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Scrat [10]
3 years ago
10

Hint: This problem requires a train of logic. (1) Analyze force diagram, (2) use Newton’s Laws, and (3) solve the equations of m

otion. A block starts from rest at a height of 3.9 m on a fixed inclined plane. The acceleration of gravity is 9.8 m/s 2 . 3.8 kg µ = 0.12 31◦ What is the speed of the block at the bottom of the ramp? Answer in units of m/s.
Physics
1 answer:
gregori [183]3 years ago
6 0

8 . 55599 m / s.  
Let : h = 8 . 2 m , m = 5 . 1 kg , = 0 . 22 , = 22 , and v f = final speed . The normal force to the inclined plane is N = mg cos . The sum of the forces par- allel to the inclined plane is F net = ma = mg sin - mg cos a = g sin - g cos Since v 2 f = v 2 + 2 ax = 2 ad (1) along the plane, and neglecting the dimension of the block, the distance, d, to the end of the ramp is d sin = h d = h sin (2) therefore v f = r 2 ah sin = r 2 g h (sin - cos ) sin = p 2 g h (1- cot ) (3) = q 2(9 . 8 m / s 2 )(8 . 2 m)[1- (0 . 22)cot22 ] = 8 . 55599 m / s .
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Answer:

The maximum acceleration of the system is 359.970 centimeters per square second.

Explanation:

The motion of the mass-spring system is represented by the following formula:

x(t) = A\cdot \cos (\omega \cdot t + \phi)

Where:

x(t) - Position of the mass with respect to the equilibrium position, measured in centimeters.

A - Amplitude of the mass-spring system, measured in centimeters.

\omega - Angular frequency, measured in radians per second.

t - Time, measured in seconds.

\phi - Phase, measured in radians.

The acceleration experimented by the mass is obtained by deriving the position equation twice:

a (t) = -\omega^{2}\cdot A \cdot \cos (\omega\cdot t + \phi)

Where the maximum acceleration of the system is represented by \omega^{2}\cdot A.

The natural frequency of the mass-spring system is:

\omega = \sqrt{\frac{k}{m} }

Where:

k - Spring constant, measured in newtons per meter.

m - Mass, measured in kilograms.

If k = 12\,\frac{N}{m} and m = 0.40\,kg, the natural frequency is:

\omega = \sqrt{\frac{12\,\frac{N}{m} }{0.40\,kg} }

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Lastly, the maximum acceleration of the system is:

a_{max} = \left(5.477\,\frac{rad}{s})^{2}\cdot (12\,cm)

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The maximum acceleration of the system is 359.970 centimeters per square second.

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They realize there is a thin film of oil on the surface of the puddle. If the index of refraction of the oil is 1.81, and they o
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Explanation:

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