A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 1313 feet. The ball is started in motion from the equilibrium position with a downward velocity of 33 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second. y=

A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 1313 feet. The ball is started in motion from the equilibrium position with a downward velocity of 33 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second. y=

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter4: The Laws Of Motion

Section: Chapter Questions

Problem 54P: A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using...

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A pendulum consists of a 382.3 gram mass on the end of a 3.9 meter long string that swings back and forth. It is observed that when the string makes an angle 68 degrees from the vertical, the mass is moving at 5.7 m/s. If there is no air resistance, what will be the maximum speed of the mass, in m/s?
A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position x along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively. (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data. (b) Determine the acceleration of the cart from the slope of this graph. (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin as derived in Example 4.3.
A student working on a school project modeled a trampoline as a spring obeying Hookes law and measured the spring constant of a certain trampoline as 4617 N/m. If a child of mass 27.0 kg compresses the trampoline vertically by a maximum of 0.25 m, while bouncing up and down, what is the childs acceleration at the moment of maximum compression?
A weight is hung from a spring and set in motion so that it moves up and down continuously. The velocity v of the weight at any time t is given by the equation v = 3.5sin 4πt where v is measured in meters per second and t is measured in seconds. Find the maximum velocity of the weight and the amount of time it takes for the weight to move from its lowest position to its highest position.
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How much weight should a diver put in order to gain a gravitational potential energy of 75 kJ if he is going to dive at a height of 10 m? He weighs 60 kg.
An object has a kinetic energy of 226 J and a mass of 11 kg. How fast, in m/s, is the object moving?
50-kilogram block of wood rest on the top of the smooth plane whose length is 3 m and whose altitude is 0.8 m. How long will it take in seconds for the block to slide to the bottom of the plane when released?
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If a 3.15 kg object is placed on a frictionless incline of 70.5 º and released from rest, what is speed of the object down the incline after traveling a distance of 1.5 m? Enter a number rounded to 2 decimal places and assume it has proper SI units.
A 0.072 kg mass uses the potential energy of a spring in acquiring a speed of 0.4 m/s when the spring was decompressed from 0.1 meter. What is the total energy developed during the process if the spring constant is 0.5 N/m?
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