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A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2. If the mass is released from rest and falls a distance of 0.5 m in 1.5 s, calculate: (a) The linear acceleration of the mass. (b)...

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A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2. If the mass is released from rest and falls a distance of 0.5 m in 1.5 s, calculate: (a) The linear acceleration of the mass. (b) The angular acceleration of the wheel. (c) The tension in the rope. (d) The frictional torque, resisting motion. 5 m 6 kg Start t = 0 80 N t = 0.92 s 3 Teesside University Open Learning (Engineering) © Teesside University 2011 FIG. 2 3. A mass of 0.3 kg is suspended from a spring of stiffness 200 N m–1. If the mass is displaced by 10 mm from its equilibrium position and released, for the resulting vibration, calculate: (a) (i) the frequency of vibration (ii) the maximum velocity of the mass during the vibration (iii) the maximum acceleration of the mass during the vibration (iv) the mass required to produce double the maximum velocity calculated in (ii) using the same spring and initial deflection. (b) Plot a graph of acceleration against displacement (x) (for values of x from x = –10 mm to x = +10 mm) x 0.5 kg Mass of wheel = 3 kg Outside radius of wheel = 300 mm Radius of gyration = 212 mm
Answered Same Day Dec 26, 2021

Solution

Robert answered on Dec 26 2021
111 Votes
Problem 1:
Given:
Mass of the FlyWheel = 3.0 Kg
Mass of suspended block = 0.5 Kg
Radius of Gyration of Flywheel = 212 mm
Outer Radius of the Flywheel = 300 mm
Distance Travelled = 0.5 m
Time required to travel that distance = 1.5 seconds.
Solution:
Force equation acting on the suspended body:
mg – T = ma ---------------------- 1
Force equation acting on the Flywheel:
Torque = Ix(angular acceleration)
TR = Ix(angular acceleration) ---------------------- 2
TR = I(a/R) [ R = Radius of the Flywheel, a = Linear acceleration]
T = mg -ma
(mg-ma)R = I(a/R) = [(MR^2a)/2R]
mg-ma = [(MR^2a)/2R^2]
mg-ma = Ma/2
mg = a(m + M/2)
a = mg/(m+M/2) = Linear Acceleration
This acceleration is the net acceleration of the system when the system is...
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