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 108 N m–2, what is the maximum load the cable can support?
Answers
Explanation:
Radius of the steel cable, r = 1.5 cm = 0.015 m
Maximum allowable stress = 108 N m–2
Maximum stress = Maximum force / Area of cross-section
∴ Maximum force = Maximum stress × Area of cross-section
= 108 × π (0.015)2
= 7.065 × 104 N
Hence, the cable can support the maximum load of 7.065 × 104 N.
7.07 x 10^4 Newtons
Given:
Radius steel cable = 1.8 cm
Maximum Stress = 10^8 N m^-2
Formula For Calculating The Stress:
STRESS = FORCE /AREA
Rebuilding this formula for calculating the maximum stress:
MAXIMUM STRESS= MAXIMUM FORCE /AREA MAXIMUM FORCE
Rearranging we get:
MAXIMUM FORCE= MAXIMUM STRESS × AREA
= 108 x pi x r^2
Substituting the values into this formula we get:
= 108 x 3.14 x (1.5 x 10^-2)^2
= 7.07 x 10^4 Newtons
Therefore, the maximum load the cable can support is 7.07 x 10^4 Newtons.