Question

Two forces A and B act at a point at right angles. If their resultant is 50N and their sum is 70N, find their magnitudes

Answer 1

Answer:

(A^2 + B^2)^1/2 = 50      since they are at right angles

A^2 + B^2 = 2500

(A + B)^2 = A^2 + 2 AB + B^2 = 4900     since A + B = 70

2500 + 2 A B = 4900

A B = 1200

A * (70 - A) = 1200        since B = 70 - A

A^2 - 70 A + 1200 = 0

A = 30     solving the quadratic

B = 40       since A + B = 70

So you have a 3, 4, 5 right triangle with the resultant of 50 N

Answer 2

30N,40N

Explanation:

• We have two forces A and B acting at right angles. It is given that the resultant of thir forces is 50N and the sum is 70N.

• If we have two forces p,q acting then sum of the forces and resultant of forces is given by

$s=p+q\\ r=\sqrt{p^{2}+q^{2}+2pq  }$

• From the above given data s=70N and r=70N.

$A+B=70\\ \\B=70-A\\ \\50^{2}=A^{2}  +(70-A)^{2}+2*A*(70-A)co\alpha \alpha \\\\ 50^{2}=2A^{2}  +70^{2}-140A+(140A-2A^{2})cos\alpha  \\\\\alpha=90 \\ \\ 50^{2}=2A^{2}  +70^{2}-140A\\\\(A-30)*(A-40)=0$

• Let us take A=30, then B=70-A ,so B=40.

• Hence the magnitudes are 30N,40N.