A 4.00 m-long steel cable is used to support a church chandelier. After the 226-kg chandelier is attached to the cable hanging from the ceiling, the steel cable is lengthened by 3.00 mm. Calculate the tensile stress in the cable. The Young's modulus for steel is QUOTE 2.00×1011N/m2 .)

Question

Quizplus · Accepted Answer

The tensile stress in the cable can be calculated using the formula: 
stress = (force / area) 
where force = mass x gravity and area = cross-sectional area of the cable

First, we need to find the force exerted by the chandelier: 
force = 226 kg x 9.81 m/s^2 = 2215.06 N

Next, we need to find the change in length of the cable: 
change in length = 3.00 mm = 0.003 m

Finally, we can calculate the cross-sectional area of the cable: 
area = (pi/4) x (diameter)^2 
Since the cable is assumed to be circular, we can use the diameter to find the area: 
diameter = 0.001 m 
area = (pi/4) x (0.001 m)^2 = 7.85 x 10^-7 m^2

Now we can calculate the tensile stress: 
stress = (force / area) = (2215.06 N) / (7.85 x 10^-7 m^2) 
stress = 2.82 x 10^9 N/m^2

Using the Young's modulus for steel, we can convert this stress into a strain: 
strain = stress / Young's modulus 
strain = (2.82 x 10^9 N/m^2) / (2.00 x 10^11 N/m^2) 
strain = 0.0000141

Finally, we can use the equation for strain to calculate the change in length of the cable: 
change in length = strain x original length 
change in length = (0.0000141) x 4.00 m 
change in length = 0.0000564 m

Therefore, the cable lengthens by 0.0564 mm.

The correct choice is B because it matches the calculated value of the tensile stress.

A 400 M-Long Steel Cable Is Used to Support a Church