Form:
Where:
- g = gravitational field strength
- F = gravitational force on test mass
- m = mass of test object
Unit:
Newton per kilogram (N/kg)
This is equivalent to meters per second squared (m/s²), which is the unit of acceleration.
Values:
- Earth's surface: g ≈ 9.8 N/kg
- Moon's surface: g ≈ 1.6 N/kg
- Jupiter's surface: g ≈ 24.8 N/kg
Formula for Point Mass:
Where:
- G = gravitational constant (6.67 × 10⁻¹¹ Nm²/kg²)
- M = mass of the attracting body
- r = distance from center of mass
11. How does an electronic balance measure the mass of an object?
Electronic balances measure mass indirectly through the force of gravity, but they are calibrated to display mass readings. Here's how they work:
Working Principle:
- Load Cell: The object's weight causes deformation in a load cell (usually a strain gauge).
- Strain Gauge: This deformation changes the electrical resistance of the strain gauge.
- Wheatstone Bridge: The resistance change is measured using a Wheatstone bridge circuit.
- Signal Processing: The electrical signal is amplified and converted to digital form.
- Calibration: The balance is calibrated using known masses to convert force measurements to mass readings.
Key Points:
- Electronic balances actually measure weight (force), not mass directly.
- They assume a constant gravitational field strength (g ≈ 9.8 m/s²).
- The displayed mass is calculated as: m = W/g
- If used where gravity is different (like on the Moon), they would give incorrect mass readings unless recalibrated.
Advantages over Mechanical Balances:
- Higher precision and accuracy
- Digital display eliminates reading errors
- Faster measurements
- Can interface with computers
- Automatic tare function
12. Show that Newton's second law can also be stated in terms of momentum.
Newton originally formulated his second law in terms of momentum. Let's derive this relationship:
Starting from the standard form:
Substitute acceleration definition:
For constant mass, m can be moved inside the derivative:
Recognize that mv is momentum (p):
Final Form:
Interpretation:
"The net force acting on an object equals the rate of change of its momentum."
Advantages of this formulation:
- More general than F = ma
- Applies to systems with changing mass (like rockets)
- Fundamental in advanced physics
- Leads directly to conservation of momentum
For constant mass:
So both forms are equivalent for constant mass systems.
13. What is an isolated system? Prove the law of conservation of momentum for an isolated system of two balls moving in the same direction.
Isolated System:
An isolated system is one that doesn't interact with its surroundings. No external forces act on the system, and no mass enters or leaves the system.
Law of Conservation of Momentum:
"The total momentum of an isolated system remains constant if no external forces act on it."
Proof for Two Balls Moving in Same Direction:
Consider two balls with masses m₁ and m₂ moving in the same direction with initial velocities u₁ and u₂ (u₁ > u₂). They collide and then move with velocities v₁ and v₂.
Before collision:
After collision:
During collision:
According to Newton's third law, the force on ball 1 by ball 2 (F₁₂) is equal and opposite to the force on ball 2 by ball 1 (F₂₁):
From Newton's second law in momentum form:
Therefore:
This means the total momentum (p₁ + p₂) is constant:
Conclusion:
The total momentum before collision equals the total momentum after collision, proving the law of conservation of momentum for an isolated system.
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