(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Diagram from picture attached

R= 200 + 50sin (2pi nt), n=2

R= 200+ 50sin(4pi*t) mm

ThetaDot = 120 rev/minute

= 12.566 rad/s

Gamma(Y) = 30 degrees

Calculate acceleration when velocity is max

2. Relevant equations

a_{r}= r_{Dotdot}- r*(theta_{Dot})^2

a_{Theta}= r*theta_{Dotdot}+ 2*r_{Dot}*theta_{Dot}

a_{z}= z_{Dotdot}

3. The attempt at a solution

At max velocity, cos(4pi*t) = 1

so t=0, 0.25, or 0.5

so sin(4pi*t) will always = 0

Resolve R to get the radius at max velocity

r = Rsin(theta)

= (0.2+ 0.05sin(4pi*t)) * sin 30 , sin(4pi*t) = 0

=0.2 * sin 30 = 0.1 m

Differentiate R and we will get oscillation velocity

dR/dt= 0.2pi*cos(4pi*t)

Resolve the velocity to get V_{r}

V_{r}= [0.2pi*cos(4pi*t)] * sin 30

=0.1pi*cos(4pi*t)

= 0.1pi

Differentiate dR/dt would get the oscillation acceleration

d^{2}R/dt^{2}= -0.8*pi^2*sin(4pi*t)

at max velocity, -0.8*pi^2*sin(4pi*t) = 0

So all there is left is a_{Theta}

a_{Theta}= r*theta_{Dotdot}+ 2*r_{Dot}*theta_{Dot}

= 0 + 2 * (0.1pi) * 12.566

= 7.895

a of ball = a_{Theta}

=7.895 m/s^2

But the real answer is 17.66!! I asked my friends, my senior, and even my TUTOR cant answer the question! This is just an exercise, not an assignment.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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