A mad scientist invents an antigravity device that shields the region of space above a large metal plate from the earth’s gravitational field. Specifically, if the device is turned on at time t = 0, the effective magnitude of the gravitational acceleration in the region above the plate decreases exponentially with time according to mag(a→a→) = ge−q t , where g is the usual gravitational field strength and q is a constant. When enough time has passed that qt becomes large, the effective gravitational field above the plate becomes very small compared to g. Assume that the value of q is 3.0 when expressed in the appropriate SI units. (a) What are the SI units of q? Choose one _____(m, m/s, s, 1/s) (b) The mad scientist keeps a 10-kg bowling ball on a shelf above the plate. When the mad scientist throws the gigantic wall switch to turn on the apparatus one day, the vibrations jostle the bowling ball loose, and it rolls off the shelf. The scientist watches in horror as the ball smashes into the plate 1.0 s later. If the ball leaves the shelf with essentially zero vertical velocity at time t = 0, what is its velocity when it smashes into the delicate apparatus? (Hints:Using the equation ∫ebt dt = 1b ebt∫ebt dt = 1b ebt, and set b = −q. Note that e0 = 1.)_________ m/s (c) How high was the shelf above the plate? ______m
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
A mad scientist invents an antigravity device that shields the region of space above a large metal plate from the earth’s gravitational field. Specifically, if the device is turned on at time t = 0, the effective magnitude of the gravitational acceleration in the region above the plate decreases exponentially with time according to mag(a→a→) = ge−q t , where g is the usual gravitational field strength and q is a constant. When enough time has passed that qt becomes large, the effective gravitational field above the plate becomes very small compared to g. Assume that the value of q is 3.0 when expressed in the appropriate SI units.
(a) What are the SI units of q? Choose one _____(m, m/s, s, 1/s)
(b) The mad scientist keeps a 10-kg bowling ball on a shelf above the plate. When the mad scientist throws the gigantic wall switch to turn on the apparatus one day, the vibrations jostle the bowling ball loose, and it rolls off the shelf. The scientist watches in horror as the ball smashes into the plate 1.0 s later. If the ball leaves the shelf with essentially zero vertical velocity at time t = 0, what is its velocity when it smashes into the delicate apparatus? (Hints:Using the equation ∫ebt dt = 1b ebt∫ebt dt = 1b ebt, and set b = −q. Note that e0 = 1.)_________ m/s
(c) How high was the shelf above the plate? ______m
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