The sum of magnitudes of two forces is 16N.if the resultant force is 8N and its direction is perpendicular to minimum force then the forces are:
(a)6N,10N(b)8N,8N(c)4N,12N(d)2N,14N
I dont get it cuh
can u make it more simple.I cant understand ur answer completely..!thanks
please explain it.....
break the L into two components. One has to be 8, and one has to be 6.
it is a 3,4,5 triangle.
answer (a)
the sum of magnitudes o 2 forces is 16N if the resultant force is 8N and its direction is perpendicular to mimimum force then the fores are
a) 6N 10N
b) 8N 8N
c) 4N 12N
d) 2N 14N
a)6N 10N
how to solve it?
To solve this problem, we can use the Pythagorean theorem and trigonometric ratios. Let's denote the magnitudes of the two forces as F1 and F2.
Given:
Sum of magnitudes of two forces = 16 N
Resultant force = 8 N
Direction between the resultant force and the minimum force = 90° (perpendicular)
We know that the sum of the magnitudes of the two forces is given by:
F1 + F2 = 16 N -- (equation 1)
Since the direction between the resultant force and the minimum force is perpendicular (i.e., 90°), we can use the Pythagorean theorem to find the relationship between the magnitudes of the forces:
F1^2 + F2^2 = Resultant force^2 -- (equation 2)
Substituting the given values, we have:
F1^2 + F2^2 = 8^2
F1^2 + F2^2 = 64 -- (equation 3)
To find the forces, we can solve equations 1 and 3 simultaneously.
From equation 1:
F1 + F2 = 16 -- (equation 1)
Rearranging equation 1 to solve for F1:
F1 = 16 - F2 -- (equation 4)
Substituting equation 4 into equation 3, we have:
(16 - F2)^2 + F2^2 = 64
Expanding and simplifying this equation gives:
256 - 32F2 + F2^2 + F2^2 = 64
2F2^2 - 32F2 + 192 = 0
Dividing the equation by 2 to simplify it further:
F2^2 - 16F2 + 96 = 0
This is a quadratic equation. To find the values of F2, we can either factorize it or use the quadratic formula:
Using the quadratic formula: F2 = (-b ± √(b^2 - 4ac)) / 2a
In this case:
a = 1, b = -16, c = 96
Substituting these values into the quadratic formula, we have:
F2 = (16 ± √(16^2 - 4 * 1 * 96)) / (2 * 1)
F2 = (16 ± √(256 - 384)) / 2
F2 = (16 ± √(-128)) / 2
Since we have a negative value inside the square root, the forces F1 and F2 will be imaginary. However, forces are real physical quantities, so we can conclude that there are no real solutions to this problem.
Therefore, none of the given options (a), (b), (c), or (d) represents the forces in this scenario.