IB Physics HL A 3 Work Energy and Power Questions

Practise IB Physics HL A.3 by interpreting force–displacement evidence, tracking energy transfers, and calculating power, efficiency and fuel requirements.

Exam points

Find work from force–displacement data, using W = Fs cos θ for constant force or average force when it varies.
Use net work to relate energy transferred or dissipated to a change in kinetic energy.
Track transfers between energy stores while explaining how the total energy remains conserved.
Apply mechanical-energy conservation to find speed or height when losses are absent, including rotational motion.
Calculate kinetic energy and relate it to momentum using Ek = ½mv² = p²/(2m).
Calculate gravitational or elastic potential-energy changes using mgΔh and ½kx².
Calculate power from energy per time or force and speed, including P = Fv.
Interpret Sankey diagrams and energy/power ratios to calculate efficiency or identify losses.
Use fuel energy density per kilogram or cubic metre to estimate fuel required or energy available.

Covered syllabus points

A.3.1—Conservation of energy A.3.2—Work as energy transfer A.3.3—Sankey diagrams A.3.4—Work by constant force A.3.5—Work-energy change A.3.6—Mechanical energy A.3.7—Mechanical energy conservation A.3.8—Mechanical energy transformations A.3.9—Kinetic energy A.3.10—Gravitational potential energy A.3.11—Elastic potential energy A.3.12—Power A.3.13—Efficiency A.3.14—Fuel energy density

[Maximum number: 1]

Two sources of light produce an interference pattern on a screen.

Light of wavelength 720 nm is incident on two narrow slits that are separated by 0.12 mm . An interference pattern is observed on a screen. $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ are the points of destructive interference closest to the central maximum M .

Suggest how energy conservation is consistent with the fact that the energy at $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ is zero.

A beam of light containing all wavelengths in the range $[550 \mathrm{~nm}, 650 \mathrm{~nm}]$ is incident normally on a diffraction grating. The grating has 580 lines per mm . A diffraction pattern is observed on a screen as shown.

The energy missing at $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ is found at the maxima

[Maximum number: 11]

This question is about the motion of a ship and observing objects from it.

(a)

Outline the meaning of work.

[ 2 ]

work done = force × distance moved;
(distance moved) in direction of force;
or
energy transferred;
from one location to another;
or
work done $=F s \cos \theta$ ;
with each symbol defined;

(b)

Some cargo ships use kites working together with the ship's engines to move the vessel.

The tension in the cable that connects the kite to the ship is 250 kN . The kite is pulling the ship at an angle of $39^{\circ}$ to the horizontal. The ship travels at a steady speed of $8.5 \mathrm{~m} \mathrm{~s}^{-1}$ when the ship's engines operate with a power output of 2.7 MW .

[ 6 ]

(i)

Calculate the work done on the ship by the kite when the ship travels a distance of 1.0 km .

[ 2 ]

horizontal force $=250000 \times \cos 39^{\circ}\left(=1.94 \times 10^{5} \mathrm{~N}\right)$ ;
work done $=1.9 \times 10^{8} \mathrm{~J}$ ;

(ii)

Show that, when the ship is travelling at a speed of $8.5 \mathrm{~m} \mathrm{~s}^{-1}$ , the kite provides about 40 % of the total power required by the ship.

[ 4 ]

power provided by kite $=\left(1.94 \times 10^{5} \times 8.5=\right) 1.7 \times 10^{6} \mathrm{~W}$ ;
total power $=(2.7+1.7) \times 10^{6}(\mathrm{~W})\left(=4.4 \times 10^{6} \mathrm{~W}\right)$ ;
fraction provided by kite $=\frac{1.7}{2.7+1.7}$ ;
38 % or 0.38 ;
(must see answer to 2+ sig figs as answer is given)

Marking guidance:

Allow answers in the range of 37 to 39 % due to early rounding.
or
Award [3 max] for a reverse argument such as:
if 2.7 MW is 60 %;
then kite power is $\frac{2}{3} \times 2.7 \mathrm{MW}=1.8 \mathrm{MW}$ ;
shows that kite power is actually 1.7 MW ;
(QED)

(c)

The kite is taken down and no longer produces a force on the ship. The resistive force F that opposes the motion of the ship is related to the speed v of the ship by

F=k v^{2}

where k is a constant.
Show that, if the power output of the engines remains at 2.7 MW , the speed of the ship will decrease to about $7 \mathrm{~ms}^{-1}$ . Assume that k is independent of whether the kite is in use or not.

[ 3 ]

$\quad P=\left(k v^{2}\right) \times v=k v^{3}$ ;
$\frac{v_{1}}{v_{2}}=\left(\sqrt[3]{\left(\frac{P_{1}}{P_{2}}\right)}=\right) \sqrt[3]{\left(\frac{2.7}{4.4}\right)} ;$
final speed of ship $=7.2 \mathrm{~ms}^{-1}$ ; (at least 2 sig figs required).

Approximate answer given, marks are for working only.

[Maximum number: 1]

The Sankey diagram shows the energy input from fuel that is eventually converted to useful domestic energy in the form of light in a filament lamp.

What is true for this Sankey diagram?

The overall efficiency of the process is 10 %.

Generation and transmission losses account for 55 % of the energy input.

Useful energy accounts for half of the transmission losses.

The energy loss in the power station equals the energy that leaves it.

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Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question 3