Sobre uma caixa de massa 20 kg atuam duas forças de módulos constantes, F₁ = 15 N e F₂ = 20 N. Determine o módulo da aceleração adquirida pelo corpo no caso em que essas forças apresentem mesma direção e sentidos opostos.

If the two forces have the same direction, the acceleration = 1.75 m/s² (in the direction of the two forces).

If the two forces have opposite direction, the acceleration = 0.25 m/s² (in the direction of the larger of the two forces, the 20 N force).

Explanation:

English Translation

Two constant modulus forces act on a 20 kg mass box, F₁ = 15 N and F₂ = 20 N. Determine the acceleration module acquired by the body in the event that these forces have the same direction and opposite directions.

Solution

According to one of Newton's laws of motion, the resultant of the forces acting on a body is what causes the acceleration of that body.

Two forces, F₁ = 15 N and F₂ = 20 N, act on a 20 kg Mass box.

If the resultant of the forces acting on the mass is F, the resultant is related to the mass (m) and acceleration (a) of the body by

F = ma

If the two forces have the same direction, the resultant of the two forces acting on the mass is

F = F₁ + F₂ = 15 + 20 = 35 N

F = ma

35 = 20×a

a = (35/20) = 1.75 m/s² (in the direction of the two forces).

If the two forces have opposite direction, the resultant of the two forces acting on the mass is

F = F₂ - F₁ = 20 - 15 = 5 N

F = ma

5 = 20×a

a = (5/20) = 0.25 m/s² (in the direction of the larger of the two forces, the 20 N force).

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