Question

The diagram shows two forces acting perpendicularly on an object. The forces have magnitudes F1 = 8.2 N and F2 = 20.6 N. What is the net force acting on the object?

a) magnitude 22 N; direction 68 degrees counterclockwise from
b) magnitude 22 N; direction 22° counterclockwise from
c) magnitude 25 N; direction 34° counterclockwise from
d) magnitude 25 N; direction 68° counterclockwise from

Answer 1

Option (b).

Step-by-step explanation:

Two forces are acting perpendicularly on an object. We have, F₁ = 8.2 N and F₂ = 20.6 N

We need to find the net force acting on the object. When two forces are acting in perpendicular to each other, the net force on it is given by :

`F=√(F_1^2+F_2^2) \\\\=√(8.2^2+20.6^2) \\\\=22.17\ N`

or

F = 22 N

Let
`\theta` is the angle. It can be given by :

`\tan\theta=(F_1)/(F_2)\\\\\tan\theta=(8.2)/(20.6)\\\\=21.7^(\circ)`

or

`\theta=22^(\circ)`

So, the net force is 22 N and the direction is 22° counterclockwise from F₁. Hence, the correct option is (b).