Force and Laws of Motion Solved Examples (Class 9 Physics)
Newton's laws of motion describe how objects move when forces act upon them. Force is a push or pull that changes the state of motion. Understanding mass,
TL;DR: Newton's laws of motion describe how objects move when forces act upon them. Force is a push or pull that changes the state of motion. Understanding m…
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Newton's laws of motion describe how objects move when forces act upon them. Force is a push or pull that changes the state of motion. Understanding mass,
Force and Laws of Motion — Solved Numerical Examples (Step by Step)
Example 1: A force of 100 N is applied to a mass of 20 kg. Calculate the acceleration produced.
Solution: Given:
Force F = 100 N
Mass m = 20 kg
Using Newton's second law: F = ma
100 = 20 × a
a = 100 / 20
a = 5 m/s^2
Example 2: What is the weight of a 5 kg object on Earth? (g = 10 m/s^2)
Solution: Given:
Mass m = 5 kg
Acceleration due to gravity g = 10 m/s^2
Using the formula: Weight = mg
Weight = 5 × 10
Weight = 50 N
Example 3: Two objects with masses 10 kg and 15 kg are connected by a string and pulled with a force of 100 N. Assuming no friction, find the acceleration of the system.
Solution: Given:
Mass m1 = 10 kg
Mass m2 = 15 kg
Force F = 100 N
Total mass = m1 + m2 = 10 + 15 = 25 kg
Using Newton's second law: F = Mtotal × a
100 = 25 × a
a = 100 / 25
a = 4 m/s^2
Example 4: Calculate the force needed to accelerate a 4 kg mass at 3 m/s^2.
Solution: Given:
Mass m = 4 kg
Acceleration a = 3 m/s^2
Using Newton's second law: F = ma
F = 4 × 3
F = 12 N
Example 5: A car of mass 1000 kg is accelerating at 2 m/s^2. If the resistance (friction) is 500 N, find the driving force.
Solution: Given:
Mass m = 1000 kg
Acceleration a = 2 m/s^2
Resistance (friction) f = 500 N
Using Newton's second law:
Net force = ma
Driving force - Resistance = ma
Driving force - 500 = 1000 × 2
Driving force = 2000 + 500
Driving force = 2500 N
Example 6: An object of mass 2 kg is moving with velocity 10 m/s. A constant force is applied for 5 seconds, after which its velocity becomes 20 m/s. Find the magnitude of the force.
Solution: Given:
Mass m = 2 kg
Initial velocity u = 10 m/s
Final velocity v = 20 m/s
Time t = 5 seconds
First find acceleration: v = u + at
20 = 10 + a × 5
a × 5 = 10
a = 2 m/s^2
Now find force: F = ma
F = 2 × 2
F = 4 N
Example 7: Calculate the momentum of a 3 kg object moving at 8 m/s.
Solution: Given:
Mass m = 3 kg
Velocity v = 8 m/s
Using the formula: Momentum p = mv
p = 3 × 8
p = 24 kg·m/s
Tips
- Newton's second law F = ma is the most important formula. It relates force, mass, and acceleration. Always use this when you need to find any of these three quantities.
- Remember that weight is the force due to gravity on a mass. Weight = mg, where g = 10 m/s^2 on Earth. Weight is a force measured in Newtons, not mass.
- In problems with multiple objects, find the total mass first, then apply Newton's second law to the entire system, unless specifically asked for forces on individual objects.
Frequently Asked Questions
What is the difference between mass and weight?
Mass is the amount of matter in an object and remains constant everywhere. Weight is the force of gravity acting on the mass and changes with location. On Earth, weight = mg. On the Moon, weight is less because g is smaller, but mass remains the same.
What is the difference between momentum and velocity?
Velocity is the rate of change of position (measured in m/s). Momentum is the product of mass and velocity (measured in kg·m/s). A light object moving fast can have the same momentum as a heavy object moving slowly if mv is the same.
More Physics Solved Examples
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