As the wheel of radius r cm in Figure 21 rotates, the rod of length L attached

Question:

As the wheel of radius r cm in Figure 21 rotates, the rod of length L attached at point P drives a piston back and forth in a straight line. Let x be the distance from the origin to point Q at the end of the rod, as shown in the figure.

L X Piston moves back and forth Q

(a) Use the Pythagorean Theorem to show that

(b) Differentiate Eq. (1) with respect to t to prove that

Eq.(1)

dh dt || X -0.8- h

2(x-r cos 8) dx dt de + r sin 0- dt do + 2r sin 0 cos 0 = 0

(c) Calculate the speed of the piston when θ = π/2, assuming that r = 10 cm, L = 30 cm, and the wheel rotates at 4 revolutions per minute.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Nov 11, 2023 08:24 AM

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As the wheel of radius r cm in Figure 21 rotates, the rod of length L attached

Question:

L X Piston moves back and forth Q

Step by Step Answer:

a The distance formula gives Thus L xr cos 0 r sin0 Note that L the length of t...View the full answer

Calculus

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