Physics Example 4.2 & 4.3 Solutions | Newton's Second Law Step by Step

 - Dr.Sanjaykumar pawar

Step-by-step solutions for NCERT Physics Examples 4.2 and 4.3 demonstrating Newton's Second Law and force calculations.

Physics Solved Examples

Example 4.2

Question:
A bullet of mass 0.04 kg moving with a speed of 90 m/s enters a heavy wooden block and is stopped after travelling a distance of 60 cm. What is the average resistive force exerted by the block on the bullet?

Given:

• Mass of bullet, m = 0.04 kg
• Initial velocity, u = 90 m/s
• Final velocity, v = 0 m/s (bullet stops)
• Distance travelled, s = 60 cm = 0.6 m

To Find:

Average resistive force exerted by the block on the bullet.

Step 1: Use the equation of motion
v² = u² + 2as

Substitute the values:
0² = 90² + 2(a)(0.6)
0 = 8100 + 1.2a
1.2a = -8100
a = -8100 / 1.2
a = -6750 m/s²

The negative sign indicates retardation (deceleration).

Step 2: Apply Newton's Second Law
F = ma

F = 0.04 × 6750
F = 270 N

Final Answer: Average resistive force = 270 N

Example 4.3

Question:
The motion of a particle of mass m is described by the equation: y = ut + ½gt². Find the force acting on the particle.

Given:

y = ut + ½gt²

To Find:

Force acting on the particle.

Step 1: Find Velocity
Velocity is the rate of change of displacement.

v = dy/dt

Differentiate y = ut + ½gt²
v = u + gt

Step 2: Find Acceleration
Acceleration is the rate of change of velocity.

a = dv/dt

Differentiate v = u + gt
a = g

Step 3: Apply Newton's Second Law
F = ma

Since a = g,
F = mg

Final Answer: F = mg

Therefore, the particle moves under the influence of gravitational force.