Chapter 1: Q41E (page 360)

A steel cable with cross-sectional area 3.00 cm² has an elastic limit of 2.40 x 10⁸ Pa. Find the maximum upward acceleration that can be given a 1200-kg elevator supported by the cable if the stress is not to exceed one-third of the elastic limit.

Short Answer

Expert verified

The maximum upward acceleration that can be given in a 1200 kg elevator supported by the cable is $10.2 m / s^{2}$

Step by step solution

The given data

The elastic limit of the cable $= 2.40 \times 10^{8}$ Pa

The cross-sectional area of steel cable, $A = 3 m^{2}$

Mass of elevator, m = 1200 kg

Formula used

Stress of wire $φ = \frac{F_{⊥}}{A}$

Where $F_{⊥}$ is the tensile force applied to an object (tension in the cable), A is the cross-sectional area

Net force, $\sum_{} F = ma$

Where m is the mass of the object and a is the acceleration

Find the tension in the cable

Since stress cannot exceed one-third of the elastic limit, so stress

$\begin{aligned} φ = \frac{1}{3} (2.4 \times 10^{8} Pa) \\ = 0.8 \times 10^{8} Pa \end{aligned}$

Now, tension $F_{⊥} = Aφ$

$F_{⊥} = (3 \times 10^{- 4} m^{2}) (0.8 \times 10^{8} Pa) = 2.4 \times 10^{4} N$

Hence, $F_{⊥} = 2.4 \times 10^{4} N$

Find the acceleration

Since net force is $\sum_{} F = ma$

$F_{⊥} - mg = ma a = \frac{F_{⊥}}{m} - g$

Hence acceleration is

$\begin{aligned} a = \frac{2.4 \times 10^{4} N}{1200 kg} - 9.8 m / s^{2} \\ = 10.2 m / s^{2} \end{aligned}$

Therefore, the maximum upward acceleration that can be given in a 1200-kg elevator supported by the cable is $10.2 m / s^{2}$

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A steel cable with cross-sectional area 3.00 cm² has an elastic limit of 2.40 x 10⁸ Pa. Find the maximum upward acceleration that can be given a 1200-kg elevator supported by the cable if the stress is not to exceed one-third of the elastic limit.

Short Answer

Step by step solution

The given data

Formula used

Find the tension in the cable

Find the acceleration

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A steel cable with cross-sectional area 3.00 cm2 has an elastic limit of 2.40 x 108 Pa. Find the maximum upward acceleration that can be given a 1200-kg elevator supported by the cable if the stress is not to exceed one-third of the elastic limit.

Short Answer

Step by step solution

The given data

Formula used

Find the tension in the cable

Find the acceleration

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Conservation of Energy and Momentum

Physical Quantities And Units

Fields in Physics

Kinematics Physics

Thermodynamics

Study anywhere. Anytime. Across all devices.

A steel cable with cross-sectional area 3.00 cm² has an elastic limit of 2.40 x 10⁸ Pa. Find the maximum upward acceleration that can be given a 1200-kg elevator supported by the cable if the stress is not to exceed one-third of the elastic limit.