Answered: c. Derive the piston instantaneous…

c. Derive the piston instantaneous acceleration as a function of the crank angle. • Piston Acceleration Speed dUp dUp d dt de @= de (a sin(0) [1- 1+ 2DD) 4² cos (0) √R²-sin²(

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

c. Derive the piston instantaneous acceleration as a function of the crank angle.
. Piston Acceleration Speed
dUp dUp d
de
dt dᎾ
- (a sin(0) [1.
+
=
@=
cos(0)
√R²-sin²(
Son ² (1)D) w ²

Expert Solution

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Step 1: Determine the given variables:

VIEW

Step 2: Find the expression for the piston velocity with respect to the crank angle:

VIEW

Step 3: Differentiate the expression with respect to θ:

VIEW

Step 4: Differentiate sin(θ) and apply the chain rule to differentiate further:

VIEW

Step 5: Simplify the expression:

VIEW

Step 6: Combine like terms:

VIEW

Step 7: Cancel out suitable terms from the numerator and denominator:

VIEW

Step 8: Use the chain rule to differentiate the above expression with respect to time (t):

VIEW

Solution

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