Question

The greatest and least resultant of two forces acting at a point is 10N and 6N respectively . If each of force is increased by 3N , find the resultant of new forces when acting at a point at angle of 90' with each other

Answer 1

If two forces are F1 and F2 then,

F1 + F2 = 10N

F1 - F2 = 6N

Add above two equations

2F1 = 16
F1 = 8N

From first equation
F2 = 10 - 8 = 2N

When increased by 3N
F1 = 8N + 3N = 11N
F2 = 2N + 3N = 5N

Resultant = sqrt(11^2 + 5^2) = sqrt(121 + 25) = sqrt(146) = 12.083N

Answer 2

Answer:

Explanation:

Solution,

Let P and Q be the two forces.

Then,

Greatest resultant = P + Q = 29 N ..... (i)

Least resultant = P - Q = 5 N ..... (ii)

On Solving eq (i) and (ii), we get

P = 17 N and,

Q = 12 N

When each force is increased by 3 N,

Then,

New forces are

p = P + 3 = 17 + 3 = 20 N

q = Q + 3 = 12 + 3 = 15 N

As the new forces actat right angle to each other,

Then their resultant are,

R = √p² + q²

R = √20² + 15²

R = √625

R = 25 N

If resultant R makes angle β with the force p, then

tan β = p/q

tan β = 15/20

tan β = 0.75

or β = tan (0.75)

β = 36°52'.