The resultant of two forces applied to the body at right angles to each other is equal to 50 N.

The resultant of two forces applied to the body at right angles to each other is equal to 50 N. One of the acting forces is equal to 40N. Find the second one.

∠α = 90 ° C.

Fr = 50 N.

F1 = 40 N.

F2 -?

The resultant of all forces Fр is called the vector sum of all forces that act on the body: Fр = F1 + F2.

Since the forces F1 and F2, which act on the body, are mutually perpendicular according to the condition of the problem, then according to the rule of addition of vectors, their resultant will be the hypotenuse of a right-angled triangle with legs F1 and F2.

By the Pythagorean theorem: Fр ^ 2 = F1 ^ 2 + F2 ^ 2.

F2 ^ 2 = Fр ^ 2 – F1 ^ 2.

F2 = √ (Fр ^ 2 – F1 ^ 2).

F2 = √ ((50 N) ^ 2 – (40 N) ^ 2) = 30 N.

Answer: the second force that acts on the body is F2 = 30 N.