Upcoming Physics Olympiad Test

[physics517]

Homework Statement

Abullet of mass m strikes a pendulum of mass M suspended from a pivot by a string of length L with a horizontal velocity v0. The collision is perfectly INelastic and the bullet sticks to the bob. Find the minimum velocity v0 such that the bob (with the bullet inside) completes a sircular vertical loop

Homework Equations

p=mv

KE=1/2 mv^2

PE=mgh

The Attempt at a Solution

mvo=(m+M)vf

mg(2L)=1/2 m vf^2 --------- This is the Vf needed to comlete one whole loop (also i think this is where I am missing something)

vf=2 sqrt(Lg)

and so the answer i got was vo= ((m+M)2 sqrt(Lg)) / m

but the ACTUAL asnwer is vo= ((m+M) sqrt(5Lg)) / m

 

[gneill]

What equations are relevant? Where's your attempt at a solution?

By the way, your post title is pretty unspecific about the actual problem content.

 

[Fightfish]

mg(2L)=1/2 m vf^2 --------- This is the Vf needed to comlete one whole loop (also i think this is where I am missing something)

Indeed. That is NOT the velocity needed to complete one loop, that is the minimum velocity required for the bob (and bullet) to just reach the top of the circular loop. For the bob and bullet to complete a circular loop, it cannot have zero velocity at the top of the loop! There is a minimum velocity that it must possesses - think back to your concepts of circular motion.

 

[physics517]

Lol I shouldve drew a diagram.

so up top its F+mg=mv^2/r and the F (tension) cancels out since we're trying to find minimum speed. so v=sqrt(gr) and if we go back to my original work equation

it should be 1/2 m vf^2 = mgh + 1/2 m vtop ^2

then you find the Vf and then plug that into the momentum equation

Thanks so much guys!

 

[rwisz]

I would first commend the student for their attempt at solving the problem and using the correct equations. However, there seems to be a mistake in the calculation of the final velocity needed to complete the circular loop. The correct expression for the final velocity should be vf=sqrt(5Lg), which can be derived from the conservation of energy equation. Therefore, the minimum velocity v0 should be vo= ((m+M)sqrt(5Lg))/m. I would also suggest the student to double check their calculations and equations to ensure accuracy in their solution. Additionally, it would be helpful to explain the reasoning behind the use of the conservation of energy equation in this problem, as it is a key concept in solving many physics problems. Overall, the student has shown a good understanding of the concepts involved in this problem and with some minor adjustments in their calculations, they can arrive at the correct solution.