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

Photo by Math Principles in Everyday Life

For F = 400 lbs.,

For P = 1200 lbs.,

Word Problem - Number Problem, 5

Category: Algebra

"Published in Daly City, California, USA"

The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

Solution:

From the description of a given word problem, it is an application of linear equation with two equations, two unknowns. 

Let x = be the value of one's digit
      y = be the value of ten's digit 

From the statement "The sum of the digits of a two-digit number is 7.", then the working equation is
 

From the statement "When the digits are reversed, the number is increased by 27.", then the working equation is
 

 

 

 

Hence, the working equations for the given problem are
 

If you add the two working equation, y will be cancelled and the value of x which is the one's digit is
 

 

Substitute the value of x to any of the working equations. The value of y which is the ten's digit is
 

 

 

 

Therefore, the value of a two-digit number is 25. 

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