Inclined Plane Problems, 3

Category: Mechanics, Physics

"Published in Newark, California, USA"

The block shown in the figure is acted on by its weight W = 400 lbs., a horizontal force F = 600 lbs., and the pressure P exerted by the inclined plane. The resultant R of these forces is parallel to the incline. Determine P and R. Does the block move up or down the incline?

Photo by Math Principles in Everyday Life

Solution:

The first thing that we need to do is to get the x and y components of each forces and then isolate the given figure as follows 

Photo by Math Principles in Everyday Life

Since we don't know the direction of the resultant, let's assume that the direction is upward because the value of F is greater than the weight of a block. 

The sum of x component is

The sum of y component is

Substitute the value of P to the first equation. Therefore, the value of R is

Since the value of R is positive, then the block is moving upward the incline. 
 

Resultant of Forces and Components, 2

Category: Mechanics, Physics

"Published in Newark, California, USA"

The force system as shown in the figure has a resultant of 200 lbs. pointing up along the y axis. Compute the values of F and θ required to give this resultant.

Photo by Math Principles in Everyday Life

Solution:

The first thing that we need to do is to get the x and y components of each forces and then isolate the given figure as follows

Photo by Math Principles in Everyday Life

The sum of y components is

The sum of x components is

 

 

 

 

Divide the first equation by the second equation in order to solve for θ, we have
 

Take the inverse tangent on both sides on the equation, we have

                                or

Substitute the value of θ to either of the two working equations, we have
 

 

 

 

 

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