Two children playing on a frictionless garden gate invent a new game called "gate". The idea is that they will get on opposite sides of the gate and each push such that the gate does not move. If they both push horizontally and perpendicular to the gate and one child pushes with a force of 170 N at a distance of 0.590 m from the hinges, determine the force the second child must exert in order to keep the gate from moving if she pushes at a distance of 0.430 m from the hinges.

Question

Physics

Kason Jarvis

Today, 04:34

Two children playing on a frictionless garden gate invent a new game called "gate". The idea is that they will get on opposite sides of the gate and each push such that the gate does not move. If they both push horizontally and perpendicular to the gate and one child pushes with a force of 170 N at a distance of 0.590 m from the hinges, determine the force the second child must exert in order to keep the gate from moving if she pushes at a distance of 0.430 m from the hinges.

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Answers (1)

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Abraham Riggs · Answer 1

233 N

Explanation:

The balance condition, to keep the gate from moving, requires that the net torque be zero, this is, the torques on both sides of the gate must be equal.

Torque equation: τ = F * d

a) Torque applied by one of the children:

F = 170 N d = 0.590 m

τ₁ = 170 N * 0.590 m

b) Torque applied by the second child:

F = ? d = 0.430 m

τ₂ = F * 0.590 m

c) Equilibrium condition:

τ₁ = τ₂ 170 N * 0.590m = F * 0.430m

F = 170 N * 0.590 m / 0.430 m = 233 N ← answer