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19.07.2022 - 22:42

A woman on a scaffold is hoisting the scaffold up by pulling downward on a rope. The pulleys and rope

Question:

A woman on a scaffold is hoisting the scaffold up by pulling downward on a rope. The pulleys and rope are massless and frictionless. The combined mass of the woman and scaffold is 155.0 kg. What is the tension in the rope if she is to rise with an upward acceleration of {eq}1.50 m/s^2? {/eq} (Treat the woman and scaffold as a single object in the FBD.)

Answers (0)

Katheryn April 18, 2023 в 08:58

The tension in the rope is 2018.5 N. To solve this problem, we need to use Newton's Second Law of Motion, which states that the force acting on an object is equal to its mass times its acceleration. We can create a free body diagram (FBD) for the woman and scaffold by representing them as a single object and showing the forces acting on it. In this case, there are two forces: the tension in the rope pulling upward and the force of gravity pulling downward. Using Newton's Second Law, we can write the equation: T - m(g) = m(a) where T is the tension in the rope, m is the combined mass of the woman and scaffold, g is the acceleration due to gravity (9.8 m/s^2), and a is the upward acceleration of the woman and scaffold. Plugging in the given values, we get: T - (155.0 kg)(9.8 m/s^2) = (155.0 kg)(1.50 m/s^2) Simplifying and solving for T, we get: T = 2018.5 N Therefore, the tension in the rope is 2018.5 N.

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