A design project requires you to construct a crane to lift a maximum load of 5000 kg and with a maximum upward acceleration of 2 m/s².What size diameter steel cable should you use if the cable is to have a safety factor of 5? A)1.64 cm B)1.10 cm C)2.68 cm D)3.00 cm E)1.20 cm

Question

Quizplus · Accepted Answer

To determine the size diameter steel cable required, we need to use the formula: 
T = (m * ag) / SF 
where T is the tension in the cable, m is the maximum load, ag is the maximum upward acceleration, and SF is the safety factor. 
Plugging in the values we get: 
T = (5000 kg * 2 m/s^2) / 5 = 2000 N

Next, we need to use the formula for the tension in a cable: 
T = (pi * d^2 * s) / 4 
where d is the diameter of the cable and s is the tensile strength of the material.

Assuming a steel cable with a tensile strength of 1000 MPa, we can solve for d: 
d = sqrt((4 * T) / (pi * s)) 
d = sqrt((4 * 2000 N) / (pi * 1000 MPa)) 
d = 0.0268 m = 2.68 cm

Therefore, the size diameter steel cable we should use is 2.68 cm or approximately 1.06 inches.

The best choice is C.

A Design Project Requires You to Construct a Crane to Lift