A simple pendulum oscillates in simple harmonic motion. It can be assumed that there are no energy losses in the system.
(a)
Prove dimensionally that the work-energy principle applies for this system.
[2]
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(b)
Complete the following table by giving the SI base units. Then estimate the order of magnitude for each of the physical quantities.
[4]
Physical Quantity
SI Base Unit
Order of Magnitude
Acceleration of freefall Earth (g )
m s−2
Stephan-Boltzmann constant (σ)
10−7
Speed of a β particle
Specific heat capacity of water (c )
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The density, ρ , and pressure, p , of a gas are related by the expression:
where x and γ are constants.
(c)
Given that the constant γ is dimensionless
(i)
Determine the unit of x .
[1]
(ii)
Suggest what quantity is being represented by the symbol x .
[1]
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(a)
Identify the quantity with the SI base units of m3 kg−1 s−2 .
[3]
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(b)
Convert the following measurements to the appropriate unit, and express to an appropriate number of significant figures.
90 000 GW = ____________ mW
45 .1 hF = _____________ fF
0.60 pm = _____________ km
214 minutes = _____________ ms
[4]
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A sheet of silver has a thickness of 0.671 µm. A silver atom has a radius of 172 pm.
(c)
Estimate the number of layers of atoms in this sheet to the nearest thousand.
[2]
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(a)
Identify the variable that has the SI base units kg m2 s−3 A−2 .
[3]
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(b)
Explain why potential difference is not defined as current × resistance.
[2]
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(c)
Convert 0.01 kWh into PeV.
[3]
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Tensile stress (σ) is defined as the force applied per unit cross-sectional area on a material. The tensile strength is the maximum amount of tensile stress a material can be subjected to before fracturing, meaning that it is equivalent to the tensile stress at the breaking point.
The humerus bone is approximately cylindrical and has a tensile strength of 0.17 GPa and a diameter of 20 mm.
(a)
Calculate the maximum force on the humerus bone before it fractures.
[4]
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The femur bone is the strongest bone in the body. It has a tensile strength of 0.135 kN mm– 2 .
(b)
Calculate the tensile strength of the femur bone in GPa.
[4]
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(c)
Calculate the number of cubic millimetres (mm3 ) in 23 km3 .
[2]
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(a)
Estimate the time it takes light to cross the nucleus of a hydrogen atom.
[2]
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(b)
Estimate the order of magnitude with an appropriate SI unit and correct prefix for the following quantities.
(i) Mass of an aeroplane.
[1]
(ii) Current through an LED.
[1]
(iii) Time between two heartbeats.
[1]
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1 u is the atomic mass unit and a common unit used in nuclear physics.
(c)
Show that its value in kg is approximately equal to the mass of a proton in kg.
[3]
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The cross-sectional area of nuclei are commonly measured in the units barn , which are represented by the symbol b . 1 barn = 100 fm2
(d)
Calculate the value of a nano barn (nb) in m2 .
[4]
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