Q: A steel cable in a suspension bridge stretches by 2.0 cm when a load of 10,000 N is applied. If the cable is 20 m long and has a cross-sectional area of $$2.5 \times 10$$^{-4}$$ \ \mathrm{m}^2$$, what is the Young modulus $$E of $$the steel used in the cable?

$$E = \dfrac{F L}{A \Delta L} = \dfrac{10,000 \times 20}{2.5 \times 10$$^{-4}$$ \times 0.02} = 4 \times 10$$^{9}$$ \ \mathrm{Pa}$$

Q: A submarine is at a depth of $$500 \ \mathrm{m} in $$seawater ($$\rho = 1025 \ \mathrm{kg/m}^3). $$What is the gauge pressure at this depth? (Take $$g = 9.8 \ \mathrm{m/s}^2)$$

$$P = \rho g h = 1025 \times 9.8 \times 500 = 5.02 \times 10$$^{6}$$ \ \mathrm{Pa}$$

Q: A block of wood floats in water with $$60\% of $$its volume submerged. What is the density of the wood if the density of water is $$1000 \ \mathrm{kg/m}^3$$?

$$\rho_{wood} = 0.6 \times 1000 = 600 \ \mathrm{kg/m}^3$$

Q: A laboratory experiment measures the time constant $$\tau of an RC $$circuit as $$5 \ \mathrm{s}. If $$the resistance is $$2 \ \mathrm{k\Omega}$$, what is the capacitance $$C$$?

$$C = \dfrac{\tau}{R} = \dfrac{5}{2000} = 2.5 \times 10$$^{-3}$$ \ \mathrm{F}$$

Q: A wire of length $$2 \ \mathrm{m}$$ and cross-sectional area $$1 \times 10$$^{-6}$$ \ \mathrm{m}^2$$ has a resistance of $$0.34 \ \Omega. $$What is the resistivity $$\rho of $$the material?

$$\rho = \dfrac{R A}{L} = \dfrac{0.34 \times 1 \times 10$$^{-6}$$}{2} = 1.7 \times 10$$^{-7}$$ \ \Omega \cdot \mathrm{m}$$

Question 1

A steel cable in a suspension bridge stretches by 2.0 cm when a load of 10,000 N is applied. If the cable is 20 m long and has a cross-sectional area of $$2.5 	imes 10$$^{-4}$$ \ \mathrm{m}^2$$, what is the Young modulus $$E of $$the steel used in the cable?

Accepted Answer

$$E = \dfrac{F L}{A \Delta L} = \dfrac{10,000 	imes 20}{2.5 	imes 10$$^{-4}$$ 	imes 0.02} = 4 	imes 10$$^{9}$$ \ \mathrm{Pa}$$

Question 2

A laboratory experiment uses a spring that obeys Hooke’s Law. If a force of $$8 \ \mathrm{N}$$ causes an extension of $$0.04 \ \mathrm{m}$$, what is the spring constant $$k$$?

Accepted Answer

$$k = \dfrac{F}{x} = \dfrac{8}{0.04} = 200 \ \mathrm{N/m}$$

Question 3

Which of the following best describes the difference between elastic and plastic deformation in engineering materials?

Accepted Answer

Elastic deformation is reversible, while plastic deformation is permanent.

Question 4

A submarine is at a depth of $$500 \ \mathrm{m} in $$seawater ($$\rho = 1025 \ \mathrm{kg/m}^3). $$What is the gauge pressure at this depth? (Take $$g = 9.8 \ \mathrm{m/s}^2)$$

Accepted Answer

$$P = ho g h = 1025 	imes 9.8 	imes 500 = 5.02 	imes 10$$^{6}$$ \ \mathrm{Pa}$$

Question 5

A hydraulic lift uses Pascal’s law to lift a car of mass $$1200 \ \mathrm{kg}. If $$the area of the input piston is $$0.01 \ \mathrm{m}^2$$ and the output piston is $$0.5 \ \mathrm{m}^2$$, what minimum force must be applied to the input piston to lift the car? ($$g = 9.8 \ \mathrm{m/s}^2)$$

Accepted Answer

$$F_{in} = \dfrac{A_{in}}{A_{out}} F_{out} = \dfrac{0.01}{0.5} 	imes 1200 	imes 9.8 = 235.2 \ \mathrm{N}$$

Question 6

A block of wood floats in water with $$60\% of $$its volume submerged. What is the density of the wood if the density of water is $$1000 \ \mathrm{kg/m}^3$$?

Accepted Answer

$$ho_{wood} = 0.6 	imes 1000 = 600 \ \mathrm{kg/m}^3$$

Question 7

A laboratory experiment measures the time constant $$	au of an RC $$circuit as $$5 \ \mathrm{s}. If $$the resistance is $$2 \ \mathrm{k\Omega}$$, what is the capacitance $$C$$?

Accepted Answer

$$C = \dfrac{	au}{R} = \dfrac{5}{2000} = 2.5 	imes 10$$^{-3}$$ \ \mathrm{F}$$

Question 8

Which of the following statements about Kirchhoff’s laws is correct?

Accepted Answer

Kirchhoff’s first law states that the sum of currents entering a junction equals the sum leaving it.

Question 9

A wire of length $$2 \ \mathrm{m}$$ and cross-sectional area $$1 	imes 10$$^{-6}$$ \ \mathrm{m}^2$$ has a resistance of $$0.34 \ \Omega. $$What is the resistivity $$ho of $$the material?

Accepted Answer

$$ho = \dfrac{R A}{L} = \dfrac{0.34 	imes 1 	imes 10$$^{-6}$$}{2} = 1.7 	imes 10$$^{-7}$$ \ \Omega \cdot \mathrm{m}$$

Question 10

A $$12 \ \mathrm{V}$$ battery with internal resistance $$0.5 \ \Omega is $$connected to a $$5.5 \ \Omega$$ resistor. What is the current in the circuit?

Accepted Answer

$$I = \dfrac{\mathcal{E}}{R + r} = \dfrac{12}{5.5 + 0.5} = 2 \ \mathrm{A}$$

Question 11

A laboratory experiment finds that a wire stretches by $$0.5 \ \mathrm{mm}$$ when a force of $$100 \ \mathrm{N} is $$applied. If the original length is $$1 \ \mathrm{m}$$ and the cross-sectional area is $$1 	imes 10$$^{-6}$$ \ \mathrm{m}^2$$, what is the stress in the wire?

Accepted Answer

$$	ext{Stress} = \dfrac{F}{A} = \dfrac{100}{1 	imes 10$$^{-6}$$} = 1 	imes 10$$^{8}$$ \ \mathrm{Pa}$$

Question 12

A capacitor in a timing circuit is charged through a resistor. Which graph best describes the voltage across the capacitor as a function of time?

Accepted Answer

An exponential increase approaching a maximum value: $$V(t) = V_0$ (1 - e$$^{-t/RC}$$)$$

Question 13

A laboratory experiment uses a potential divider circuit with a thermistor. As the temperature increases, what happens to the output voltage across the thermistor?

Accepted Answer

The output voltage decreases because the resistance of the thermistor decreases.

Question 14

A conductor moves perpendicularly through a magnetic field of $$0.2 \ \mathrm{T} at a $$speed of $$5 \ \mathrm{m/s}. If $$the charge is $$3 	imes 10$$^{-6}$$ \ \mathrm{C}$$, what is the magnetic force on the charge?

Accepted Answer

$$F = B q v = 0.2 	imes 5 	imes 3 	imes 10$$^{-6}$$ = 3 	imes 10$$^{-6}$$ \ \mathrm{N}$$

Question 15

A generator coil of area $$0.1 \ \mathrm{m}^2$$ rotates in a uniform magnetic field of $$0.5 \ \mathrm{T}. If $$the coil makes one complete rotation in $$0.2 \ \mathrm{s}$$, what is the maximum induced emf according to Faraday’s law?

Accepted Answer

$$\mathcal{E}_{max} = B A \omega = 0.5 	imes 0.1 	imes \dfrac{2\pi}{0.2} = 0.05 	imes 10\pi = 0.5\pi \ \mathrm{V}$$

Question 16

A student plots a graph of force versus extension for a wire and finds a straight line passing through the origin. What does the gradient of this graph represent?

Accepted Answer

The spring constant $$k in $$Hooke’s law.

Question 17

A car battery rated at $$12 \ \mathrm{V}$$ and $$60 \ \mathrm{Ah} is $$used to power a $$120 \ \mathrm{W}$$ headlamp. How long can the headlamp be powered before the battery is depleted?

Accepted Answer

$$t = \dfrac{60 \ \mathrm{Ah} 	imes 12 \ \mathrm{V}}{120 \ \mathrm{W}} = 6 \ \mathrm{h}$$

Physics UOL Module Handbook: Foundation Study Guide

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