Two forces with magnitudes of 45 pounds and 62pounds are applied to an object. The magnitude ofthe resultant is 100 pounds. Find the measurementof the angle between the resultant vector and thevector of the 45-pound force and the anglebetween the resultant vector and the 62-poundforce to the nearest whole degree. Show all yourwork and label your answers.

Answered: Two forces with magnitudes of 45 pounds…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Two forces with magnitudes of 45 pounds and 62
pounds are applied to an object. The magnitude of
the resultant is 100 pounds. Find the measurement
of the angle between the resultant vector and the
vector of the 45-pound force and the angle
between the resultant vector and the 62-pound
force to the nearest whole degree. Show all your
work and label your answers.

Expert Solution

Step 1

To calculate the angle between the resultant vector and the two constituent vectors.

Given:
The first initial force is: $F_{1} = 45 lb$
The second initial force: $F_{2} = 62 lb$
The resultant force: $F_{R} = 100 lb$

To calculate:
The angle between the resultant force and the first initial force: $θ_{1}$
The angle between the resultant force and the second initial force: $θ_{2}$

The resultant vector of two vectors is given by the formula:
$R = \sqrt{{|A_{1}|}^{2} + {|A_{2}|}^{2} + 2 A_{1} A_{2} \cos (θ)}$
where,
$R$ is the resultant vector,
$A_{1}$ is the first vector,
$A_{2}$ is the second vector and
$θ$ is the angel between the first and the second vector.
This is the parallelogram rule of vector addition.

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