Calculating Max Speed & Acceleration of Pistons in 4-Cylinder Engine

[ibysaiyan]

Homework Statement

The pistons of a 4 cylinder car engine when idling move approx. in SHM with an Amplitude of 50mm and at a frequency of 110Hz.Calculate
*the max speed of the pistons.
*max acceleration of the pistons.

Homework Equations

max velocity = A(omega),max acceleration =A(omega)^2, omega= 2pie/T,T=1/f

The Attempt at a Solution

for the first bit i did:
Ax2pie/T
=>0.05x2(pie)/9.09x10^-3 (from T=1/F)
=> 34.56m/s.
The second bit is simply
acceleration=A(omega)^2
=>0.05 x (34.56)^2
=> 59.71m/s^2
hm.. is this how i am supposed to do it ? :)
Thanks in advance.

 

[alseth]

Your method is fine but you have substituted the wrong value for omega in the second part of the problem. Just correct it and add a minus sign in the formula for acceleration.

 

[ibysaiyan]

ermm i thought for max acceleration the formula was:A(omega)^2 and for acceleration a=-A(OMEGA)^2cos(omega)t... maybe (confused) =/

 

[alseth]

ermm i thought for max acceleration the formula was:A(omega)^2 and for acceleration a=-A(OMEGA)^2cos(omega)t... maybe (confused) =/

Yeah, you are right. In fact, it's the same thing.

Ax2pie/T
=>0.05x2(pie)/9.09x10^-3 (from T=1/F)
=> 34.56m/s.
The second bit is simply
acceleration=A(omega)^2
=>0.05 x (34.56)^2
=> 59.71m/s^2

The thing I wanted to point out was that you substituted the speed you calculated instead of the angular frequency (omega) in that second part of the problem.