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Please answer all part of question 6 with clear explanations and remarks !
Thank you !
QUESTION 6 The device shown in Figure 5 is to be used as part of an automated parcel sorting system. Small packages slide slowly from left to right down the top ramp, before hitting the fast spinning wheel They leave the fast spinning wheel and continue along the bottom counter. In a test, a small package, m, slides until it touches the top of the wheel, Figure 5 Draw a free body diagram for the package, m, when it is located at the top of the fast spinning wheel. (a)

(b) Write out the equations of motion and determine a general equation that shows the required angular velocity of the wheel for the normal force to be zero. (c) Consider the package as it rests on a random position on the wheel (for example the dot in figure 5). Draw a free body diagram for the package at this position, and write out the equations of motion. Using part (c), write a general equation for the wheels angular velocity with the normal force being equal to zero. (d)

2 (e Write out a general equation for the angle at which the body will leave the wheel as a function of the wheel radius and angular velocity. (f) 3m, g-10 me and a-1.7 rad/s. Determine the angle at Given the wheel radius r which the package just loses contact with the wheel. Show all working. (g) With reference to figure 5, knowing that vo-5.1 m/s, e-30, 3 m and g 10m/s, find how far the package travels horizontally before hitting the horizontal bottom counter

These are the short final answers to question 6 , please explain !


Question 6 a) mg COS θ f e 30 ) t0.15 sec2.25 m Question 7 a) ωmi.-3.44 rad/s b) wmax=7.28 rad/s c T-1.039 Nm Question 8 a) b) c)V-4.34 m/s d) X 0.935 m
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Answer #1

Here small package m goes in a circular motion when it travels on spinning wheel. So we can use angular variables to solve such questions

Calculation and work is shown below.

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