Inclined Plane Problems, 2

Category: Mechanics, Physics

"Published in Newark, California, USA"

The body of a 30° incline as shown in the figure is acted upon by a force P inclined at 20° with the horizontal. If P is resolved into components parallel and perpendicular to the incline and the value of the parallel component is 300 lbs., compute the value of the perpendicular component and of P.

Photo by Math Principles in Everyday Life

Solution:

Did you notice that the direction of force P is not vertical nor horizontal? The direction of force P is 20° above the horizontal towards to the body or block. Let's isolate the given figure so that we can draw the x and y components of force P as follows
 

Photo by Math Principles in Everyday Life

 
If P_x = 300 lbs., then we can solve for the value of P by using trigonometric functions of a right triangle as follows

Therefore, by using trigonometric functions of a right triangle, the value of P_y is 

 

Inclined Plane Problems

Category: Mechanics, Physics

"Published in Newark, California, USA"

The body on the inclined plane is subjected to the vertical and horizontal forces as shown in the figure. Find the components of each force along x-y axes oriented parallel and perpendicular to the incline.

Photo by Math Principles in Everyday Life

Solution:

Draw the x and y components of the given forces and then isolate the given figure as follows

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For F = 400 lbs.,

For P = 1200 lbs.,

Resultant of Forces and Components

Category: Mechanics, Physics

"Published in Newark, California, USA"

Determine the x and y components of each of the forces shown in the figure. Also, determine the resultant of the forces and its direction.

Photo by Math Principles in Everyday Life

Solution:

The first thing that we need to do is to draw the rectangular component of the given forces and then isolate into x and y components as follows

Photo by Math Principles in Everyday Life

By using trigonometric functions of right triangles, we can solve for the x and y components of the three given forces.

For F = 390 lbs:

For P = 300 lbs:

 

 

 

 

 

For T = 400 lbs:
 

 

 

 

 

 

         
The sum of the x components of the three given forces is
 

 

The sum of the y components of the three given forces is
 

 

 

Since the sign of R_x and R_y are both negative, then they are located at the 3rd quadrant as shown in the figure 

Photo by Math Principles in Everyday Life

By Pythagorean Theorem, the value of the resultant of the given three forces is

The direction of the resultant is

 

 

 

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