Calculate Marble Velocity at Angle Theta in a Smooth Pipe

[go2cnavy]

These are tough for me. How do I go about setting up an algebraic equation to solve for the velocity of a marble at Angle theta?

Q: A marble spins in a vertical plane around the inside of a smooth, 20--diameter horizontal pipe. The marble's speed at the bottom of the circle is 3.0 m/s. The speed at the top is 2.25 m/s.

The marble's position in the pipe can be specified by an angle theta measured counterclockwise from the bottom of the pipe. Find an algebraic expression for the marble's speed when it is at angle theta . Use numerical values for r, g, and the initial speed, leaving theta as the only symbol in the equation. Your expression should give 3.0 m/s for theta= 0 and 2.25 m/s for theta = 180.

v(theta)=?

 

[go2cnavy]

I know that for angular velocity (w = d angle/dt). But how in the world do we get to Speed?

 

[civil_dude]

If you know the angular velocity and the radius of the pipe, can't you find the speed?

 

[OlderDan]

This is a conservation problem. What is conserved? How do you know?

 

[go2cnavy]

Got it thanks.

V(theta)^2=V(top)^2+2g(1-COS(theta))

Right?

 

[OlderDan]

Got it thanks.

V(theta)^2=V(top)^2+2g(1-COS(theta))

Right?

You are probably on the right track, but look at the dimensions in your answer. Not possible.