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Murrr4er [49]
3 years ago
14

A 13kg box slides 4.0m down the frictionless ramp shown in the figure , then collides with a spring whose spring constant is 170

N/m.
What is the maximum compression of the spring?
At what compression of the spring does the box have its maximum speed?

Physics
1 answer:
Svetradugi [14.3K]3 years ago
7 0
The force on the box is:
F = mgsin∅
If we multiply by this with the distance it traveled, we will know the work done by the box. 
W = dmgsin∅

This work will be converted to elastic potential energy in the spring which is:
1/2 kx². Equating these and substituting values:
1/2 * 170 * x² = 4 * 13 * 9.81 * sin(30)
x = 1.73 m

The box's maximum speed will at the point right before contact with the spring, when the compression is 0.
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r1 = 5*10^10 m , r2 = 6*10^12 m

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0.5*(9*10^4)^2 - (6.67*10^-11*1.98*10^30/(5*10^10)) = 0.5v2^2 - (6.67*10^-11*1.98*10^30/(6*10^12))

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A particle is traveling in the positive direction along an x axis, at a constant 5 m/s. Which of the following
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Find the magnitude of the free-fall acceleration at the orbit of the Moon (a distance of 60RE from the center of the Earth with
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Answer:

The magnitude of the free-fall acceleration at the orbit of the Moon is 2.728\times 10^{-3}\,\frac{m}{s^{2}} (\frac{2.784}{10000}\cdot g, where g = 9.8\,\frac{m}{s^{2}}).

Explanation:

According to the Newton's Law of Gravitation, free fall acceleration (g), in meters per square second, is directly proportional to the mass of the Earth (M), in kilograms, and inversely proportional to the distance from the center of the Earth (r), in meters:

g = \frac{G\cdot M}{r^{2}} (1)

Where:

G - Gravitational constant, in cubic meters per kilogram-square second.

M - Mass of the Earth, in kilograms.

r - Distance from the center of the Earth, in meters.

If we know that G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}, M = 5.972\times 10^{24}\,kg and r = 382.26\times 10^{6}\,m, then the free-fall acceleration at the orbit of the Moon is:

g = \frac{\left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (5.972\times 10^{24}\,kg)}{(382.26\times 10^{6}\,m)^{2}}

g = 2.728\times 10^{-3}\,\frac{m}{s^{2}}

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