The slotted arm OA rotates about a fixed axis through O. At the instant under consideration, θ = 36°, θ˙ = 36 deg/s, and θ¨ = 26 deg/s2. Determine the magnitude of the force F applied by arm OA and the magnitude of the force N applied by the sides of the slot to the 0.5-kg slider B. Neglect all friction, and let L = 0.72 m. The motion occurs in a vertical plane.

Question

Physics

Joshua

12 May, 00:18

The slotted arm OA rotates about a fixed axis through O. At the instant under consideration, θ = 36°, θ˙ = 36 deg/s, and θ¨ = 26 deg/s2. Determine the magnitude of the force F applied by arm OA and the magnitude of the force N applied by the sides of the slot to the 0.5-kg slider B. Neglect all friction, and let L = 0.72 m. The motion occurs in a vertical plane.

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Answers (1)

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Omar Cannon · Answer 1

F = 0.0545 N

Explanation:

Let's use Newton's second law for rotational movement

τ = I α

The moment of inertia for a bar supported by some ends is

I = 1/3 m L²

Torque is

τ = F L

Let's replace

F L = 1/3 m L² α

F = 1/3 m L α

Let's reduce angular acceleration to SI units

Alf = 26º / s² (π rad / 180º) = 0.454 rad / s²

Let's calculate

F = 1/3 0.5 0.72 0.454

F = 0.0545 N