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[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?

A

The overall efficiency of the process is 10 %.

B

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

C

Useful energy accounts for half of the transmission losses.

D

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

IB Physics HL A 3 Work Energy and Power Topic Practice

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IB Physics HL A 3 Work Energy and Power Topic Practice

Learn this topic

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Question (b)

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