# Bullet and Block Circular Problem

• matt-83
In summary, the conversation is about a problem in the 2008 F=ma past Olympiad exam involving a bullet colliding with a pendulum and finding the minimum velocity for the pendulum to complete a vertical loop. The conversation includes equations and attempts at solving the problem, but the correct answer is still unknown. The summary also mentions the need to equate the centripetal force to the weight of the block to find the velocity at the top for minimum tension.
matt-83

## Homework Statement

I am going through past Olympiad qualifying exams as practice for this year's test. I came upon the following problem in the 2008 F=ma and continue to come up with the wrong answer. I keep coming up with C and that is not the answer provided in the answer key.

22. A bullet of mass m1 strikes a pendulum of mass m2 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 circular
vertical loop.
(a) 2√Lg
(b) √5Lg
(c) (m1 + m2)2√Lg/m1
(d) (m1 − m2)√Lg/m2
(e) (m1 + m2)√5Lg/m1

m1v1= (m1+m2)v2
1/2 mv ^2 = mgh

## The Attempt at a Solution

m1v1 = (m1+m2)v2
v2 = (m1v1)/(m1+m2)

So the kinetic energy of the block should be:
1/2 (m1+m2)v2^2
Then I set the initial kinetic energy of the block equal to the potential energy it would have at height 2L.

1/2 (m1+m2)v2^2 = 2L(m1+m2)g

Since v2 = (m1v1)/(m1+m2):

1/2(m1+m2)*((m1v1)/(m1+m2))^2 = 2L(m1+m2)g

m1+m2 should cancel:

((m1v1)/(m1+m2))^2 = 4Lg

(m1v1)^2 / (m1+m2) ^2 = 4Lg

m1 ^2 * v1 ^ 2 = 4Lg / ((m1+m2) ^2)

Take the Square Root of the whole thing:

m1 * v1 = 2sqrt(Lg)/(m1+m2)

SO my answer is (c) (m1 + m2)2√Lg/m1, which is apparently incorrect.

If someone could help me correct this that would be great.

Thanks.

Then I set the initial kinetic energy of the block equal to the potential energy it would have at height 2L.
At the hight 2L the block has kinetic energy as well as the potential velocity.
To find the velocity at the top for minimum tension( = 0), equate the centripetal force to the weight of the block.

Last edited:

Dear student,

Thank you for sharing your work and thought process for this problem. It seems like you have approached the problem correctly and have used the appropriate equations. However, there may be a small error in your calculations. Let's take a closer look at your final equation:

m1 * v1 = 2sqrt(Lg)/(m1+m2)

The left side of the equation is correct, but the right side seems to be missing a square root. It should be:

m1 * v1 = 2sqrt(Lg)/√(m1+m2)

Therefore, your final answer should be (c) (m1 + m2)√Lg/√(m1+m2), which matches with the correct answer given in the answer key.

Keep up the good work and good luck on your upcoming test!

## 1. What is the Bullet and Block Circular Problem?

The Bullet and Block Circular Problem is a physics problem that involves a bullet being fired horizontally at a block that is hanging from a string. The goal is to determine the minimum velocity of the bullet needed to cause the block to make a full circle around the pivot point without the string breaking.

## 2. What are the key factors that affect the solution to this problem?

The key factors that affect the solution to the Bullet and Block Circular Problem are the mass of the bullet and the block, the length and strength of the string, and the force of gravity.

## 3. How is this problem solved?

This problem is typically solved using the principles of conservation of energy and centripetal force. By equating the kinetic energy of the bullet with the potential energy of the block-string system, and using the equation for centripetal force, the minimum velocity of the bullet can be calculated.

## 4. What are the real-life applications of this problem?

The Bullet and Block Circular Problem has applications in ballistics, where it can be used to determine the minimum velocity needed for a bullet to penetrate a certain material. It also has applications in engineering, where it can be used to design structures and machines that involve circular motion.

## 5. Are there any variations of this problem?

Yes, there are variations of the Bullet and Block Circular Problem that involve different scenarios, such as a hanging weight instead of a block, or a bullet being fired at an angle instead of horizontally. These variations may require different equations and approaches to solve.

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