1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
faust18 [17]
3 years ago
12

An aluminum wire is held between two clamps under zero tension at room temperature. Reducing the temperature, which results in a

decrease in the wire's equilibrium length, increases the tension in the wire. Taking the cross-sectional area of the wire to be 5.75 10-6 m2, the density to be 2.70 103 kg/m3, and Young's modulus to be 7.00 1010 N/m2, what strain (ΔL/L) results in a transverse wave speed of 118 m/s
Physics
1 answer:
Blababa [14]3 years ago
6 0

Answer:

\frac{\Delta L}{L} =5.37\times 10^{-4}

Explanation:

Given:

  • cross sectional area of the wire, A=5.75\times 10^{-6}\ m^2
  • density of aluminium wire, \rho=2.7\times 10^3\ kg.m^{-3}
  • young's modulus of the material, E=7\times 10^{10}\ N.m^{-2}
  • wave speed, v=118\ m.s^{-1}

<u>We have mathematical expression for strain as:</u>

\frac{\Delta L}{L} =\frac{\sigma}{E} ...............................(1)

and since, \sigma =\frac{T}{A}

where, T = tension force in the wire

equation (1) becomes:

\frac{\Delta L}{L} =\frac{T}{A.E} ............................(2)

<u>Also velocity ofwave in tensed wire:</u>

v=\sqrt{\frac{T}{\mu} } ...................................(3)

where: \mu= linear mass density of the wire

\therefore \mu=\rho \times A

Now, equation (3) becomes

v=\sqrt{\frac{T}{\rho \times A} }

T=v^2.\rho \times A ............................(4)

Using eq. (2) & (4) for tension T

v^2.\rho \times A=A.E\times \frac{\Delta L}{L}

\frac{\Delta L}{L} =\frac{v^2.\rho}{E}

putting the respective values

\frac{\Delta L}{L} =\frac{118^2\times 2.7\times 10^3}{7\times 10^{10}}

\frac{\Delta L}{L} =5.37\times 10^{-4}

You might be interested in
A mass m at the end of a spring oscillates with a frequency of 0.89 hz. when an additional 603 g mass is added to m, the frequen
MrMuchimi

The solution for this problem:

Given:

f1 = 0.89 Hz

f2 = 0.63 Hz

Δm = m2 - m1 = 0.603 kg 


The frequency of mass-spring oscillation is: 
f = (1/2π)√(k/m) 
k = m(2πf)² 

Then we know that k is constant for both trials, we have: 
k = k 


m1(2πf1)² = m2(2πf2)² 

m1 = m2(f2/f1)² 


m1 = (m1+Δm)(f2/f1)² 


m1 = Δm/((f1/f2)²-1)

 m 1 = 0.603/ (0.89/0.63)^2 – 1

= 0.609 kg or 0.61kg or 610 g

5 0
3 years ago
An astronaut drops a rock on the surface of an asteroid.The rock is released from rest at a height of 0.86 m above the ground, a
SCORPION-xisa [38]

Answer:

a_y=0.92m/s^2

Explanation:

To solve this problem we use the formula for accelerated motion:

y=y_0+v_{y0}t+\frac{a_yt^2}{2}

We will take the initial position as our reference (y_0=0m) and the downward direction as positive. Since the rock departs from rest we have:

y=\frac{a_yt^2}{2}

Which means our acceleration would be:

a_y=\frac{2y}{t^2}

Using our values:

a_y=\frac{2(0.86m)}{(1.37s)^2}=0.92m/s^2

5 0
3 years ago
According to the law of refraction, light passing from air into a piece of glass at an angle of 30 degrees will cause the light
pantera1 [17]

Answer:

bend toward the normal line

Explanation:

When light passes from a less dense to a more dense substance, (for example passing from air into water), the light is refracted (or bent) towards the normal.   In your question the light is moving from rarer to denser medium

4 0
3 years ago
The source of Earth's magnetic field is
valkas [14]
The magma in the wake the core
3 0
3 years ago
Read 2 more answers
an electric device is plugged into a 110v wall socket. if the device consumes 500 w of power, what is the resistance of the devi
andreev551 [17]

Answer: R=24.2Ω

Explanation: <u>Power</u> is rate of work being done in an electric circuit. It relates to voltage, current and resistance through the following formulas:

P=V.i

P=R.i²

P=\frac{V^{2}}{R}

The resistance of the system is:

P=\frac{V^{2}}{R}

R=\frac{V^{2}}{P}

R=\frac{110^{2}}{500}

R = 24.2Ω

<u>For the device, resistance is 24.2Ω.</u>

4 0
3 years ago
Other questions:
  • 013 Indianapolis 500 champion Tony Kanaan holds his hand out of his IndyCar while driving through still air with standard atmosp
    11·1 answer
  • When all parts of a circuit are composed of conducting materials, the circuit is said to be
    6·1 answer
  • The principal of uniformitarian states that
    5·1 answer
  • An 0.80-m aluminum bar is held with its length parallel to the east-west direction and dropped from a bridge. Just before the ba
    6·1 answer
  • Marcus is on a train that travels 20 and takes 5 seconds to slow to 10 .
    13·1 answer
  • Earthquakes typically occur
    14·1 answer
  • Three point charges (some positive and some negative) are fixed to the corners of the same square in various ways, as the drawin
    14·1 answer
  • How is light bent when light is going from a less dense medium to a denser medium?
    13·2 answers
  • Come play among us with me the code is MTZTFF
    8·2 answers
  • How is it possible for the same object to have different amounts of gravitational potential energy?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!