The greatest and least resultant of two forces acting at a point is 29 kgwt and 5 kgwt respectively.If each force is increased by 3 kgwt.Find the resultant of the two new forces when acting at right angles to each other?
Let x be the magnitude of the first force (and the larger force).
Let y be the magnitude of the second force.
Greatest resultant happens when they act in the same direction:
x + y = 29
Least resultant happens when they act in opposite directions:
x - y = 3
Solve this system of equations for x and y.
Use Pythagorean Theorem to find magnitude of resultant for right angle scenario.
Use trig to find direction of resultant w.r.t. force x.
To find the resultant of the two new forces when acting at right angles to each other, we first need to find the magnitudes of the individual forces.
Let's assume the two original forces are F1 and F2, and their magnitudes are x and y kgwt, respectively.
According to the given information, we have two equations:
1) x + y = 29 (equation 1) - This equation represents the sum of the magnitudes of the two forces, resulting in 29 kgwt.
2) x - y = 5 (equation 2) - This equation represents the difference between the magnitudes of the two forces, resulting in 5 kgwt.
We can solve these two equations simultaneously to find the magnitudes of the individual forces.
Adding equations 1 and 2, we get:
(x + y) + (x - y) = 29 + 5
2x = 34
x = 17
Substituting the value of x in equation 1, we get:
17 + y = 29
y = 29 - 17
y = 12
Therefore, the magnitudes of the original forces are:
F1 = 17 kgwt
F2 = 12 kgwt
Now that we know the magnitudes of the original forces, we can find the new magnitudes after increasing each force by 3 kgwt. Let's call the new magnitudes F1' and F2'.
F1' = F1 + 3 = 17 + 3 = 20 kgwt
F2' = F2 + 3 = 12 + 3 = 15 kgwt
Since the two forces are acting at right angles to each other, their resultant can be found using the Pythagorean theorem:
Resultant = sqrt(F1'^2 + F2'^2)
Resultant = sqrt(20^2 + 15^2)
Resultant = sqrt(400 + 225)
Resultant = sqrt(625)
Resultant = 25 kgwt
Therefore, the resultant of the two new forces when acting at right angles to each other is 25 kgwt.