Math Problem Statement

  1. A mail sack with a mass of 85 kg hangs from a vertical rope 2.5 m long. the worker moves the mail sack to the side 0.9 m (measured horizontally) while keeping the length of the rope time is tight. (The attachment point of the upper part of the rope remains in place.) a. What horizontal force is needed to hold the mail sack in the new location? b. When the sack is moved to this location, how much work does the worker do?

Solution

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Math Problem Analysis

Mathematical Concepts

Static Equilibrium
Work and Energy
Trigonometry

Formulas

sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
F = T * sin(θ)
T = W / cos(θ)
W = F * x

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 11-12