A body with a mass of m = 4 kg moves with acceleration, the modulus of which is a = 2.5 m / s ^ 2

| May 5, 2021 | education

A body with a mass of m = 4 kg moves with acceleration, the modulus of which is a = 2.5 m / s ^ 2, under the action of two mutually perpendicular forces F1 and F2. Determine the modulus of force F1 if the modulus of force F2 = 8 H.

m = 4 kg.

a = 2.5 m / s ^ 2.

F2 = 8 N.

∠α = 90 °.

F1 -?

According to Newton’s 2 law, the resultant of all forces F that act on the body is equal to the product of the body’s mass m by its acceleration a: F = m * a.

Since the body is acted upon by two forces F1 and F2, their resultant will be a vector sum: F = F1 + F2.

Since the forces are mutually perpendicular, then according to the Pythagorean theorem, F ^ 2 = F1 ^ 2 + F2 ^ 2.

F1 ^ 2 = F ^ 2 – F2 ^ 2.

F1 = √ ((m * a) ^ 2 – F2 ^ 2).

F1 = √ ((4 kg * 2.5 m / s ^ 2) ^ 2 – (8 N) ^ 2) = 6 N.

Answer: F1 = 6 N.



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