Question

A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed $10^{8} N/m^{-2}$, what is the maximum load the cable can support?

Answer 1

7.0714 x 10^4 Newtons

Given:

The measurement of the radius of the steel cable = 1.5 centimetre

Converting the radius to meters by dividing by 100:

= 1.5 / 100

= 0.015 meters

Therefore, the radius of the steel cable in meters is 0.015 m.

The maximum allowable stress given in the question = 10^8 N/m^-2

To Find:

The maximum load the cable can support.

Calculating:

The formula we use to calculate maximum stress:

Maximum Stress = Maximum Force / Area of cross section

Taking Area of cross section to the other side of the formula we get:

Maximum Force = Maximum Stress x Area of cross section

Calculating the area of cross section:

We know that the area of cross section of a cable will be in the form of a circle.

The formula that we use to calculate the area of a circle:

= $\pi r^{2}$

Substituting the values known to us in this formula use to calculate maximum force we get:

= 22/7 x 0.015 x 0.015

= 0.000707142  (Approximately)

Now calculating maximum force,

= 0.000707142 x 10^8

= 7.0714 x 10^4 Newtons

Therefore, the maximum load which the cable can support is 7.0714 x 10^4 Newtons.

Answer 2

7.0714 x 10^4 Newtons

Given:

The measurement of the radius of the steel cable = 1.5 centimetre

Converting the radius to meters by dividing by 100:

= 1.5 / 100

= 0.015 meters

Therefore, the radius of the steel cable in meters is 0.015 m.

The maximum allowable stress given in the question = 10^8 N/m^-2

To Find:

The maximum load the cable can support.

Calculating:

The formula we use to calculate maximum stress:

Maximum Stress = Maximum Force / Area of cross section

Taking Area of cross section to the other side of the formula we get:

Maximum Force = Maximum Stress x Area of cross section

Calculating the area of cross section:

We know that the area of cross section of a cable will be in the form of a circle.

The formula that we use to calculate the area of a circle:

= 

Substituting the values known to us in this formula use to calculate maximum force we get:

= 22/7 x 0.015 x 0.015

= 0.000707142  (Approximately)

Now calculating maximum force,

= 0.000707142 x 10^8

= 7.0714 x 10^4 Newtons

Therefore, the maximum load which the cable can support is 7.0714 x 10^4 Newtons.