# Linear momentum problem (ballistic pendulum)

• Dennis Heerlein
In summary, the ballistic pendulum is a device used to measure the muzzle speed of a bullet. It consists of a wooden block suspended from a horizontal support by cords, with a bullet shot into the block resulting in a perfectly inelastic impact. The maximum height and horizontal displacement of the block after impact are denoted by y and x, respectively. To determine the speed of the bullet, the equation (1/2)(m)v2 = (m + M)(g)(y) is used, where m, M, g, and y represent the mass and gravitational acceleration of the block, and the maximum height. This equation can also be rewritten as v = √[(2)(g)(m + M)(y)/m
Dennis Heerlein

## Homework Statement

A ballistic pendulum is a device that may be used to measure the muzzle speed of a bullet. It is composed of a wooden block suspended from a horizontal support by cords attached at each end. A bullet is shot into the block, and as a result of the perfectly inelastic impact, the block swings upward. Consider a bullet (mass m) with velocity v as it enters the block (mass M). The length of the cords supporting the block each have length L. The maximum height to which the block swings upward after impact is denoted by y, and the maximum horizontal displacement is denoted by x.

a) In terms of m, M, g and y, determine the speed of the bullet.

mgh=1/2 m v2

## The Attempt at a Solution

(1/2)(m)v2 = (m + M)(g)(y)
v =sqroot { [(2)(g)(m + M)(y)]/m }

The real solution states that one must find the initial velocity of the bullet-block system, and then use this equation. Why can I not just use the initial velocity of the bullet? The real final answer is what I have, except the (m+M)/m is outside the sqroot.

Dennis Heerlein said:

## Homework Statement

A ballistic pendulum is a device that may be used to measure the muzzle speed of a bullet. It is composed of a wooden block suspended from a horizontal support by cords attached at each end. A bullet is shot into the block, and as a result of the perfectly inelastic impact, the block swings upward. Consider a bullet (mass m) with velocity v as it enters the block (mass M). The length of the cords supporting the block each have length L. The maximum height to which the block swings upward after impact is denoted by y, and the maximum horizontal displacement is denoted by x.

a) In terms of m, M, g and y, determine the speed of the bullet.

mgh=1/2 m v2

## The Attempt at a Solution

(1/2)(m)v2 = (m + M)(g)(y)
v =sqroot { [(2)(g)(m + M)(y)]/m }

The real solution states that one must find the initial velocity of the bullet-block system, and then use this equation. Why can I not just use the initial velocity of the bullet? The real final answer is what I have, except the (m+M)/m is outside the sqroot.

What can you say about energy in an inelastic collision?

Dennis Heerlein
PeroK said:
What can you say about energy in an inelastic collision?
:( I stared at that for 30 minutes, thinking I was using conservation of momentum and not conservation of energy. Thank you for reading that block of text and helping me though! Much appreaciated

## 1. What is a ballistic pendulum?

A ballistic pendulum is a device used to measure the velocity of a projectile. It consists of a pendulum with a bullet or other projectile suspended from it. When the projectile is fired into the pendulum, it becomes embedded in the pendulum and causes it to swing. The height of the swing can be used to calculate the projectile's initial velocity.

## 2. How does a ballistic pendulum work?

When the projectile is fired into the pendulum, it transfers its momentum to the pendulum. The pendulum then swings up to a certain height based on the amount of momentum it received. By measuring the height of the swing, the initial velocity of the projectile can be calculated using the principle of conservation of momentum.

## 3. What is the principle of conservation of momentum?

The principle of conservation of momentum states that the total momentum of a closed system remains constant. In the case of a ballistic pendulum, the system is considered closed because no external forces act on it (neglecting air resistance). This means that the total momentum before and after the collision between the projectile and pendulum is the same.

## 4. What factors can affect the accuracy of a ballistic pendulum experiment?

There are several factors that can affect the accuracy of a ballistic pendulum experiment. These include friction, air resistance, and the accuracy of measurements. Friction can slow down the pendulum's swing, resulting in a lower measured height. Air resistance can also slow down the projectile, leading to an inaccurate measurement of its velocity. Additionally, any errors in measuring the height of the pendulum swing can affect the accuracy of the results.

## 5. How is the momentum of the projectile calculated in a ballistic pendulum experiment?

The momentum of the projectile can be calculated using the equation p = m1v1, where m1 is the mass of the projectile and v1 is its initial velocity. This can be solved for v1 by rearranging the equation to v1 = p/m1. The momentum of the projectile is equal to the momentum of the pendulum after the collision, so this value can be used in the calculation.

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