Ballistic pendulum, finding final height

In summary: The ball will go over the top of the pendulum. In summary, the ball will go over the top of the pendulum.
  • #1
jorcrobe
12
0

Homework Statement


t8qkxh.jpg


The Attempt at a Solution



I used conservation of momentum for the initial velocity of mass 2, and conservation of mechanical energy for the movement from rest to highest position, KE=PE.

The answer that I received is selected in the screenshot. However, when the calculations were completed, I received a value of 1.81m... Which is longer than the string. Does anyone spot my problem? Thank you.
 
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  • #2
Explain why KE=PE at the highest position.
 
  • #3
So, the KE is not being conserved as PE? I see that there is also a horizontal displacement.
 
  • #4
Forget what I said, I misread/misunderstood your explanation. Yes, energy is conserved here.

When you are calculating h from the potential energy equation, what does h represent?
 
  • #5
Ericv_91 said:
Forget what I said, I misread/misunderstood your explanation. Yes, energy is conserved here.

When you are calculating h from the potential energy equation, what does h represent?

The distance from the x axis, y=0.
 
  • #6
Right. y=0, which is the position where the ball is hanging, to the position where the ball is at a max height. One would assume that to create an equation relating this height to the distance between the ball and the ceiling, you would need to have the variable L somewhere in the equation you choose. Right?
 
  • #7
Ericv_91 said:
Right. y=0, which is the position where the ball is hanging, to the position where the ball is at a max height. One would assume that to create an equation relating this height to the distance between the ball and the ceiling, you would need to have the variable L somewhere in the equation you choose. Right?

Well, I used the first equation, and I am receiving a negative number.

Why is it that when I solved for h, it was a number greater than the maximum height, L?

I'm very sorry, I had never taken physics before this course.
 
  • #8
jorcrobe said:

Homework Statement


t8qkxh.jpg


The Attempt at a Solution



I used conservation of momentum for the initial velocity of mass 2, and conservation of mechanical energy for the movement from rest to highest position, KE=PE.

The answer that I received is selected in the screenshot. However, when the calculations were completed, I received a value of 1.81m... Which is longer than the string. Does anyone spot my problem? Thank you.

When you say "The answer I received", do you mean that you were given this as a correct answer, or that it is the answer you obtained by working the problem? The reason that I ask is that to me the selected option doesn't appear to be a correct answer for the given problem.

If the change of elevation of the second ball, as computed from the "randomized variables" happens to be greater than the length of string, what can you conclude will happen? What will be the minimum separation of ceiling and ball?
 
  • #9
Unless I've made a terrible mistake in my calculations, it seems as though either the question gave you a wrong number for the length of the string, or somehow the ball will go above the height of the pendulum, even though there is a ceiling in the way.
 

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 bob (a small weight) attached to it. When a projectile hits the bob, it causes the pendulum to swing, and the height of the pendulum's swing can be used to calculate the projectile's velocity.

2. How does a ballistic pendulum work?

A ballistic pendulum works by converting the kinetic energy of a projectile into potential energy of a swinging pendulum. The equation used to calculate the projectile's velocity is based on the conservation of energy, where the initial kinetic energy of the projectile is equal to the final potential energy of the pendulum.

3. What is the formula for finding the final height of a ballistic pendulum?

The formula for finding the final height of a ballistic pendulum is: h = (m + M) * v2 / (M * g), where h is the final height, m is the mass of the projectile, M is the mass of the pendulum, v is the velocity of the projectile, and g is the acceleration due to gravity (9.8 m/s2).

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

The accuracy of a ballistic pendulum can be affected by various factors, such as air resistance, friction, the alignment of the pendulum, and the precision of the measurements. Other factors, such as the elasticity of the materials used and the angle of the pendulum's swing, can also impact the accuracy of the results.

5. What are some real-world applications of a ballistic pendulum?

A ballistic pendulum has various real-world applications, including measuring the muzzle velocity of firearms, testing the performance of ammunition, and determining the force of impact in collisions. It has also been used in laboratory experiments to study the conservation of energy and momentum in projectile motion.

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