Physics 1st Ch 05 Work, Energy and Power

Physics - First Paper Chapter 5: Work, Energy and Power Selected Questions and Answers (HSC English Version) Chapter 5: Work, Energy and Power B. Creative Questions 1. A person dropped a body of mass m from the roof of a building at height of 30 m. Let us consider that the body is dropped freely without hindrance. (a) What is kinetic energy? (b) What are the characteristics by which conservative force can be distinguished from non- conservative force? (c) If the mass of the body is 20 g, what will be the kinetic energy just before touching the ground? (d) Does the body in the stimulus follow the conservation principle of mechanical energy? Ex- plain with argument. Answer: (a) Kinetic energy is the capacity of a body to do work by virtue of its state of motion. For mass m moving with speed v: KE = 1 2mv2. (b) Distinguishing characteristics: ˆ Conservative force: Work done is path-independent, depending only on initial and final positions. Work done around any closed loop is zero ( H⃗ F ·d⃗r = 0). Total mechanical energy is conserved (e.g., gravity, ideal spring force). ˆ Non-conservative force: Work done depends on the actual path taken. Work done around a closed loop is non-zero. M

A B C F s θ (a) What is non-conservative force? (b) What is meant by work done by a force? (c) If F = 20 N, s = 50 m and work done is 500 J, then find the angle between F and s. (d) For what value of θ, work is done by the force and work is done against the force - analyse. Answer: (a) A non-conservative force is a force for which the work done in moving a particle between two points depends on the path taken, and the total work done in a closed cycle is non-zero (e.g., frictional force). (b) Work done by a constant force is defined as the dot product of the force vector⃗F and the displacement vector⃗s: W =⃗F ·⃗s = Fs cos θ, where θ is the angle between force and displacement. (c) Given: F = 20 N, s = 50 m, W = 500 J. Formula: W = Fs cos θ =⇒cos θ = W Fs = 500 20×50 = 500 1000 = 0.5. θ = arccos(0.5) = 60◦ (d) Analysis of work based on angle θ: ˆ For 0◦≤θ < 90◦: cos θ > 0, so W > 0. Work is done by the force (force aids the displacement). Maximum positive work occurs at θ = 0◦(W = Fs). ˆ For θ = 90◦: cos 90◦= 0, so W = 0. No work is done (force is perpendicular to displacement). ˆ For 90◦< θ ≤180◦: cos θ < 0, so W < 0. Work is done against the force (force opposes displacement, e.g.

(a) Spring constant (force constant) k is the restoring force per unit extension or compression of a spring: k = F/x (SI unit: N/m). A stiffer spring has a larger k. The potential energy stored in a spring deformed by x is U = 1 2kx2. (b) When the spring of the toy car is wound (compressed/twisted), work is done against the restoring force, storing elastic potential energy U = 1 2kx2 in the spring. When released, this stored potential energy converts to kinetic energy of the car: 1 2kx2 → 1 2mv2. The spring pushes against the car’s mechanism, turning the wheels. The car decelerates as elastic PE runs out and eventually stops due to friction (converting remaining KE to heat). This illustrates conversion of elastic PE →KE →thermal energy. (c) (d) k = 100 N/m. Work to extend spring by x: Wextend = R x 0 kx′ dx′ = 1 2kx2. Work to compress spring by x: Wcompress = R x 0 k|x′| dx′ = 1 2kx2. Both give the same result: W = 1 2kx2 = 1 2(100)x2 = 50x2 J. For example, for x = 0.1 m: W = 50 × 0.01 = 0.5 J in both cases. Since W = 1 2kx2 depends only on the magnitude |x| and not on the sign (direction), equal contraction and expansion require equal work. □ 4. A science student named Rafi of Loh