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ASPhysicsCIEExam Questions1. Physical Quantities & Units1.2 SI Units

SI Units (CIE AS Physics)

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1.2 SI Units

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1.2 SI Units

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1a
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Table 1.1 shows SI base quantities and their corresponding base unit.

Table 1.1
SI base quantity SI base unit
Mass kilogram, kg
Time  
Length  

(i)
Complete the missing SI base units for time and length in Table 1.1.
[2]
(ii)
Complete Table 1.1 by adding two other base quantities and their units.
[2]

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1b
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Newton's second law of motion describes the relationship between force F mass m and acceleration a:

F space equals space m a

The derived unit for force is the newton (N).

Use Newton's second law to write 1 N in SI units.

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1c
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The kinetic energy equation describes the relationship between energy E, mass, m, and velocity, v.

E subscript k space equals space 1 half m v squared

The derived unit for energy is the joule (J).

Use the equation linking kinetic energy and speed to write 1 J in SI base units.

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1d
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The derived unit for power P is the watt W.

Given that power is the energy transferred E per unit time t, deduce the SI base units for power

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2a
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Identify the SI base quantities by drawing a circle around those listed in Fig. 1.1.

1-2-e-q2a-sq-cie-ial-physics

Fig. 1.1

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2b
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Complete the missing prefixes and powers of ten in Fig. 1.2

 
 

Prefix

Power of ten

tera

 
 

109 

 

103 

 centi

 10−2

milli

 

micro

 

 

10−9

pico

10−12

Fig. 1.2

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2c
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Convert the following measurements into standard form and to the specified number of significant figures.

i)
0.71 GJ to 3 s. f.

[1]

ii)
24.5 kW to 4 s .f.

[1]

iii)
0.003823 mm to 1 s. f.

[1]

iv)
644.9 pN to 2 s.f.

[1]

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2d
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Convert the following from their standard form into measurements with the most suitable prefixes

 

         9.3 × 106 J = __________ J

         7.4 × 103 W = __________ W

         1.0 × 10−2 m = __________ m

         5.3 × 10−9 C = __________ C

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3a
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Scientists around the world use the same internationally agreed system of units. These are called the fundamental SI base units and are listed in Fig. 1.1. 

 

Quantity

Name

Symbol

length

 

 

 

kilogram

 

 

 

s

 

ampere

 

temperature

 

K

Fig. 1.1

Complete the missing quantities, names and symbols in Fig. 1.1.           

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3b
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Use the equation linking kinetic energy and speed to write 1 Joule in SI base units. 

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3c
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Use the equation Charge = Current × Time to write 1 Coulomb in SI base units.

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3d
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Use the equation Energy = Charge × Potential Difference to write 1 volt in SI base units.

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1a
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Define the following quantities and state their SI base units

(i)
velocity
[2]
(ii)
acceleration
[2]
(iii)
density
[2]

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1b
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The pressure P due to a liquid of density rho is related to the depth h by the expression   

      P space equals space rho g h

where g is the acceleration of free fall.

Use this expression to determine the derived units of pressure P.

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1c
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The speed v of a sound wave through a gas of pressure P and density rho is given by the equation

         v space equals space square root of fraction numerator straight gamma P over denominator rho end fraction end root

where straight gamma is a constant.

Show that the constant straight gamma has no unit.

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2a
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Derive the SI base unit of force.

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2b
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As a spherical object of radius r moves through the air at speed v, it experiences a force F due to air resistance.

The resistive force F is given by 

      F space equals space k r v

Where k is a constant.

Derive the SI base unit of the constant k.

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3a
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Fig 1.2 shows a turbine that is used to generate electrical power P from wind travelling with velocity v.

1-1-wind-turbine-catalogue-cie-sq-ial

The useful power output P of the turbine is given by

P space equals space C subscript P L squared rho v cubed

Where L is the length of each blade, ρ is the density of air, v is the wind velocity and CP is a constant.

Show that the constant CP has no units.

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3b
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A local council is looking into building wind turbines to supply power to 2500 households in a village. The average energy consumption of a household in the village is 3000 kWh a year.

Fig. 1.3. shows an image from a catalogue detailing the different sizes and power outputs of available wind turbines.

1-1-4d-m-1-1-vector-force-triangle-cie-ial-sq

They decide to build 8 of the same wind turbine to supply the entire village with electricity. 

(i)
Determine which of the wind turbines in Fig. 1.3. the council decided to build.
[3]
(ii)
The chosen turbine delivers the power specified at a CP value of 0.45. This value can only be achieved above certain wind velocities.
Estimate the average wind velocity needed to power the village for a year. The density of air is 1.3 kg m−3.
[2]

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1a
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Convert the following measurements

 
(i)
42 km3 into mm3 
[2]
(ii)
25 light-years into nm
[3]
(iii)
0.05 kWh into PeV
[3]

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1b
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The frequency f of a stationary wave on a string is given by 

         f to the power of k space equals space fraction numerator T over denominator 4 m L squared end fraction

where L is the length of the string, T is the tension in the string, m is the mass per unit length of the string and k is a dimensionless constant.

By considering the homogeneity of the equation, determine the value of k.

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1c
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The current I through a semiconductor diode given by 

I space equals space I subscript 0 space e to the power of negative fraction numerator q V over denominator n T end fraction end exponent

where I subscript 0 is the initial current, q is the charge of an electron, V is the applied potential difference, T is the temperature and n is a constant.

(i)
By considering the homogeneity of the equation, determine the units of n.
[3]
(ii)
Use the datasheet to determine the name of this constant.
[1]

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2a
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Estimate the time it takes light to cross the nucleus of a hydrogen atom.

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2b
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A foil made from gold has a thickness of 0.132 µm. A gold atom has a radius of 146 pm.

(i)
Estimate the number of layers of atoms in the gold foil to the nearest hundred.
[2]

(ii)
The radius of a gold nucleus is about 20 000 times smaller than its atomic radius. The cross-sectional area of a nucleus is commonly measured using the unit barn, which is represented by the symbol b. 
 
Estimate the cross-sectional area of a gold nucleus in barns (b).
 
1 b = 100 fm2
[4]

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2c
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The atomic mass unit u is a common unit used in nuclear physics. 1u is equivalent to 931.5 MeV c–2

Show that 1u is approximately equal to the mass of a proton in kg.

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2d
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An acre is a unit of land measurement approximately equal to 4050 m2 which is roughly equivalent to the size of a football field.

An Astronomical Unit, or 1 AU, is defined as the average distance between the Earth and the Sun and is approximately equal to 150 million km.

Estimate the number of football fields that could fit lengthways between the Earth and the Sun.

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