Assignment 2 Work Energy Theorem by Deepu Thomas Sir Answers | Physics | Submission Date 10.09.2025

Physics Practice Solutions

Q1.Work–Energy Theorem and Kinematics

1. Wagon Problem

Given: m = 7.00 kg, v_i = 4.00 m/s, F = 10.0 N, d = 3.0 m.

(a) Work–Energy:
Work = F × d = 10.0 × 3.0 = 30.0 J.
ΔK = W → v_f² = v_i² + 2W/m = 16.0 + 8.57 = 24.6.
v_f = 4.96 m/s.

(b) Kinematics:
a = F/m = 10.0/7.00 = 1.43 m/s².
v_f² = v_i² + 2ad = 16.0 + 8.57 = 24.6.
v_f = 4.96 m/s (same result).

2. Soccer Ball

Given: m = 0.420 kg, v_i = 2.00 m/s, v_f = 6.00 m/s, F = 40.0 N.

ΔK = ½m(v_f² − v_i²) = 0.5(0.420)(36 − 4) = 6.72 J.
d = W/F = 6.72/40.0 = 0.168 m.

Q2.Spring Mechanics

1. Stretching a Spring

(a) k = 2W/x² = 24.0 / 0.0009 = 2.67 × 10⁴ N/m.
(b) F = kx = 2.67×10⁴ × 0.0300 = 800 N.
(c) For x = 0.0400 m: W = ½kx² = 21.3 J, F = kx = 1.07 × 10³ N.

2. Block and Spring

(a) Work = ½kx² = 0.5(200)(0.025²) = 0.0625 J.
(b) ½mv² = 0.0625 → v = √(0.125/4.00) = 0.177 m/s.

Q3.Friction and Power

1. Rock Sliding

f = μmg = 0.200×20.0×9.8 = 39.2 N.
Work = −½mv² = −640 J.
a = f/m = 1.96 m/s² → time = 8.00/1.96 = 4.08 s.
P = W/t = −640/4.08 = −157 W (magnitude 157 W).

2. Tandem Bicycle

P_total = Fv = 165×9.00 = 1485 W.
Per rider = 742.5 W ≈ 743 W ≈ 1.00 hp.

3. Airplane Climb

P_climb = mgh/t = mgv = 700×9.8×2.5 = 17,150 W.
Fraction = 17,150 / 75,000 = 22.9%.