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?
13
a + b = 29
a - b = 5
2a = 34 ... a = 17 ... b = 12
(17 + 3)^2 + (12 + 3)^2 = r^2
Ha
To find the resultant of two forces acting at right angles to each other, we can use the Pythagorean theorem.
Let's denote the original forces as F1 and F2, with their resultants being R1 and R2, respectively. We also know that R1 - R2 = 29 kgwt and R2 - R1 = 5 kgwt.
In this case, since the forces are acting at right angles to each other, we can use the Pythagorean theorem:
R^2 = R1^2 + R2^2
Now, let's solve for the original resultants:
R1^2 = (R1 - R2)^2 = (29 kgwt)^2 = 841 kgwt^2
R2^2 = (R2 - R1)^2 = (5 kgwt)^2 = 25 kgwt^2
Since the forces are increased by 3 kgwt, we need to calculate the new resultants, which we'll call R1_new and R2_new. We can express the new resultants as:
R1_new = R1 + 3 kgwt
R2_new = R2 + 3 kgwt
Now, let's calculate the new resultants:
R1_new^2 = (R1 + 3 kgwt)^2
R2_new^2 = (R2 + 3 kgwt)^2
Finally, to find the resultant of the new forces acting at right angles to each other, we can apply the Pythagorean theorem again:
(R_new)^2 = (R1_new)^2 + (R2_new)^2
Plug in the values we know and solve for (R_new)^2.
Once you have the value of (R_new)^2, take the square root to find R_new.