Q- A motor boat, with its engine on in a running river and blown over by a horizontal wind is observed to travel at 20 km/hr in a direction 530 East of North. The velocity of the boat with its engine on in still water and blown over by the horizontal wind is 4 km/hr Eastward and the velocity of…
Solution Search
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Motion in two dimensions
Q- A bus is running along a highway at a speed of v1 =16 ms-1. A man is at a distance a = 40m from the highway and at a distance b = 196 m from the bus. In what direction should the man run to reach any point on the highway at the same time as the bus or before? The man can run at a speed of v2=4 ms
Conservation of energy
Q- An object of mass m starts from rest and slides a distance d down a frictionless incline of angle θ. While sliding, it contacts an unstressed spring of negligible massand force constant k. The object slides an additional distance x as it is brought momentarily to rest by compression of the spr…
Heat and Thermodynamics
Q- 0.110 mol of a monatomic gas follows the process shown in the figure.
(a) How much heat energy is transferred to or from the gas during process 1 → 2 ?
(b) How much heat energy is transferred to or from the gas during process 2 → 3?
(c) What is the total change in thermal energy of the ga…
Ray Optics: Achromatic Lens
Q- An achromatic doublet consists of a biconvex positive lens of refractive index μ1 in contact with a plano concave lens of refractive index μ2. All curved surfaces have a radius of curvature R = 25 cm.
(a) If μ1red = 1.49 what is the focal length of the biconvex lens for red light?
(b) If μ2…
Circular Motion
A 1.9 kg ball is attached to the lower end of a length of fishline with a breaking strength of 35 N. The top end of the fishing line is held stationary. The ball is released from rest with the line taut and horizontal. At what angle (measured from the vertical) will the fishline break?
D C Circuits
Q- Consider the circuit in the figure. The switch is closed for long time prior to t = 0.
(a) Determine the voltage Vc across the capacitor before t = 0 and long time after t = 0
(b) Find the expression for the voltage across the capacitor as a function of time
(c) Determine the time constant a…
Rotetional Motion
Q- A thin rod is held vertically with its lower end resting on a frictionless horizontal surface. The rod is then released to fall freely.
(a) Determine the speed of its center of mass just before it hits the horizontal surface. Use h, M, and g for length, mass, and gravitational acceleration res…
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…
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…
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?
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 …
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