University:
Angelo State University
Course:
ENGR 2302 | Engineering Mechanics - Dynamics
Academic year:

2024
Views:

337

Pages:

4
Author:

Dania Lynch

SOLUTIONS TO HOMEWORK PROBLEMS CHAPTER 16 Acceleration, Angular Acceleration Chap 16.7 HW#6 16-108, 112, 116 Problem 16-108 The rod of length r_AB slides down the inclined plane, such that when it is at B it has the motion shown. Determine the velocity and acceleration of A at this instant. Given: r_AB = 10 ft r_CB = 4 ft v_B = 2 ft/s a_B = 1 ft/s² θ = 60 deg Solution: Guesses: ω = 1 rad/s α = 1 rad/s² v_A = 1 ft/s a_A = 1 ft/s² φ = 1 deg Given r_AB sin(θ - φ) = r_CB sin(θ) Equations: v_A = v_B - ω x r_AB a_A = a_B - α x r_AB - ω x (ω x r_AB) Problem 16-112 At a given instant the wheel is rotating with the angular velocity and angular acceleration shown. Determine the acceleration of block B at this instant. Given: ω = 2 rad/s1 α = 6 rad/s² L = 0.5 m r = 0.3 m θ = 60 deg φ = 45 deg Solution: r1 = r * (cos(θ), -sin(θ), 0) r2 = L * (cos(φ), sin(φ), 0) k = (0, 0, 1) Guesses: ω_AB = 1 rad/s α_AB = 1 rad/s² v_B = 1 m/s a_B = 1 m/s² Given -ωk x r1 + αk x r2 = v_B -αk x r1 - ωk x (-ωk x r1) + α_ABk x r2 + ω_ABk x (ω_ABk x r2) = a_B ω_AB = Find(ω_AB, α_AB, v_B, a_B) α_AB = Find(ω_AB, α_AB, v_B, a_B) ω_AB = -1.47 rad/s α_AB = -8.27 rad/s² v_B = -0.82 m/s a_B = -3.55 m/s²