# ProblemA winch, located at \( M \), pulls a box up an incline with a cable. The distance from the box to the winch is \( s \). Suppose that, starting from rest, the box travels the full distance \( s \) and the tension in the cable is a constant value \( T \). Assume the box has mass \( m \) and a sliding coefficient of friction of \( \mu_k \). What is the speed of the box, \( v_M \), when it reaches the winch at point \( M \)? Assume the values \( g = 9.81 \, \text{m/s}^2 \), \( T = 300 \, \text{N} \), \( \mu_k = 0.3 \), \( m = 20 \, \text{kg} \), \( \theta = 30^\circ \), and \( s = 10 \, \text{m} \).## Diagram ExplanationThe diagram shows an inclined plane with an angle \( \theta \) to the horizontal. A box of mass \( m \) is on the incline, and a cable runs from the box over a pulley at point \( B \) to a winch located at point \( M \). The incline is marked with the distance \( s \) from the box to the winch. The gravitational force \( g \) acts vertically downward, while kinetic friction acts along the plane with a coefficient \( \mu_k \).

Given:To find:Speed of the box when it reaches the winch M.

A winch, located at M, pulls a box up an incline with a cable. The distance from the box to the winch is s. Suppose that, starting from rest, the box travels the full distances and the tension in the cable is a constant value T. Assume the box has mass m and a sliding coefficient of friction of Mk. What is the speed of the box, UM, when it reaches the winch at point M? Assume the values 8 = 9.81 m/s², T =300 N, k = 0.3, m = 20 kg, 0 = 30 deg, and s=10 m.

A winch, located at M, pulls a box up an incline with a cable. The distance from the box to the winch is s. Suppose that, starting from rest, the box travels the full distances and the tension in the cable is a constant value T. Assume the box has mass m and a sliding coefficient of friction of Mk. What is the speed of the box, UM, when it reaches the winch at point M? Assume the values 8 = 9.81 m/s², T =300 N, k = 0.3, m = 20 kg, 0 = 30 deg, and s=10 m.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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# Problem

A winch, located at \( M \), pulls a box up an incline with a cable. The distance from the box to the winch is \( s \). Suppose that, starting from rest, the box travels the full distance \( s \) and the tension in the cable is a constant value \( T \). Assume the box has mass \( m \) and a sliding coefficient of friction of \( \mu_k \). What is the speed of the box, \( v_M \), when it reaches the winch at point \( M \)? Assume the values \( g = 9.81 \, \text{m/s}^2 \), \( T = 300 \, \text{N} \), \( \mu_k = 0.3 \), \( m = 20 \, \text{kg} \), \( \theta = 30^\circ \), and \( s = 10 \, \text{m} \).

## Diagram Explanation

The diagram shows an inclined plane with an angle \( \theta \) to the horizontal. A box of mass \( m \) is on the incline, and a cable runs from the box over a pulley at point \( B \) to a winch located at point \( M \). The incline is marked with the distance \( s \) from the box to the winch. The gravitational force \( g \) acts vertically downward, while kinetic friction acts along the plane with a coefficient \( \mu_k \).

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