Laws of Motion Solved Examples (Class 11 Physics)
Newton's laws of motion explain how forces affect the movement of objects. These examples demonstrate how to calculate forces, acceleration, tension, and f
TL;DR: Newton's laws of motion explain how forces affect the movement of objects. These examples demonstrate how to calculate forces, acceleration, tension,…
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Newton's laws of motion explain how forces affect the movement of objects. These examples demonstrate how to calculate forces, acceleration, tension, and f
Laws of Motion — Solved Numerical Examples (Step by Step)
Example 1: A force of 50 N is applied to a body of mass 10 kg. Calculate the acceleration produced.
Solution: Given: Force F = 50 N, mass m = 10 kg
Using Newton's second law: F = ma
50 = 10 × a
a = 50/10 = 5 m/s²
Example 2: A 5 kg block is pulled horizontally by a force of 30 N on a frictionless surface. Find the acceleration of the block.
Solution: Given: Mass m = 5 kg, applied force F = 30 N, friction = 0 (frictionless)
Net force = Applied force = 30 N (no friction to oppose)
Using F = ma
30 = 5 × a
a = 30/5 = 6 m/s²
Example 3: Two masses 4 kg and 6 kg are connected by a light string over a frictionless pulley. Find the acceleration and tension in the string.
Solution: Given: m1 = 6 kg (heavier), m2 = 4 kg (lighter), g = 10 m/s²
The 6 kg mass will move downward.
For the system: Net driving force = (m1 - m2)g = (6 - 4) × 10 = 20 N
Total mass = m1 + m2 = 6 + 4 = 10 kg
Acceleration: a = (m1 - m2)g / (m1 + m2)
a = 20/10 = 2 m/s²
Tension: For mass m2 (4 kg) moving upward:
T - m2g = m2a
T - 4 × 10 = 4 × 2
T - 40 = 8
T = 48 N
Example 4: A block of mass 8 kg is on a surface with friction coefficient 0.25. A horizontal force of 40 N is applied. Find the net force and acceleration. (g = 10 m/s²)
Solution: Given: m = 8 kg, coefficient of friction μ = 0.25, applied force F = 40 N, g = 10 m/s²
Normal force: N = mg = 8 × 10 = 80 N
Frictional force: f = μN = 0.25 × 80 = 20 N
Net force: Fnet = Applied force - Friction
Fnet = 40 - 20 = 20 N
Acceleration: a = Fnet/m = 20/8 = 2.5 m/s²
Example 5: A person of mass 60 kg stands in an elevator. Calculate the normal force when the elevator is (a) at rest and (b) moving upward with acceleration 2 m/s². (g = 10 m/s²)
Solution: Given: m = 60 kg, g = 10 m/s²
(a) When elevator is at rest:
Normal force N = mg = 60 × 10 = 600 N
(b) When elevator moves upward with a = 2 m/s²:
Applying Newton's second law in upward direction:
N - mg = ma
N = mg + ma = m(g + a)
N = 60(10 + 2) = 60 × 12 = 720 N
Example 6: An object of mass 2 kg is placed on an inclined plane at angle 30° to horizontal. If the coefficient of friction is 0.1, find whether the object slides or remains stationary. (g = 10 m/s²)
Solution: Given: m = 2 kg, θ = 30°, μ = 0.1, g = 10 m/s²
Component of weight along the plane: mg sin θ = 2 × 10 × sin 30° = 20 × 0.5 = 10 N
Component of weight perpendicular to plane: mg cos θ = 2 × 10 × cos 30° = 20 × (√3/2) = 10√3 N
Normal force: N = mg cos θ = 10√3 ≈ 17.32 N
Maximum friction: f_max = μN = 0.1 × 17.32 ≈ 1.73 N
Since component along plane (10 N) > maximum friction (1.73 N), the object will slide.
Net force down the plane: F = 10 - 1.73 = 8.27 N
Acceleration: a = 8.27/2 = 4.135 m/s²
Tips
- Always identify all forces acting on the body: applied force, friction, normal force, weight, and tension.
- Draw a free body diagram to visualize all forces and their directions before solving.
- Remember that friction always opposes motion and acts opposite to the direction of applied force.
- For connected bodies or pulleys, apply Newton's second law to each mass separately and then solve simultaneously.
Frequently Asked Questions
What is the difference between static and kinetic friction?
Static friction acts when an object is at rest and prevents motion up to a maximum value (μs × N). Kinetic friction acts when an object is already moving and has a constant value (μk × N). Generally, μs is greater than μk, which is why it is harder to start moving an object than to keep it moving.
Why do we use mass instead of weight in Newton's second law?
Newton's second law is F = ma, where m is mass (a fundamental property of an object) and a is acceleration. Weight (W = mg) is the force due to gravity and depends on the gravitational field. Mass remains constant everywhere, but weight changes with location.
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