Question

A 200-kg load is hung on a wire of length 4.00 m, cross-sectional area 0.2 cm2, and Young’s modulus 8.00 x 1010 N/m2 . What is its increase in length?

Answer 1

Answer:

Given data:

m

=

200

 

k

g

is the mass hung to the wire

L

=

4.00

 

m

is the length of the wire

A

=

0.200

×

10

−

4

 

m

2

is the cross-sectional area of the wire

E

=

8.00

×

10

10

 

N

/

m

2

is Young's modulus of the given material

Young's modulus is given by:

E

=

t

e

n

s

i

l

e

 

s

t

r

e

s

s

t

e

n

s

i

l

e

 

s

t

r

a

i

n

E

=

F

A

Δ

L

L

Δ

L

=

F

L

A

E

=

(

m

g

)

L

A

E

=

200

 

k

g

×

9.81

 

m

s

2

×

4.00

 

m

0.200

×

10

−

4

 

m

2

×

8.00

×

10

10

 

N

m

2

≈

4.91

×

10

−

3

 

m

Therefore, the increase in the length of the wire is  

4.91

×

10

−

3

 

m

.