Solving Force on Rotating Bar at Pivot

[Jennifer001]

Homework Statement

A 60-cm-long, 500 g bar rotates in a horizontal plane on an axle that passes through the center of the bar. Compressed air is fed in through the axle, passes through a small hole down the length of the bar, and escapes as air jets from holes at the ends of the bar. The jets are perpendicular to the bar's axis. Starting from rest, the bar spins up to an angular velocity of 150 rpm at the end of 10 s.

How much force does each jet of escaping air exert on the bar?

Homework Equations

w1=w0t+1/2alpha(t^2)
f=ma
a=r(alpha)

The Attempt at a Solution

change velocity into rad/s

150rpm=15.71rad/s

F=ma
a=r(alpha)

so i subbed in a into the force equation

F=m(r(alpha))
and i sub in the velocities to find alpha

w1=1/2(alpha)t^2
15.71=1/2(alpha)(10)^2

alpha=0.3142

sub all the known #s into F=mr(alpha)
F=.5(.3)(.3142)
F=0.04713N

what did i do wrong??

 

[bowma166]

Isn't the equation for angular velocity
$$\omega=\omega_{0}+\alpha t$$?

I think you're confusing it with
$$\phi=\phi_{0}+\omega t+\frac{1}{2}\alpha t^{2}$$

 

[thomate1]

Your attempt at the solution looks correct. However, it is important to note that the force calculated in this problem is the net force on the bar, not the force exerted by each individual jet of air. This is because the air jets are acting in opposite directions, canceling each other out. Therefore, the force calculated is the total force exerted by all the jets combined. Additionally, it would be helpful to include units in your calculations and final answer. Overall, your approach and calculations seem correct, but it is important to clarify the type of force being calculated in this problem.