Solving Force on Rotating Bar at Pivot

In summary, the problem involves a 60-cm-long, 500 g bar rotating in a horizontal plane on an axle, with compressed air passing through the axle and escaping as air jets from holes at the ends of the bar. The jets exert a force on the bar, and using the equations for angular velocity and force, the force of each jet is calculated to be 0.04713N.
  • #1
Jennifer001
22
0

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??
 
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  • #2
Isn't the equation for angular velocity
[tex]\omega=\omega_{0}+\alpha t[/tex]?

I think you're confusing it with
[tex]\phi=\phi_{0}+\omega t+\frac{1}{2}\alpha t^{2}[/tex]
 
  • #3




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.
 

1. What is the definition of force on a rotating bar at pivot?

Force on a rotating bar at pivot refers to the amount of external force acting on a bar that is rotating around a fixed point or pivot. This force can affect the rotation of the bar and can be calculated using principles of rotational dynamics.

2. How is the force on a rotating bar at pivot calculated?

The force on a rotating bar at pivot can be calculated using the equation F = m * r * ω^2, where F is the force, m is the mass of the bar, r is the distance from the pivot to the point where the force is applied, and ω is the angular velocity of the bar.

3. What factors affect the force on a rotating bar at pivot?

The force on a rotating bar at pivot is affected by the mass of the bar, the distance from the pivot, and the angular velocity of the bar. Additionally, the direction and magnitude of the applied force can also impact the force on the bar.

4. How does the force on a rotating bar at pivot affect the rotation of the bar?

The force on a rotating bar at pivot can affect the rotation of the bar by changing its angular velocity. If the force is applied in the direction of the rotation, it can increase the angular velocity and cause the bar to rotate faster. If the force is applied in the opposite direction, it can decrease the angular velocity and cause the bar to rotate slower. Additionally, if the force is applied at a distance from the pivot, it can create a torque that can cause the bar to rotate in a different direction or even come to a stop.

5. How can the force on a rotating bar at pivot be used in real-life applications?

The force on a rotating bar at pivot can be used in various real-life applications, such as in the design of machines and structures that involve rotating components. It can also be used in sports, such as in the rotation of a discus or hammer throw, where the force applied at a distance from the pivot can increase the angular velocity and result in a longer throw. Additionally, understanding the force on a rotating bar at pivot can also be useful in analyzing and predicting the behavior of objects in motion, such as satellites orbiting around a planet.

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