An elevator cable can withstand a maximum tension of 1.83×104 N before breaking. The elevator has a mass of 420 kg and a maximum acceleration of 2.27 m/s2 . Engineering safety standards require that the cable tension never exceed two-thirds of the breaking tension
Er, what's the question?
The Question is How many 75kg people can the elevator safely accomodate?
What planet are we talking about here, Earth?
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To determine whether the elevator cable meets the engineering safety standards, we need to calculate the maximum tension on the cable during operation.
First, we calculate the weight of the elevator using the formula:
Weight (W) = mass (m) × acceleration due to gravity (g)
Given:
mass (m) = 420 kg (given)
acceleration due to gravity (g) = 9.8 m/s² (standard value)
Using the formula:
W = m × g
W = 420 kg × 9.8 m/s²
W ≈ 4116 N
Next, we calculate the maximum tension on the cable by multiplying the weight of the elevator by the maximum acceleration:
Maximum tension = Weight × maximum acceleration
Maximum tension = 4116 N × 2.27 m/s²
Maximum tension ≈ 9350.76 N
Now, to determine if the cable tension exceeds two-thirds of the breaking tension, we need to find two-thirds of the breaking tension:
Two-thirds of breaking tension = (2/3) × breaking tension
Two-thirds of breaking tension = (2/3) × 1.83 × 10⁴ N
Two-thirds of breaking tension = 1.22 × 10⁴ N
Finally, we compare the maximum tension with two-thirds of the breaking tension:
Maximum tension ≈ 9350.76 N
Two-thirds of breaking tension ≈ 1.22 × 10⁴ N
Since the maximum tension (9350.76 N) is less than two-thirds of the breaking tension (1.22 × 10⁴ N), the elevator cable meets the engineering safety standards.