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

2024
Views:

227

Pages:

3
Author:

Kevin Riddle

SOLUTIONS TO HOMEWORK PROBLEMS CHAPTER 17 Planar Kinetics of Rigid Bodies: HW#8 17-88, 98, 102 Problem 17-88 The punching bag of mass M has a radius of gyration about its center of mass G of kG. If it is subjected to a horizontal force F, determine the initial angular acceleration of the bag and the tension in the supporting cable AB. Given: 1 M = 20 kg kG = 0.4 m F = 30 N a = 1 m b = 0.3 m c = 0.6 m g = 9.81 m/s² Solution: T - Mg = 0 T = Mg T = 196.2 N Fc = MkG²α α = Fc / MkG² α = 5.625 rad/s² Problem 17-98 The truck carries the spool which has weight W and radius of gyration kG. Determine the angular acceleration of the spool if it is not tied down on the truck and the truck begins to accelerate at the rate aA. The coefficients of static and kinetic friction between the spool and the truck bed are μs and μk, respectively. Given: W = 200 lb kG = 2 ft aA = 5 ft/s² r = 3 ft g = 32.2 ft/s² μs = 0.15 μk = 0.1 Solution: Assume no slip Guesses: F = 1 lb FN = 1 lb Fmax = 1 lb aG = 1 ft/s² α = 1 rad/s² Given F = (W/g)aG F = (W/g)kG²α FN - W = 0 Fmax = μsFN Calculations: Fmax = 30.00 lb aG = 1.538 ft/s² α = 1.154 rad/s² Since F = 9.56 lb < Fmax = 30 lb then our no-slip assumption is correct. Problem 17-102 The lawn roller has mass M and radius of gyration kG. If it is pushed forward with a force F when the handle is in the position shown, determine its angular acceleration. The coefficients of static and kinetic friction between the ground and the roller 1 are μs and μk, respectively. Given: M = 80 kg kG = 0.175 m F = 200 N θ = 45 deg μs = 0.12 μk = 0.1 r = 200 mm = 0.2 m g = 9.81 m/s² Solution: Guesses: Ff = 1 N FN = 1 N ax = 1 m/s² α = 1 rad/s² Fmax = 1 N Given -Fcos(θ) + Ff = -Max FN - Mg - Fsin(θ) = 0 Ff = MkG²α ax = αr Fmax = μsFN Calculations: Fmax = 111.147 N FN = 926.221 N Ff = 61.324 N ax = 1.001 m/s² α = 5.01 rad/s² Since Ff = 61.3 N < Fmax = 111.1 N, then our no-slip assumption is true.