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211_Dynamics 11ed Manual

# 211_Dynamics 11ed Manual - Engineering Mechanics Dynamics F...

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Unformatted text preview: Engineering Mechanics - Dynamics F a − k( δ 1 + z) = Chapter 13 ⎛ W ⎞ z'' ⎜⎟ ⎝g⎠ F a = k⎡δ 1 + ( a)sin ( 2θ )⎤ − ⎣ ⎦ ⎛ W ⎞ 4( a) sin (2θ ) θ' 2 ⎜⎟ ⎝g⎠ The maximum values occurs when sin(2θ) = -1 and the minimum occurs when sin(2θ) = 1 F amin = k( δ 1 − a) + ⎛ W ⎞ 4aθ' 2 ⎜⎟ ⎝g⎠ F amin = 1.535 lb F amax = k( δ 1 + a) − ⎛ W ⎞ 4aθ' 2 ⎜⎟ ⎝g⎠ F amax = 3.265 lb Problem 13-87 The spool of mass M slides along the rotating rod. At the instant shown, the angular rate of rotation of the rod is θ', which is increasing at θ''. At this same instant, the spool is moving outward along the rod at r' which is increasing at r'' at r. Determine the radial frictional force and the normal force of the rod on the spool at this instant. Given: M = 4 kg r = 0.5 m θ' = 6 rad s r' = 3 m s θ'' = 2 rad r'' = 1 m 2 s g = 9.81 2 s m 2 s Solution: ar = r'' − rθ' 2 F r = M ar aθ = rθ'' + 2r' θ' F θ = M aθ Fz = M g F r = −68.0 N 2 2 Fθ + Fz = 153.1 N *Problem 13-88 The boy of mass M is sliding down the spiral slide at a constant speed such that his position, measured from the top of the chute, has components r = r0, θ = bt and z = ct. Determine the components of force Fr, Fθ and F z which the slide exerts on him at the instant t = t1. Neglect 209 ...
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