Question

muscle has a force of 100LBS and is pulling on a bone at an angle of 15 degrees. muscle B has a force of 150 lbs and is pulling on the same bone at the same spot but at an angle of 30. muscle c has a force of 75Ibs and is pulling at the same spot with an angle of 10. what is the resultant force of the muscles in the terms of the amount of force and direction? draw a diagram, label and show your work

Answer 1

To solve this problem, we need to use vector addition. We can start by breaking down each force into its x and y components.

For muscle A:

Force = 100 lbs

Angle = 15 degrees

X-component = 100 * cos(15) = 96.93 lbs

Y-component = 100 * sin(15) = 25.04 lbs

For muscle B:

Force = 150 lbs

Angle = 30 degrees

X-component = 150 * cos(30) = 129.90 lbs

Y-component = 150 * sin(30) = 75.00 lbs

For muscle C:

Force = 75 lbs

Angle = 10 degrees

X-component = 75 * cos(10) = 73.83 lbs

Y-component = 75 * sin(10) = 13.03 lbs

Next, we can add up the x and y components separately:

X-component = 96.93 + 129.90 + 73.83 = 300.66 lbs

Y-component = 25.04 + 75.00 + 13.03 = 113.07 lbs

We can use these components to find the magnitude and direction of the resultant force:

Magnitude = sqrt(X^2 + Y^2) = sqrt((300.66)^2 + (113.07)^2) = 321.23 lbs

Direction = tan^-1(Y/X) = tan^-1(113.07/300.66) = 21.65 degrees (measured counterclockwise from the positive x-axis)

Therefore, the resultant force of the muscles is 321.23 lbs at an angle of 21.65 degrees. Here is a diagram to illustrate the vectors:

Explanation:

25.04 lbs 73.83 lbs 129.90 lbs

/\ /\ /\

/ \ / \ / \

/ \ / \ / \

100 lbs 15° 75 lbs 10° 150 lbs 30°

\ / \ / \ /

\ / \ / \ /

\ / \ / \ /

96.93 lbs 13.03 lbs 75.00 lbs