Worksheet solutions

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1 Units of measure

1 S.I.: Systéme International, French for International System.

2 a To provide scientists with a common metric based system of units.

b In 1960.

3 a metre, m b kilogram, kg c second, s

4 a 7.8 × 100 b 3.6 × 10−2c 5.200 712 × 106

5 a 610 b 103 000 c 0.0592 d 0.000 032 14

6 a 10−6 g b 10−9 g c 10−3 l d 100 t

e 103 g f 106 t

7 a 1000 (103) b 1 000 000 (106) c 0.000 001 (10−6)

d 0.001 (10−3)

8 a 1.0 × 103 kg b 1.0 × 106 m c 1.0 × 10−3 s

d 3.7 × 10−1 kg

9 a 2700 mm b 224 mm c 330 mm d 0.056 mm

10 a 5 s b 40 000 s

11 a 200 b 200 000

2 Speed, acceleration and motion graphs

1 12.5 km/hr = 13 km/hr (2 s.f.)

2 400 s

3 7.5 s

4 10 m/s2

5 a

b The car starts from rest and for the first 12 s speeds up to 18 m/s with a constant acceleration, given by the constant slope of the speedtime graph. Its acceleration decreases to zero between 12 and 16 s until the car has a constant speed of 21 m/s. c 15 m/s d 1.5 m/s2

6 a The object starts from rest and for the first 20 s speeds up to 20 m/s with a constant acceleration, given by the constant slope of the velocity-time graph. b The objects acceleration becomes zero between 20 and 27.5 s with a constant speed of 20 m/s. c The object decelerates (negative acceleration) and slows down from 20 m/s to rest. d (× 20 × 20) + ((27.5 − 20) × 20) + ( × (40 − 27.5) × 20) = 200 + 150 + 125 = 475 m e 1 m/s2

7 a The object starts from an initial position and in the first 10 s moves with a constant speed, given by the constant slope of the distance-time graph, covering a distance of 20m. b The object remains stationary for the 20 s, 20m from its initial position.

c The object returns to its initial position in the 15 s.

d Since the object returns to its original position its displacement is zero. e The object moved 20 m forward and 20 m back, so travelled a total distance of 40 m.

3 Gas laws

1 a As the molecules collide and rebound off the walls of the container they receive an impulse from the wall to change their momentum. An impulse is a force  time. From Newton’s 3rd law of motion forces only occur in pairs (for every force there is an equal and opposite force. Therefore the molecules must exert a force onto the walls of the container. This force is distributed over the surface area of the chamber walls that constitutes a pressure (P=F/A). b If the number of molecules in the container increases then there will be more collisions per unit time between the molecules and the wall, hence an increased pressure. c If one measures the pressure of a constant quantity of gas inside a rigid container as a function of temperature, the temperatures tends to −273 °C when the pressure tends to zero. Of course the pressure will go to zero before −273 °C as the gas liquefies. Alternatively, if one measures the volume of a flexible container of a constant quantity of gas as a function of temperature, the temperatures tends to −273 °C when the volume tends to zero.

2 a 15 cm3b 6 cm3

3 100 cm3

4 Since no gas may exit the aerosol can does not mean that it is empty. Rather that the pressure inside the can is the same as that outside the can (atmospheric pressure). By heating the can up, by throwing it on a fire, will increase the pressure inside the can, potentially causing the can to explode when the can no longer maintain such a large pressure difference.

5 Take a flexible container, such as a spherical balloon, and fill it with a fixed quantity of air. Estimate its volume by measuring its diameter. Place the balloon in the freezer until cold. Re-estimate its volume. Place the balloon in the sun and re-estimate its diameter, if it does not burst. Allow the balloon to return to the original temperature. If no gas has escaped it should have the same initial volume.

6 12.5 cm3

4 Work, energy and power

1 Work is the force multiplied by the distance moved in the direction of the force.

2 Work done by a force on an object is equal to the change in the kinetic energy of that object, i.e. the work-kinetic energy theorem.

3 a 1000 J b 150 J

4 a 7071 J b 75.2 N

5 10 J

6 a 50 000 J b 150 000 J

7 289 m

8 120 000 J

9 mgh =mv2→ v = (2gh) =(2×10×10) = 14 m/s

10 a 1900 W b Since the P is inversely proportional to time, doubling the power of the electric motor will half the time to raise the curtain: 2 s. c Frictional forces are present that reduce the net force applied by the electric motor. d 40 %

5a Thermal physics

1 Fill in the missing words: a The three states of matter are solids, liquids and gases b Gases consist of tiny particles or molecules travelling at high speed. c A solid has a definite size and a definite volume because the forces between its particles are very strong.

d A liquid has weaker forces between its particles and so does not have a definite shape. e If a substance is cooled down, its molecules move at a slower or lower speed. f When some molecules pass through some other molecules, we call it diffusion g The twisting and jerking of smoke particles when air particles or molecules hit them is called Brownian motion.

2 The gas molecules move at high speed colliding occasionally with other molecules. In doing so they continually change their velocity (speed and direction), giving rise the observed Brownian motion or random walk behaviour. Molecules move from regions of high concentration to regions of lower concentration giving rise to the observed diffusion effect.

3 When heated, molecules travel at higher speeds between collisions.

4 a Capillary rise b The adhesive forces are stronger than the cohesive forces so that the liquid gets pulled up the wall of the container. This is most pronounced in thin tubes or capillaries.

c Capillary rise is to be avoided in the construction of buildings where ground water could rise up the capillaries in the bricks resulting in damp walls, so-called rising damp. This causes mould to cultivate in and on the walls and is extremely dangerous in winter if this water were to freeze creating internal stresses in the brickwork. This can be avoided by laying an impermeable layer close to the ground level in the brickwork to inhibit the water from rising above it.

5 Cohesion is the force between similar molecules, i.e. water and water Adhesion is the force between dissimilar molecules, i.e. water and glass

6 The mercury cohesive force is very strong and stronger than the adhesive force, such as with glass. This means that at the meniscus the mercury molecules try to avoid contact with container and favour contact with similar mercury molecules, resulting in an ‘n-shaped’ meniscus.

7 a 25 cm b i the oil drop is spherical ii the oil film is circular

iii the film is one molecule thick

5b Specific heat capacity and latent heat

1

Material /
Mass/kg
/ Temp. rise/°C / Specific heat capacity/ (J/kg K)
A / 1.0 / 1.0 / 2000
B / 2.0 / 5.0 / 200
C / 0.5 / 4.0 / 1000

2 2750 J

3 1680 J

4 9 200 000 J

525 100 J

6 a i Heats up from −10°C to 0°C ii Changes phase from solid to liquid iii Heats up from 0°C to 6°C b 210 J c 3400 J

d 3862 J

6 Waves

1 Human wave at a sports stadium, electromagnetic waves

2 Sound

3 104 m/s

4 a 4 cm b 20 m c The point at 30 m along the rope.

d 2 Hz e 0.5 s

5 Between 20 and 20000 Hz, depending on age and exposure.

6 0.138 s

7 128 ms

8 0.777 m

7 Electromagnetic waves

1 c = 3 × 108 m/s

2 They all reflect, refract and diffract; they are non-mechanical waves so do not need a medium through which to travel; they are transverse waves

3 400 nm to 750 nm

4 Radio waves

5 a UV b microwave c gamma d IR e microwave

or IR f X-ray g UV, X-ray or gamma h UV and X-ray i microwave

6 UV: causes skin cancer by ionising cells X-ray: causes cancer by ionising cells Gamma: causes cancer by ionising cells

7 For X-rays: v = 3 × 1017 × 1 × 10−9 = 3 × 108 m/s

For radio waves: v = 1 × 106 × 3 × 102 = 3 × 108 m/s

8 Placing a thermometer just beyond the red end of the visible spectrum would indicate a temperature rise compared with the electromagnetic source switched off or blocked by your hand.

9.

Region / Production / Detection / Application
UV / Very hot objects or gas discharge /  Photographic paper
Causescertainmaterials toGloworfluoresce /  Kills bacteria
 Provides the body with vitamin E
 Checking for fake bank notes
X-ray / Free high energy charged particles, such as electrons, into a target material, usually metallic. Some of their energy during the rapid declaration is emitted as X-rays. / Photographic
paper / X-ray photography for medical examinations
 Cancer treatment
 Inspecting the quality of welds
Gamma
rays / Emission from radioactive sources / Photographic
paper / • Cancer treatment
• Sterilizing food
and medical equipment

10 2 × 105 Hz

11 A light year is the distance that light travels in one Earth year.Using d = v × t and

1 year = 365 days × 24 hours × 60 mins × 60 secs = 31 536 000 s 1 light year = 3 × 108 × 3.15 × 107 = 9.46 × 1015 m

12 Microwaves, produced in a microwave oven, penetrate deep into the food and excite the water molecules in the food causing a heating effect.

Infrared radiation is absorbed by the food in direct sight of the infrared source, causing a heating effect. The food is then cooked by conduction from the outside inwards.

8 Electricity

1 a A source of EMF, such as a battery or power supply, to drive the charge around the circuit b Components made of conducting materials c A complete circuit

2 To regulate the current flowing through the circuit 3 a

4 a As the temperature increase its resistance decreases b As the light intensity increases its resistance decreases

5 a 1.57 m b 0.39 m

6 a and b

c 0.75 A d 3 V e Brighter as the total current in the circuit would increase.

7 C; power, P = current, I × potential difference, V

Rearranging gives

The 13 A fuse will allow the operational current of 10.4A to flow but will protect the kettle for currents, such as caused by power surges, greater than 13 A to flow.

8 3 600 000 J = 3.6 MJ

9 Magnetism and electromagnetism

1 a The field of a bar magnet b i The Earth’s magnetic north is in the Earth’s southern hemisphere and the Earth’s magnetic south is in the Earth’s northern hemisphere. ii There exists an angle of around 23° between the Earth’s magnetic field axis and the Earth’s rotational axis or geographical axis. c One end of a compass or magnet is called the north pole, or north-seeking pole, as it seeks out the Earth’s south magnetic pole, located in the Earth’s northern hemisphere.

2 Bar 1: un-magnetised ferromagnetic material, such as iron Bar 2: magnetised ferromagnetic material, such as steel Bar 3: magnetised ferromagnetic material, such as steel Since C and D repel they must be similar poles of a magnetic material. Since A is attracted to both ends of bar 2 it cannot be a magnet but is a magnetised material as magnetic induction occurs.

3 Ferromagnetic

4 Hard ferromagnetic materials, such as steel, are hard to magnetise and hard to demagnetise.

Soft ferromagnetic magnetic materials, such as iron, are easy to magnetise and easy to demagnetise.

Permanent magnets are made out of hard ferromagnetic materials.

5 i iron ii cobalt iii nickel

6

7

8 i Put it in a coil producing an alternating magnetic field, i.e. by passing a AC current through the coil, and remove the permanent magnet slowly ii Heat the permanent magnet up above the Curie temperature iii Drop the permanent magnet

9 Place the ferromagnet in a coil producing a constant magnetic field, i.e. by passing a DC current through the coil.

10 Regions of the material that have the same magnetization Magnetised ferromagnets have their domains aligned Non-magnetised ferromagnets have their domains randomly aligned

11 i Magnets of fridge doors to hold notes ii Used in loudspeakers

iii Used in electric motors.

12 a and c.

b Iron

d i Scrap yard magnet. ii Magnetic relay

10 Logic gates

1 When the temperature, in either or both rooms, drops below a set temperature the heating system should switch on.

2

Inputs / Outputs
A / Not A / B / Q
0 / 1 / 0 / 0
1 / 0 / 0 / 0
0 / 1 / 1 / 1
1 / 0 / 1 / 0

3

Inputs / Outputs
A / Not A / B / Q
0 / 1 / 0 / 0
1 / 0 / 0 / 0
0 / 1 / 1 / 1
1 / 0 / 1 / 0

4

Inputs / Outputs
A / B / C / D / E / F / Q
0 / 0 / 0 / 0 / 0 / 0 / 0
1 / 0 / 1 / 0 / 0 / 0 / 0
0 / 1 / 0 / 1 / 0 / 0 / 0
1 / 1 / 1 / 1 / 1 / 1 / 1

Other combinations of inputs can be found but all give a low output except when all inputs are high.

Any application where all 4 high inputs are required to give one high output. For example, a certain decision can only be made when the decision is without descent. A company selling shares needs all four directors approval before any sale can be made, or a jury of four to find an accused of murder.

11 Radioactivity

1 a Background radiation is the radiation in the environment and is caused by the radioactive materials in rocks, the air and our bodies, and also from cosmic rays from outer space. b i stay as far away from the source as possible ii minimize the time that one is in close contact with the source iii remove contaminated clothing and wash parts of body that came into contact with the source iv never eat or drink whilst in close proximity to radioactive sources c i irradiating foods to enhance shelf life ii irradiating medical tools for sterilization iii controlling the thickness of paper in a paper mill iv as a tracer material in medical examinations v as a tracer in identifying leaks in a water system d i Add a sheet of paper between the source and detector. The alpha source will be stopped whereas the beta source will be only attenuated slightly. ii Pass the emitted beam through an electric or magnetic field. A beam of alpha particles will be deflected in the opposite direction to the beam of beta particles.

2 a The number of nucleons (protons + neutrons) b i There are 92 protons in the nucleus ii There are 92 electrons in the neutral atom c Uranium 238 has 3 more neutrons than uranium 235

3 a The daughter nucleus has 2 less protons, i.e. −2 b The daughter nucleus has one extra proton, i.e. +1 c The daughter nucleus has the same number of protons, i.e. 0

4 a Neutrons, emitted during the decay of a radioactive nucleus such as uranium 235, can be absorbed by a neighboring radioactive nucleus, causing it to decay emitting a neutron and so on. This chain reaction can result in a huge and rapid release of energy. b Control rods, usually made from boron or cadmium, are inserted in between the fuel rods to adsorb some of the emitted neutrons.

5 25 mins

6 protons : neutrons : electrons

1 : 1 :

+1 : 0 : −1

7 a i electron ii proton iii neutron iv electron v nucleus vi nucleon vii electron b Complete the table.

electrons / protons / neutrons / nucleon number / symbol
sodium-23 / 11 / 11 / 12 / 23 /
aluminium-27 / 13 / 13 / 14 / 27 /
stronitium-90 / 38 / 38 / 52 / 90 /

c i alpha ii gamma iii beta iv gamma v alpha vi alpha

vii beta viii gamma ix gamma x beta xi alpha xii alpha

8 D

9 a Isotopes are nuclei of the same element (same atomic number or number of protons) but with a different number of neutrons (mass number b Since isotopes are the same element, they have the same number of electrons and therefore the same chemical reactivity

10 They have no charge and therefore do not experience a force in the presence of the electric field.

11

Half-life is approximately 3 mins

12 a 10 mins b 30 mins c 4 counts per second d 110 mins

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