A girl weighing 45 kg is swinging on a swing 3 meters long. What weight will the girl have when passing the central position at a speed of 6 m / s?
m = 45 kg.
R = 3 m.
V = 6 m / s.
g = 10 m / s ^ 2.
Two forces act on the girl in the lower position: the force of gravity Ft directed vertically downward, and the reaction of the seat of the swing N directed vertically upward. Let’s write 2 Newton’s law for the forces that act on the girl: m * a = N – Fт. Let us express the strength of the shop’s reaction to the girl: N = m * a + Fт.
According to Newton’s 3 laws: with what force the swing bench acts on a girl, with such force the girl presses on the bench. Therefore, the weight of the body P will be equal to the reaction force of the bench N.
P = m * a + Ft.
The force of gravity is determined by the formula: Ft = m * g.
Centripetal acceleration a is determined by the formula: a = V ^ 2 / R.
P = m * V ^ 2 / R + m * g.
P = 45 kg * (6 m / s) ^ 2/3 m + 45 kg * 10 m / s ^ 2 = 990 N.
Answer: the girl’s body weight in the central position P = 990 N.
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