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pantera1 [17]
3 years ago
7

A person wants to make a metronome for music practice. He uses a 35-g object attached to a spring to serve as the time standard.

Physics
1 answer:
alukav5142 [94]3 years ago
7 0

To develop this problem it will be necessary to apply the concepts related to the frequency of a spring mass system, for which it is necessary that its mathematical function is described as

f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}

Here,

k = Spring constant

m = Mass

Our values are given as,

m = 35g = 35*10^{-3}kg

f = 1 Hz

Rearranging to find the spring constant we have that,

k = (2\pi f \sqrt{m})^2

k = 4\pi^2 f^2 m

k = (4) (\pi)^2 (1) (35*10^{-3})

k = 1.38N/m

Therefore the spring constant is 1.38N/m

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Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. the tide measures 5.15 ft at
RSB [31]
<span>f(x) = 5.05*sin(x*pi/12) + 5.15

   First, you need to determine the period of the function. The period will be the time interval between identical points on the sinusoidal function. For this problem, the tide is rising and at 5.15 at midnight for two consecutive days. So the period is 24 hours. Over that 24 hour period, we want the parameter passed to sine to range from 0 to 2*pi. So the scale factor for x will be 2*pi/24 = pi/12 which is approximately 0.261799388. The next thing to note is the magnitude of the wave. That will simply be the difference between the maximum and minimum values. So 10.2 ft - 0.1 ft = 10.1 ft. And since the value of sine ranges from -1 to 1, we need to divide that magnitude by 2, so 10.1 ft / 2 = 5.05 ft.

   So our function at this point looks like f(x) = 5.05*sin(x*pi/12) But the above function ranges in value from -5.05 to 5.05. So we need to add a bias to it in order to make the low value equal to 0.1. So 0.1 = X - 5.05, 0.1 + 5.05 = X, 5.15 = X. So our function now looks like:
  f(x) = 5.05*sin(x*pi/12) + 5.15

   The final thing that might have been needed would have been a phase correction. With this problem, we don't need a phase correction since at X = 0 (midnight), the value of X*pi/12 = 0, and the sine of 0 is 0, so the value of the equation is 5.15 which matches the given value of 5.15. But if the problem had been slightly different and the height of the tide at midnight has been something like 7 feet, then we would have had to calculate a phase shift value for the function and add that constant to the parameter being passed into sine, making the function look like:
 f(x) = 5.05*sin(x*pi/12 + C) + 5.15
  where
 C = Phase correction offset.

   But we don't need it for this problem, so the answer is:
 f(x) = 5.05*sin(x*pi/12) + 5.15

   Note: The above solution assumes that angles are being measured in radians. If you're using degrees, then instead of multiplying x by 2*pi/24 = pi/12, you need to multiply by 360/24 = 15 instead, giving f(x) = 5.05*sin(x*15) + 5.15</span>
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3 years ago
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Kinetic energy is calculated as such: KE=\frac{1}{2} mv^{2} | therefore, KE=0.913598 J

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3 years ago
Help me, Ive been stuck for 15 minutes
natita [175]
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5 0
3 years ago
a roller coaster begins at the top of a hill if it acelerates at the rate of 2 m/s2 and has a mass of 2000 kg what net force is
AlladinOne [14]

Answer:

\boxed {\boxed {\sf 4000 \ Newtons }}

Explanation:

Force can be found by multiplying the mass by the acceleration.

F=m*a

The mass of the roller coaster is 2000 kilograms and the acceleration is 2 meters per second squared.

m= 2000 \ kg \\a= 2 \ m/s^2

Substitute the values into the formula.

F= 2000 \ kg * 2 \ m/s^2

Multiply.

F= 4000  \ kg*m/s^2

  • 1 kg*m/s² is equal to 1 N
  • Therefore our answer of 4000 kg*m/s² is equal to 4000 Newtons

F= 4000 \ N

The net force acting on the roller coaster is <u>4000 Newtons.</u>

7 0
3 years ago
What is the distance between two spheres (20 kg and 30 kg) attracted by a force of 2 x 10^-5 Newtons.
creativ13 [48]
2 times 10 to the power of 5 is your answer.
6 0
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