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Sav [38]
3 years ago
15

A heavy anvil is suspended by a 0.75 m long steel wire that has a mass of 12 g. When the wire is plucked, it hums at its fundame

ntal frequency of 120 Hz. What is the mass of the anvil?
Physics
1 answer:
Dima020 [189]3 years ago
6 0

Explanation:

It is given that,

length of steel wire, l = 0.75 m

Mass of the wire, m = 12 g = 0.012 kg

Fundamental frequency, f = 120 Hz

We need to find the mass of the anvil (m'). The fundamental frequency is given by :

f=\dfrac{v}{2l}

v is the speed of the mass

Speed is given by :

v=\sqrt{\dfrac{T}{\mu}}

\mu is the mass per unit length,\mu=\dfrac{m}{l}

f=\dfrac{1}{2l}\sqrt{\dfrac{T}{\mu}}

T is the tension in the wire,

f=\dfrac{1}{2l}\sqrt{\dfrac{Tl}{m}}

T=4f^2lm

T=4(120)^2\times 0.75\times 0.012

T = 518.4 N

Tension in the wire, T = m' g

m'=\dfrac{T}{g}

m'=\dfrac{518.4}{9.8}

m' = 52.89 kg

So, the mass of the anvil is 52.89 kg. Hence, this is the required solution.

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<u>Accelerated Motion </u>

When a body changes its speed at a constant rate, i.e. same changes take same times, then it has a constant acceleration. The acceleration can be positive or negative. In the first case, the speed increases, and in the second time, the speed lowers until it eventually stops. The equation for the speed vf at any time t is given by

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The train has two different types of motion. It first starts from rest and has a constant acceleration of 0.987 m/s^2 for 182 seconds. Then it brakes with a constant acceleration of -0.321 m/s^2 until it comes to a stop. We need to find the total distance traveled.

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Let's compute the first distance X1

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\displaystyle V_{f1}=179.6\ m/s

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\displaystyle V_o=179.6,a=-0.321\ m/s^2\ ,V_f=0

\displaystyle t=\frac{v_f-v_o}{a}=\frac{0-179.6}{-0.321}

\displaystyle t=559.5\ sec

Computing the second distance

\displaystyle X_2=179.6\times559.5\ \frac{-0.321\times 559.5^2}{2}

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\displaystyle X_t=x_1+x_2=16,346.7+50,243.2

\displaystyle X_t=66,589.9\ m

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