SOLUTION: A force of 100N acting horizontally to the right is to be combined with another force P acting upward to the right at an angle of 15 degrees with the vertical. If the resultant for
Algebra ->
Pythagorean-theorem
-> SOLUTION: A force of 100N acting horizontally to the right is to be combined with another force P acting upward to the right at an angle of 15 degrees with the vertical. If the resultant for
Log On
Question 1182677: A force of 100N acting horizontally to the right is to be combined with another force P acting upward to the right at an angle of 15 degrees with the vertical. If the resultant force of these two forces is 122.83N, solve force P.
-> Is it possible to use phytagorean theorem? I'm having a hard time understanding the problem. Please help.. Found 3 solutions by robertb, ikleyn, Edwin McCravy:Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website! UPDATE: I have edited the solution to correct the fact that cos(105) is a negative quantity, based on what solution other tutors have given.
Use the cosine law, which says that,
where is the angle between vectors and , and vector is the one opposite to .
Let , , and , the magnitude of the resultant force.
===>
<===> after simplifying.
===>
Therefore the magnitude of force P is around 50N.
You can put this solution on YOUR website! .
A force of 100 N acting horizontally to the right is to be combined with another force P acting upward to the right
at an angle of 15 degrees with the vertical. If the resultant force of these two forces is 122.83N, solve force P.
~~~~~~~~~~~~~~~~
Use the parallelogram rule of adding vectors and use the cosine law, which says that
,
where is the angle between vectors and ,
and vector is the sum of vectors and .
In our case, , , and , the magnitude of the resultant force.
===>
===> after simplifying.
===>
Therefore, the magnitude of force P is around 50 newtons. ANSWER
Since it makes a 15o angle with the vertical, it makes a 75o angle with the
horizontal.
Yes, you can use the Pythagorean theorem. I made a mistake somewhere, but
don't have time to find it and correct it. Maybe you can find the mistake.
horizontal | vertical
components | components
---------------------------------
|P|cos(75o) N ||P|sin(75o) N
100 N | 0 N
---------------------------------
|P|(cos(75o)+100 N | |P|sin(75o) N
______________________________________________________________
|Resultant| = √(sum of horizontal components)2 +(sum of vertical components)2
Square both sides
Subtract 10000 from both sides.
Since
Use the quadratic formula:
We use the + since the - gives a negative value.
That's the magnitude of the force P.
The angle it makes with the x-axis is found by
Edwin
