   Chapter 13, Problem 23P

Chapter
Section
Textbook Problem

The wheel in the simplified engine of Figure P13.23 has radius A = 0.250 m and rotates with angular frequency ω = 12.0 rad/s. At t = 0, the piston is located at x = A. Calculate the piston’s (a) position, (b) velocity, and (c) acceleration at t = 1.15 s. Figure P13.23

a)

To determine
The position of the piston.

Explanation

Given info: The radius of the wheel A=0.250m . The wheel rotates with angular frequency ω=12.0rads-1 . At t=0 , the piston is located at x=A . t=1.15s .

Explanation:

Since the piston is connected to the rotating wheel, its position is given by,

x=Asin(ωt)

Here,

x is the position of the piston

A is the radius of the reference circle

ω is the angular speed

t is the time taken

Substituting ω=12.0rads-1 , A=0

b)

To determine
The velocity of the piston.

c)

To determine
The acceleration of the piston.

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