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Find the first and second derivative with respect to x of f(x) = (exp(x/a)-exp(-x/a))/2, where exp(x)=e^x is the exponential function.
A 1500kg car skids to a halt on a wet road where coefficient of friction = 0.46. How fast was car traveling if it leaves 68m long skid marks.
For a damped oscillator with a mass of 380g, the spring constant 120 N/m and a damping coefficient of 76 g/s, what is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 28 cycles.
plan a free-body diagram for the charge.
A 55.0 kg circus performer oscillates up and down at the end of a long elastic rope at a rate of once every 8s. The elastic rope obeys Hooke's Law. By how much is rope extended beyond its unloaded length while the performer hangs at rest?
Two stationary positive point charges, charge 1 of magnitude 3.55 and charge 2 of magnitude 2.00 , are separated by a distance of 30. An electron is released from rest at the point midway between the two charges, and it moves along the line connec..
An object with a net charge of 44 µC is placed in a uniform electric ?eld of 554 N/C, directed vertically. The acceleration of gravity is 9.81 m/s^2. What is the mass of this object if it ?oats in this electric ?eld?
An archer puts a 0.33 kg arrow to the bowstring. An average force of 183 N is exerted to draw the string back 1.3 m. suppose that air resistance is negligible.
A rotating cylinder about 16 {rm km} long and 8.4 km in diameter is designed to be used as a space colony. With what angular speed should it rotate so that the residents on it will experience the similar acceleration as a result of gravity as on E..
A motorcyclist is able to ride on the vertical wall of a bowl- shaped track . his weight is counteracted by the friction of the wall on the tires. what force increase or decrease if he rides faster.
A dolphin in seawater at a temperature of 25 °C emits a sound wave directed toward the ocean floor 246 m below. How much time passes before it hears an echo? (The speed of sound in ocean water is 1533 m/s.)
A worker pushed a 27kg block 7.4m along a level floor at constant speed with a force directed 29° below the horizontal.
what the electrostatic force acts on the proton.
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