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. July 2016

Alternating Current Circuits

Q- A sinusoidal voltage v(t) = (40.0V) sin(100t) is applied to a series RLC circuit with L = 160 mH, C = 00.9 µf, and R = 68 Ohm

a) What is the impedance of the circuit?

b) What is the maximum current?

c) Determine the phase angle ϕ and the average power in the equation i (t) = Imax sin (ωt – ϕ…

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Rotating pulley - Torque

Q- A pulley wheel of radius r and mass m is free to rotate about a fixed smooth horizontal axis through its center perpendicular to the plane of the pulley? A light in-extensible string passes over the pulley and carries particles of mass 4m and 2m, one at each end of the string. It can be assumed t…

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Current in lightning

(On request - Kylie)

Q- The potential difference between a storm cloud and the ground is 100 million volts. A charge of 2 coulomb flashes in a lightning bolt from cloud to earth. How much current is in the lightning flash, if it lasted for 0.1 second?

Solution:

The current is the rate of flow of…

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Motion in 2D - Aircraft in wind

Q- The airport B is due north of airport A. On a particular day the velocity of wind is (80i+25j) km/h. Relative to the air an aircraft flies with constant speed 208 km/h. When the aircraft flies directly from A to B
(a) Show its speed relative to the ground is 217km/h
(b)After flying from A to B th…

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Interference of light

Q- A material having an index of refraction of 1.30 is used as an anti-reflective coating on a piece of glass (µ = 1.5). What should be the minimum thickness of the film in order to minimize reflection of light of wavelength 500 nm.

Solution:

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Projectile Motion

Q- A baseball is hit into the air at an initial speed of 30 m/s and an angle of 60° above the horizontal. At the same time, the center fielder starts running towards the batter and catches the ball 1 m above the level at which it was hit. If the center fielder is initially 1.25 x 102 m from home pl…

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Relativity: Work and momentum

Q- (a) How much work is required to accelerate a proton from rest to a speed of 0.998 c.

      (b) What would be the momentum of this proton.

Solution:

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Simple Harmonic Motion

Q- A piston in a gasoline engine is in simple harmonic motion. Taking the extremes of its position relative to its center point as plus or minus 5.00cm, find the maximum velocity and acceleration of the piston when the engine is running at the rate of 3600 rev/min.

Solution:

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Rotational Motion - Reaction on axis

Q- A uniform circular disc has mass 4m and radius r. A particle of mass m is attached to the disc at point A of its circumference. The loaded disc is free to rotate about a horizontal axis which is tangential to the disc at the point B, where AB is a diameter. The disc is released from rest with AB …

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Electrostatics - Energy

Q- Two identical +7.5µC point charges are initially 5.5cm apart. If they are released at the same instant from rest, how fast will they be moving when they are very far apart? Assume they have identical masses of 1.0 mg.

Solution:

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Motion in 2D - Collision

Q- Particles of masses m1 = 3kg and m2 = 5kg move on a collision course with velocities: u1 = (7 i + 3 j) m/s and u2 = (3 i + 7 j) m/s, respectively. After they collide, their velocities are v1 = (a i + b j) m/s and v2 = (c i + 4 j) m/s, respectively. If the collision is perfectly elastic, determine…

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Wave Optics - Diffraction Grating

Q1- Light from an argon laser strikes a diffraction grating that has 5310 grooves per cm. The center and the first order principal maximum are separated by 0.488 m on a wall 1.72 m from the grating. Determine the wavelength of the laser light.

Q2- A helium-neon laser (λ = 632 nm) is used to calibr…

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Motion in 1D

Q- In reaching her destination, a backpacker walks with an average velocity of 1.07 m/s, due west. This average velocity results, because she hikes for 5.36 km with an average velocity of 2.37 m/s due west, turns around, and hikes with an average velocity of 0.748 m/s due east. How far east did she …

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Refraction of light

Q- A flint glass plate (n = 1.66) rests on the bottom of an aquarium tank. The plate is 8.00 cm thick and is covered with a layer of water (n = 1.33) 12.0 cm deep. Calculate the apparent thickness of the plate as viewed from straight above the water.

Solution:

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WPE - Collision

Q- A ball is launched vertically upwards with an initial velocity of 4 m/s from a height of 8 meters above the ground. the ball rises and then falls to the ground. After hitting the ground once, the ball rises back up to a maximum height of 3 meters. Determine the coefficient of restitution between …

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Electromagnetic Waves - Poynting vector

Q- In a region of free space at an instant of time the electric field is E =(80.0i + 32.0j – 64.0k)N/C and the magnetic field is B = (0.200i + 0.0800j + 0.290k) micro-Tesla.

a) Show that the two fields are perpendicular to each other.

b) Determine the Poynting vector for these fields.

Solution:

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NLM

Q- A ball is tied to the end of an ideal small spring and when it hangs freely at rest, it is found to stretch the spring by 8cm. The ball is now attached to a long string and whirled around in a vertical circle at a constant angular speed. Determine the difference between the maximum amount that th…

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Thermal Physics

Q- Assume that a person (mass 80kg) that is performing light work has a power output of 240W and does this continuously for an hour. Also assume that 30% of this energy does useful work and that the remaining 70% only increases the temperature of the person. What is the temperature increase after 1.…

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Potentiometer- Internal resistance

Q- The circuit below shows a circuit designed to measure the internal resistance ‘r’ of a battery. Resistor R is 2Ω and AB is the potentiometer wire. With the switch S open a balancing length l1 = 55.2cm is obtained. When switch S is closed the balancing length becomes l2 = 53.2cm. Calculate th…

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Motion in 1D

Q- A stone is thrown vertically upward with a speed of 12.0 m/s from the edge of a cliff 70.0 m high.

(a) How much later does it reach the bottom of the cliff?

(b) What is the speed just before hitting?

(c) what is the total distance traveled?

Solution:

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