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Maru [420]
2 years ago
11

A mass is hung from a spring and set in motion so that it oscillates continually up and down. The velocity v of the weight at ti

me t is given by the equation y=−5 cos(4πt) with v measured in feet per second and t measured in seconds. Determine the maximum velocity of the mass and the amount of time it takes for the mass to move from its lowest position to its highest position.
Physics
1 answer:
otez555 [7]2 years ago
5 0

To solve the problem it is necessary to identify the equation in the manner given above.

This equation corresponds to the displacement of a body under the principle of simple harmonic movement.

Where,

\xi = Acos(\omega t +\phi)

PART A) Our equation corresponds to

y = -5cos(4\pi t)

Therefore the value of omega is equivalent to that of

\omega = 4\pi

From the definition we know that the period as a function of angular velocity is equivalent to

T = \frac{2\pi}{\omega}

T = \frac{2\pi}{4\pi}

T = \frac{1}{2}

This same point is the equivalent of the maximum point of the speed that the body can reach, since the internal expression of the cos\thetaIs equivalent to . So the maximum speed that the body can reach is,

y = -5cos(4\pi t)

y = -5cos(4\pi (1/2))

y = -5*(-1)

y = 5

Therefore the maximum felocity will be 5ft / s

PART B) The period of graph is the time taken to reach from one maximum point to next point maximum point, then

t = \frac{T}{2} = \frac{1}{2}*\frac{1}{2}

t = \frac{1}{4}s

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IceJOKER [234]

Answer:

0.16Hz

Explanation:

wavelength (λ) = 125 meters

speed (V) = 20 m/s

frequency (F) = ?

Recall that frequency is the number of cycles the wave complete in one

second. And its value depends on the wavelength and speed of the wave.

So, apply the formula V = F λ

Make F the subject formula

F = V / λ

F = 20 m/s / 125 meters

F = 0.16 Hz

8 0
3 years ago
7. Nancy has a mass of 60 kg and sits on the very end of a 3.00 m long plank pivoted in the middle. How much torque must her co-
netineya [11]

Answer:

Torque = 882Nm

Explanation:

Torque = Mg×distance

But plank's is pivoted ,therefore distance=3/2=1.5m

Mass of Nancy=60jg

Acceleration due to gravity, g=9.8m/s^2

Torque= 60×9.8×1.5

Torque= 882Nm

6 0
3 years ago
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zhannawk [14.2K]

Answer:

the object is decelerating

4 0
2 years ago
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3 years ago
You are at the controls of a particle accelerator, sending a beam of 2.10×107 m/s protons (mass m) at a gas target of an unknown
Kipish [7]

Answer:

a

The mass is  m_2 =21.75*10^{-27} \ kg

b

The velocity is  v_2 = 3.0*10^{6} m/s

Explanation:

From the question we are told that

     The speed of the protons is  u_1 =  2.10*10^{7} m/s

     The mass of the protons is  m

     The speed of the rebounding protons are v_1 =  -1.80 * 10^{7} \ m/s

The negative sign shows that it is moving in the opposite direction

     

Now according to the law of energy conservation mass of one nucleus of the unknown element. is mathematically represented as

        m_2 = [\frac{u_1 -v_1}{u_1 + v_1} ] m_1

Where m_1 is the mass of a single proton

          So substituting values

       m_2 = \frac{2.10 *10^{7} - (-1.80 *10^{7})} {(2.10 *10^7) + (-1.80 *10^{7})} m_1

        m_2 =13 m_1

The mass of on proton is  m_1 = 1.673 * 10^{-27} \ kg

So     m_2 =13 ( 1.673 * 10^{-27} )

        m_2 =21.75*10^{-27} \ kg

Now according to the law of linear momentum conservation the speed of the unknown nucleus immediately after such a collision is mathematically evaluated as

      m_1 u_1 + m_2u_2 = m_1 v_1 + m_2v_2

Now  u_2 because before collision the the nucleus was at rest

So

        m_1 u_1 =  m_1 v_1 + m_2v_2

=>    v_2 =  \frac{m_1(u_1 -v_1)}{m_2}

Recall that m_2 =13 m_1

So

       v_2 =  \frac{m_1(u_1 -v_1)}{13m_1}

=>         v_2 =  \frac{(u_1 -v_1)}{13}

substituting values

              v_2 =  \frac{( 2.10*10^{7} -(-1.80 *10^{7}))}{13}

              v_2 = 3.0*10^{6} m/s

   

7 0
3 years ago
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