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Kirchhoff's Law

Q. Two ideal constant voltage sources and six resistors are connected in a circuit as shown. The right most resistor is the load. Using mesh analysis calculate mesh currents I1, I2 and I3.

 

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Vectors: Force

Q- The leg and cast in the figure weigh W = 210 N, with the center of mass as indicated by blue arrow. The counter balance W1 = 140 N. Determine the weight W2 and the angle α needed so that no force exerted on the hip joint by the leg and cast.

Solution:

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Gravitation

Q- The earth orbits the sun at a distance of about 1.5*1011 m, in about 365 days(3.15*107 s).

(a) What is the earth’s speed along its orbital path?

(b) If the mass of the earth is 6*1024 kg, find the force exerted on it by the sun.

(c) What is the mass of the sun?

Solution:

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Forced Damped Harmonic Oscillator

Q- A simple fatigue testing machine has a moving base that is 15kg and is constrained to only move vertically. The base is supported by a rubber block with a spring constant, k = 18 kN/m and a viscous damping constant of c = 200N.s/m. A rotating mass which is part of the base creates a harmonic forc…

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Ray Optics: Refraction

Q- A cube of flint glass sits on a newspaper on a table. By looking into one of the vertical sides of the cube, is it possible to see the portion of the newspaper covered by the glass?

Refractive index of flint glass is m = 1.69

Solution:

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Relative Motion

Q- A boat which can travel at 12.5 m/s in still water needs to travel West across a river with a current of 8.4 m/s flowing South.

(a) What heading must the boat take in order to travel West relative to the shore? Draw a diagram.

(b) What will be the boat’s velocity relative to the shore?

Solut…

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Sound: Resonance

Q- A 1.2 m long tube is closed at one end. A stretched wire is placed near the open end. The wire is 0.330 m long and has a mass of 9.60 g. It is fixed at both ends and oscillates in its fundamental mode. By resonance it sets the air column in the tube into oscillation at the column’s fundamental fr…

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Thermodynamics

Q- Air enters the compressor of a gas turbine plant (operating at steady state) at ambient conditions of 1 bar, 250C with low velocity and exits at 10 bar, 3500C with a velocity of 90 m/s. The compressor is cooled at a rate of 1500 kJ/min and the power input to the device is 250 kW. Determine the ma…

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Electrostatics: Coulomb's Law

Q- Two positive, 1 nC charges are located on the x-axis. Charge Q1 is located at the origin and charge Q2 is located at (4,0) which is 4 cm from the origin.

(a) Calculate the magnitude and direction of the force experienced by Q2 due to Q1

(b) A third charge Q3 of 2 nC is positioned on the y-ax…

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Rotational Motion: Angular Momentum

Q- A horizontal disk of mass 150g and radius 20 cm rotates at 10 rev/min about its axis, without any external torque. A flying bug of mass 15g lands vertically on the disk at a point half way to the center and stick to it. Find the angular speed of the disk just after the collision.

Solution:

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Alternating Current Circuits

Q- A source of alternating voltage e = 10√2 sin ωt is connected to a resistor R = 100 Ω and a capacitor C = 0.5 μF in series.

(a) Plot impedance Z and phase difference θ between current and voltage versus frequency for a frequency range of zero to 10 kHz.

(b) Plot voltage across capacitor VC

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Circular Motion

Q- A disk accelerates constantly from rest. After 8 s, it has made 3 revolutions.

(a)  What is the angular acceleration of the disk?

(b) What is the angular velocity of the disk at t = 8 s?

(c) If the radius of the disk is 50 cm, what is the linear velocity of a point on the rim at time t = 8 s?

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Current Electricity: Superposition Method

Q- Consider the circuit in figure below with two ideal voltage sources. Calculate the current I in the 1 kΩ resister using the superposition theorem.

Solution:

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Sound: Doppler's Effect

Q- A commuter train passes a station platform at a constant speed of 40 m/s. The train horn sounded at its characteristic frequency of 320 Hz. What change in frequency is detected by a person standing on the platform as the train moves past from approaching to receding? (speed of sound in air is 340…

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Ray Optics: Refraction

Q- A jewel thief hides a diamond by placing it at the bottom of a public swimming pool. He places a circular raft on the surface of the water directly above the diamond as shown in the figure. The surface of water is smooth and the pool is 2.0m deep. Find the minimum diameter d of raft if it is to p…

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Thermodynamics: Heat Pump

Q- A heat pump is used to maintain a house at a constant temperature of 230C. The house is losing heat to the outside air through the walls and the windows at a rate of 60000 kJ/h and the energy generated within the house from lights and appliances amounts to 5000 kJ/h. For COP of 2.5, determine th…

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Mechanics: Conservation of Energy

Q- A roller coaster car of mass 1000 kg is riding along a track from point A to point C as in figure. (g = 10 m/s2)

(a) Assuming no friction between the track and the car, what is the speed of the car at the top of first hill A?

(b) What is the speed of the car at the top of second hill B?

(c) Wh…

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Electrostatics: Dielectric and Polarization

Q- Two parallel conducting plates are separated by distance d and the potential difference between them is V. A dielectric slab of dielectric constant k and uniform thickness nearly d is inserted between the plates. As the dielectric slab is not smooth enough, it touches the plates in some regions a…

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Force: Equilibrium

Q- A patient in therapy has a forearm that weighs 20.5 N and lifts a 112.0 N weight. The only other significant forces on his forearm come from the biceps muscle (which acts perpendicularly to the forearm) and the force at the elbow. If the biceps produce a pull of 232 N when the forearm is raised 4…

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Current Electricity

Q- For the network shown in Figure

(a) Find the current I1

(b) Calculate the power dissipated by the 4 Ω resistor

(c) Find the current I2

Solution:

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