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1. Using the definitions of the position vector r in the rectangular and spherical coordinate systems, show that ∇r = a r .
2. Find the maximum rate of change of a function f = 12x 2 + yz2 with respect to distance at point P(-1, 0, 1). Determine the rate of changeof f in the x, y, and z directions. What is the rate of change of f in the direction of point Q(1, 1, 1) from P?
Two identical 0.12 kg blocks (labeled 1 and 2) are initially at rest on a nearly frictionless surface, connected by an unstretched spring, What is the final vibrational energy of the real system
A galvanometer with a full-scale sensitivity of 700?A and a coil resistance of 58? is to be used to build an ammeter designed to read 10A at full scale
A butterfly moves with a speed of v = 12.0 m/s. the y-components of its velocity is 8.00m/s. Find the angle between the direction of its motion and the x-axis
The profile of a transverse harmonic wave on a long taut nylon thread is described in SI units by the function y =0.04sin (2*pi*x). Given that the wave travels at a speed of 2.0 m/s, decide the maximum transverse acceleration of any point on the thre..
A 1.4-m-diameter vat of liquid is 2.2m deep. The pressure at the bottom of the vat is 1.3atm. What is the mass of the liquid in the vat
A hollow ball with mass 0.50kg and radius 10cm rolls down a 3.0m high ramp without sliding.What is the maximum hight that the ball reaches?
Though slow on land, the leatherback turtle holds record for the fastest water speed of any reptile: 9.78 m/s. It is also among the largest of reptiles. Assume the largest leatherback yet discovered were to swim at the top leatherback speed. If its k..
A weight of 50lb is hung from the end of a pressurized pipe. The weight is applied at the centroid, so there is no torque pointing to the right. Find the maximum in-plane shear stress at the location of the element
A glass sheet 1.40 ?m (micrometer) thick is suspended in air. Calculate the minimum value of the index of refraction of the glass sheet that produces this effect
An electron enters a region of constant electric field that is produced by a parallel-plate capaci- tor, find the velocity of the electron when it exits the capacitor
A heavy piece of hanging sculpture is suspended by a 146.0 cm long, 8.03 gm wire. When the wind blows hard, wire hums at its fundamental frequency of 113.0 Hz. What is the mass of the sculpture (in kg) assume that the local acceleration due to gravit..
The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r = 10-5 m, length L = 0.21 m, and thickness d = 10-8 m. Find the capacitance of the membrane
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