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torisob [31]
3 years ago
5

A horizontal spring is attached to a wall at one end and a mass at the other. The mass rests on a frictionless surface. You pull

the mass, stretching the spring beyond the equilibrium position a distance A, and release it from rest. The mass then begins to oscillate in simple harmonic motion with amplitude A. During one period, the mass spends part of the time in regions where the magnitude of its displacement from equilibrium is greater than (0.66)A— that is, when its position is between −A and(−0.66)A, and when its position is between (0.66)A and A. What total percentage of the period does the mass lie in these regions?
Physics
1 answer:
LenKa [72]3 years ago
6 0

Answer:

54%

Explanation:

So, we have that the "magnitude of its displacement from equilibrium is greater than (0.66)A—''. Thus, the first step to take in answering this question is to write out the equation showing the displacement in simple harmonic motion which is = A cos w×t.

Therefore, we will have two instances t the displacement that is to say at a point 2π/w - a2 and the second point at a = a2.

Let us say that 2π/w = A, then, we have that a = A cos ^-1 (0.66)/2π. Also, we have that a2 = A/2 - A cos^- (0.66) / 2π.

The next thing to do is to calculate or determine the total length of of the required time. Thus, the total length is given as:

2a1 + ( A - 2a2) = 2A{ cos^-1 (0.66)}/ π.

Therefore, the total percentage of the period does the mass lie in these regions = 100 × {2a1 + ( A - 2a2) }/A = 2 { cos^-1 (0.66)}/ π × 100 = 54%.

Thus, the total percentage of the period does the mass lie in these regions = 54%.

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Answer:

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Explanation:

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White dwarfs:

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6 0
3 years ago
Consider a railroad bridge over a highway. A train passing over the bridge dislodges a loose bolt from the bridge, which proceed
photoshop1234 [79]

Answer:

The railroad tracks are 13 m above the windshield (12 m without intermediate rounding).

Explanation:

First, let´s calculate the time it took the driver to travel the 27 m to the point of impact.

The equation for the position of the car is:

x = v · t

Where

x = position at time t

v = velocity

t = time

x = v · t

27 m = 17 m/s · t

27 m / 17 m/s = t

t = 1.6 s

Now let´s calculate the distance traveled by the bolt in that time. Let´s place the origin of the frame of reference at the height of the windshield:

The position of the bolt will be:

y = y0 + 1/2 · g · t²

Where

y = height of the bolt at time t

y0 = initial height of the bolt

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Since the origin of the frame of reference is located at the windshield, at time 1.6 s the height of the bolt will be 0 m (impact on the windshield). Then, we can calculate the initial height of the bolt which is the height of the railroad tracks above the windshield:

y = y0 + 1/2 · g · t²

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8 0
3 years ago
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