Solution Search

• January 30, 2023
• September 11, 2021
• August 6, 2021
• Iriam
August 4, 2021
• Abhigyan Martin Ninama
September 8, 2017

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Linear Motion Combined with Rotaional Motion

Q- A m1 = 16.0 kg object and a m2 = 12.5 kg object are suspended, joined by a cord that passes over a pulley with a radius of 10.0 cm and a mass of 3.00 kg. The cord has a negligible mass and does not slip on the pulley. The pulley rotates on its axis without friction. The objects start from rest 3.…

EMI: Induced Current

Q-Two parallel circular loops of wire having the same common axis.  The smaller loop of radius r, and is above the larger loop (radius R) by a distance X>>R.  the magnetic field due to the counterclockwise current i in the larger loop is nearly uniform throughout the smaller loop.  Suppose that x is…

Circular Motion

(Requested by Tricky Bits)

Q- A wheel 1.9 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.15 rad/s2. The wheel starts from rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3o with the hori…

Conservation of Energy: Motion in Vertical Plane

Q- A pendulum consists of a string of length L and a bob of mass M.  The string is brought to a horizontal position and given the minimum initial speed enabling a pendulum to make a full turn in the vertical plane.

a) what is the maximum kinetic energy K of the bob?

b) what is the tension …

Electrostatics: Capacitance

Q- Five 1 inch square plates are arranged as shown in figure. The plate spacings are 0.01 inch. The arrangement is to be used for a displacement transducer by observing the change in capacitance with the distance x. Calculate the sensitivity of the device in picofarads per inch. Assume that the plat…

Differentiation

Q- At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute.  The diameter of the base of the cone is 3 times the altitude.  At what rate is the height of the pile changing when the pile is 15 feet high?

Solution:

Magnetic Force

Q- A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current 1.40 A, is oriented with the plane of its loop perpendicular to a uniform 1.50 T magnetic field in to the plane of the coil.

a) Calculate the net force and torque which the magnetic field exerts on the coil.

b) The coil is ro…

Refraction Through A Prism

Q- A horizontal beam of light that is incident on an equilateral prism. The base of the prism is horizontal. The prism (n = 1.40) is surrounded by a liquid whose index of refraction is 1.60. Determine the angle of emergence from the other surface, that is the exiting light makes with the normal to t…

Sound and Vibration

Q- A heavy piece of hanging sculpture is suspended by a 90 cm long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency of 80 Hz. What is the mass of the sculpture?

Solution:

Mechanics: Conservation of momentum

Q- Two railroad cars moving on same track towards each other. One of mass 10000 kg with speed 0.3 m/s and the other of mass 15000 kg with speed of 0.1 m/s.

(a) What is the magnitude of their common velocity after they coule together?

(b) How much kinetic energy is lost during collision?

So…

Thermodynamics: Specific Heat Capacity

Q- A well-sealed room contains 80 kg of air at 200 kPa and 25°C. Now solar energy enters the room from windows at an average rate of 1 kJ/s while a 100-W fan is turned on to circulate the air in the room. If heat transfer through the walls is negligible, what will be the air temperature in the room …

Rotation: Toppling

Q- I have a 1.5 m tall air compressor that weights 50 kg with a 0.5 m square base. I have a cart that is 1m x 2m. The surface of the cart where the compressor will be mounted is 0.25 m off the ground. The cart wheels are in the corners, it is rated to carry 500 kg and weighs 75 kg. If the compressor…

Electrostatics: Induced Charges

Q- A point charge q is placed between two infinitely large conducting parallel planes with distance d between them, such that it is at a distance x from one plane.  Find the charges induced on each plane.

Solution:

Motion In A Plane

Q- A small ball is suspended from point A by a thread of length L.  A nail is driven into the wall at a distance of L/2 below A, at O.  The ball is drawn so that the thread takes up a horizontal position.

(a) At what point in the ball’s trajectory will the tension in the thread disappear?
(b)…

Alternating Currents

Q - An AC generator supplies an rms voltage of 5.00 V to an RC circuit. At a frequency of 20.0 kHz the rms current in the circuit is 37.0 mA; at a frequency of 30.0 kHz the rms current is 50.0 mA. What are the values of R and C in this circuit?

Solution:

kinematics

(Requested by Merjan)

Q – Two cars were moving on parallel lanes in one direction. One car had speed 60 km/hour, while the other had speed of 65 km/hr. At time 8:30 AM, the distance between the cars was 8 km.

(a)  How far a way from each another the were at 9:20 AM that day?

(b)  At what ti…

Ray Optics: Refraction

Q- Red light (n = 1.520) and violet light (n = 1.538) traveling in air are incident on a slab of crown glass. Both colors emerge from the glass at the same angle of refraction. The red light has an angle of incidence of 35.96°. What is the angle of incidence of the violet light? Give your answer to …

Speed of Bullet

Q- A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T, as shown. Derive a formula for the bullet speed v in terms of D, T and a measured angle θ between the position of the hole in the first disk and that of the hole in the second.…

Errors: Measuring Speed of Light

Q- Galileo attempted to measure the speed of light by measuring the time elapsed between his opening a lantern and his seeing the return light from his assistant’s lantern, which is opened when the assistant sees the light from Galileo’s lantern. What distance d must separate Galileo from his assist…

Harmonic Oscillations

Q- A harmonic force F0 sin(ωt) is applied to mass m1 which in turn is coupled to springs of spring constants k1, k2 and k3. Let x1 and x2 ­be the deviations from equilibrium for m1 and m2, respectively.  The blocks moves on a horizontal frictionless table.

(a) Write the equations of motion for …

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