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
charle [14.2K]
2 years ago
11

A third wire of the same material has the same length and twice the diameter as the first. How far will it be stretched by the s

ame force
Physics
1 answer:
leonid [27]2 years ago
4 0

Complete question is;

A force stretches a wire by 0.60 mm. A second wire of the same material has the same cross section and twice the length.

a) How far will it be stretched by the same force?

b) A third wire of the same material has the same length and twice the diameter as the first. How far will it be stretched by the same force?

Answer:

0.15 mm

Explanation:

According to Hooke's Law,

E = Stress(σ)/Strain(ε)

Where E is youngs modulus

Formula for stress is;

Stress(σ) = Force(F)/Area(A)

Formula for strain is;

Strain(ε) = Change in length/original length = (Lf - Li)/Li

We are also told that a second wire of the same material has the same cross section and twice the length.

Thus;

Rearranging Hooke's Law to get the constants on one side, we have;

F/(AE) = ε

Thus from the conditions given;

ε1 = 0.6/Li

ε2 = (Change in length)/(2*Li)

And ε1 = ε2

Thus;

0.6/Li = Change in length/(2*Li)

Li will cancel out and we now have;

Change in length = 2 × 0.6 = 1.2 mm

Finally, we are told A third wire of the same material has the same length and twice the diameter as the first.

Area of a circle;A1 = πd²/4

Now, we are told d is doubled.

Thus, new area of the new circle is;

A2 = π(2d)²/4 = πd²

Rearranging Hooke's Law,we have;

F/A = εE

Since F and E are now constants, we have;

F/E = constant = Aε

Thus;

A1(ε1) = A2(ε2)

A1 = πd²/4

e1 = 0.60/Li

A2 = πd²

e2 = Change in length/Li

Thus;

((πd²/4) × 0.6)/Li = (πd² × Change in length)/ Li

Rearranging, Li and πd² will cancel out to give;

0.6/4 = Change in length

Change in length = 0.15 mm

You might be interested in
How many grams of oxygen (O2), x, are needed to react with the 700 g of iron to produce 1000 g of iron (III) oxide, Fe2O3?
Murljashka [212]

As we know that, molecular mass of ferric oxide, Fe2O3, is 159.69 grams.
Out of which, iron contributes 111.69 g (2 X 55.845 g) and oxygen contributes
48 g (3 X 16 g).   
 Each gram of iron (III) oxide contains 111.69/159.69 g of iron and 48/159.69
g of oxygen.   
 To produce 1000 g iron (III) oxide we need,    
 Iron = 111.69*1000/159.69 = 699.42 g   
 Oxygen = 48*1000/159.69 = 300.58 g
6 0
3 years ago
What acceleration is imparted to a football when the player kicked it with a force of 25 N? mass of football=0.40 kg
Bond [772]
Force = mass x acceleration

25N = 0.40kg x acceleration
25N/0.40kg = acceleration

acceleration = 62.5 N/kg
N/kg is the equivalent of m/s²

So your acceleration is 62.5 meters per second squared
6 0
3 years ago
An unstretched spring has a length of 10. centimeters. When the spring is stretched by a force of 16 newtons, its length is incr
Fed [463]

Answer:

The spring constant of this spring  is 200 N/m.

Explanation:

Given:

Original unstretched length of the spring (x₀) = 10 cm =0.10 m [1 cm =0.01 m]

Stretched length of the spring (x₁) = 18 cm = 0.18 cm

Force acting on the spring (F) = 16 N

Spring constant of the spring (k) = ?

First let us find the change in length of the spring or the elongation caused in the spring due to the applied force.

So, Change in length = Final length - Initial length

\Delta x = x_1-x_0=0.18-0.10=0.08\ m

Now, restoring force acting on the spring is directly related to its elongation or compression as:

F=k\Delta x

Rewriting in terms of 'k', we get:

k=\dfrac{F}{\Delta x}

Now, plug in the given values and solve for 'k'. This gives,

k=\frac{16\ N}{0.08\ m}\\\\k=200\ N/m

Therefore, the spring constant of this spring  is 200 N/m.

5 0
3 years ago
An object with charge q=−6.00×10−9C is placed in a region of uniform electric field and is released from rest at point A. After
shtirl [24]

Answer:

its a

Explanation:

used google

8 0
3 years ago
Which formula is used to calculate average velocity?
Flauer [41]

Answer:

Explanation:

<h3>for average velocity we use this formula                                                                                           V                                   Vavg =V1+V2<u><em>÷</em></u><u>2</u></h3>
5 0
3 years ago
Other questions:
  • A ball thrown vertically upward is caught by the thrower after 1.76 s. find the initial velocity of the ball. the acceleration o
    9·1 answer
  • 1.5kj of energy are used every second by a microwave oven, what is the power rating of the oven?
    15·2 answers
  • A toxin that inhibits the production of gtp would interfere with the function of a signal transduction pathway that is initiated
    5·1 answer
  • A child carries a 3N book at a constant velocity of 4 meters across a horizontal floor. What is the net work done?
    10·1 answer
  • What topics are included in the study of physical geology?
    11·1 answer
  • Calculate the average maximum height for all three trials When the speed of the bottle is 2 m/s, the average
    9·2 answers
  • Zeros between a decimal point and a non-zero number are <br> (blank) significant
    10·1 answer
  • If the angle of incidence is 30°, what is the value of the
    15·2 answers
  • What is the magnification when an object is placed at 2f from the pole of the convex mirror? 
    15·1 answer
  • Explain the conditions through which friction can be increased.​
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!