How Fast Must a Bullet Travel to Swing a Pendulum Bob Through a Complete Circle?

[jigs90]

Homework Statement

A bullet of mass .0179kg (m) and speed v passes completely through a pendulum bob of mass 1.3kg (M). The bullet emerges with a speed of v/2. The pendulum bob is suspended by a stiff rod of length 1.08m (L) and negligible mass. What is the minimum value of v such that the pundulum bob will barely swing through a complete vertical circle?

Suppose that the pendulum bob is suspended from a light flexible cord instead of a stiff rod. Now what is the minimum value such that the pendulum bob will swing through a complete vertical circle? Answer in m/s

Homework Equations

1/2 mv^2 = mgh

m1v1 + m2v2 = m'v' + m''v''

The Attempt at a Solution

I already solved the first question and got it right. I used Energy conservation and momentum conservation equations to solve and got and answer of 945.0944 m/s.

The equation that I simplified down to to get my answer for question one was 4M/m(sqrt gl)

I am having a big struggle with the second part. I don't know what effect the flexible string will have on the equation. I know that when it reaches the top of the circle, it will have slack and want to fall back down, so the velocity has to be faster, but I don't know how to solve for it.

 

[Doc Al]

I know that when it reaches the top of the circle, it will have slack and want to fall back down, so the velocity has to be faster, but I don't know how to solve for it.

You are on the right track. In order to make it around the top of the circle, the cord must have some tension.

Analyze the forces acting on the bob at the top of the circle. Apply Newton's 2nd law to figure out the minimum speed where the tension in the cord just goes to zero. Hint: The motion is circular.

 

[jigs90]

Analyze the forces acting on the bob at the top of the circle. Apply Newton's 2nd law to figure out the minimum speed where the tension in the cord just goes to zero. Hint: The motion is circular.

So would it just change the equation to 4M/m (sqrt gl) = v^2/r
where r is the length of the rod, because that would be the radius... is that right?

 

[Doc Al]

So would it just change the equation to 4M/m (sqrt gl) = v^2/r
where r is the length of the rod, because that would be the radius... is that right?

How can it be? The units don't match!

 

[jigs90]

How can it be? The units don't match!

See, this is where I am confused. I just don't know what to do. I thought that since it was circular motion, you would just convert the velocity to circular motion velocity. I am so confused,

 

[Doc Al]

Try what I suggested in post #2.