Work, energy and power questions in NET come down to four ideas: work as F·d cosθ, the work-energy theorem, power as work per second, and escape velocity. If you can convert km/h to m/s without thinking and you know when work is zero, most of this chapter is free marks.
Key facts
- Physics is 30% of NET-Engineering, a derived 60 of the 200 MCQs.
- Our syllabus data estimates about 6 questions from this chapter.
- Syllabus: work as a scalar product, the work-energy theorem, gravitational potential energy, power, and escape velocity.
Source: NUST NET-Engineering composition and the SailToNUST physics syllabus, checked October 2026
What the chapter covers
The chapter starts with work as the dot product of force and displacement, moves to kinetic and potential energy, and ends with power, efficiency, absolute potential energy and escape velocity. The practice bank also carries one-liners on energy sources, such as "the source of geothermal energy is the Earth" or "tides rise twice a day".
Formulas you need
Work W = F·d = Fd cosθ J = N m
Kinetic energy K = ½mv² = p² / 2m J
Potential energy U = mgh (near the surface) J
Work-energy theorem W_net = ΔK = ½mv² − ½mu²
Conservation (no friction) mgh = ½mv² so v = √(2gh)
Work done by friction W = f × d (turns into heat)
Power P = W / t = Fv cosθ W = J s⁻¹
Efficiency η = useful output / input × 100%
1 horsepower 746 W
1 kWh 3.6 × 10⁶ J
Spring W = ½kx²
Absolute PE U = −GMm / r
Escape velocity vₑ = √(2GM/R) = √(2gR) ≈ 11.2 km s⁻¹
Orbital speed near Earth v₀ = √(gR) ≈ 7.9 km s⁻¹, vₑ = √2 v₀
Worked MCQs
1. Work-energy theorem. A force accelerates a 4 kg object from 3 m/s to 6 m/s in 8 s. How much work does it do?
(a) 27 J (b) 54 J (c) 72 J (d) 96 J
W = ½m(v² − u²) = ½ × 4 × (36 − 9) = 2 × 27 = 54 J
Answer (b). The 8 s is there to tempt you into finding acceleration and distance first. You don't need either. (a) is what you get if you forget the ½m and use v² − u² alone.
2. Power at an angle. A 500 N force acts on an object moving at 10 m/s. The power delivered is 2500 W. What is the angle between the force and the velocity?
(a) 0° (b) 90° (c) 60° (d) 23°
P = Fv cosθ
2500 = 500 × 10 × cosθ
cosθ = 0.5 so θ = 60°
Answer (c).
3. Motor pulling a cable. A motor exerts 40 N on a cable and pulls it 30 m in one minute. What power does it supply?
(a) 200 W (b) 20 W (c) 10 W (d) 2 W
W = 40 × 30 = 1200 J
P = 1200 / 60 = 20 W
Answer (b). The trap is dividing by 1 instead of 60 and picking a big number. Convert time to seconds before you divide.
4. Machine gun power. A gun fires 360 bullets per minute at 360 km/h. Each bullet has a mass of 20 g. What is the power of the gun?
(a) 75 W (b) 300 W (c) 600 W (d) 1200 W
Bullets per second 360 / 60 = 6
Speed 360 km/h ÷ 3.6 = 100 m/s
KE per bullet ½ × 0.02 × 100² = 100 J
Power 6 × 100 = 600 W
Answer (c). This one question tests three unit conversions. Slow down on it.
5. Escape velocity with a shrunken Earth. Earth's radius shrinks to a quarter of its value while its mass stays the same. What happens to escape velocity?
(a) doubles (b) halves (c) stays the same (d) quadruples
vₑ = √(2GM/R)
R → R/4 so vₑ → √4 × vₑ = 2vₑ
Answer (a). Write the version with G and M here. If you use √(2gR), you will think vₑ halves, because you forget that g itself goes up 16 times when R drops to a quarter.
Traps that cost marks
- Work is zero when force is perpendicular to motion. The normal force on a sliding block, the tension in a circular whirl, and gravity on a satellite in circular orbit all do zero work.
- No displacement means no work. A ball bouncing off a rigid wall does zero work on the wall, even though it pushes hard on it. A man holding a heavy bag still does zero mechanical work on it.
- Same force or same stretch? Two springs with k₁ greater than k₂: stretch them the same distance and more work goes into the stiff one. Pull them with the same force and more work goes into the soft one, because W = F² / 2k.
- Doubling speed quadruples kinetic energy. Momentum only doubles. If KE doubles, momentum goes up by √2.
- Escape velocity does not depend on the mass of the object or the direction you launch it. A 1 g pebble and a rocket need the same 11.2 km/s from Earth's surface.
- mgh is only for small heights. For satellites and escape questions, use −GMm / r.
Speed tips for the exam
Divide km/h by 3.6 before anything else. 36 km/h is 10 m/s, 72 km/h is 20 m/s, 108 km/h is 30 m/s and 360 km/h is 100 m/s. These four come up again and again.
For "falls from height h, find speed" questions, skip the equations of motion and use v = √(2gh). From 5 m that is 10 m/s, from 20 m it is 20 m/s, from 45 m it is 30 m/s.
When a question changes one quantity and asks what happens to another, write the proportionality first (vₑ ∝ 1/√R at fixed M) and plug the ratio in. You never need actual values.
The equations here build on force and motion, and the satellite part continues in circular and rotational motion.
FAQ
Is escape velocity in the NET syllabus?
Yes. Escape velocity is in the syllabus summary for this chapter. Know the formula, the value of about 11.2 km/s for Earth, and that it does not depend on the mass of the object.
What is the difference between work and power?
Work is energy transferred, in joules. Power is how fast that transfer happens, in joules per second, or watts.
Can work be negative?
Yes. When the force points against the displacement, cosθ is negative. Friction on a sliding block and gravity on a ball thrown upward both do negative work.
How many questions come from work and energy in NET?
NUST does not publish chapter counts. Our syllabus estimate is about 6 of the derived 60 physics MCQs.
