Ballistic Pendulum Problem: Solving for Bullet and Block Speeds

In summary: Kinetic energy?yes. what is the formula for KE. Can you find the speed of the block at the bottom (right after the collision with the bullet)?In summary, the problem asks for the speed of the block of wood after the bullet has passed through it, and the initial speed of the bullet. The block of wood has conserved energy, and so the block has the same speed as the bullet.
  • #1
lando45
84
0
How do I go about solving this problem? No diagram is given, so it's a little hard-to-picture in my head, so I drew a basic diagram but it hasn't really helped.

I use a ballistic pendulum. Large block of wood has a mass M2 = 3.000 kg, and the bullet has a mass of m1 = 25 g. In this problem the bullet completely penetrates the wood and emerges with a speed of vf = 40.0 m/s. The wood, as part of a pendulum, swings up to a maximum height of h = 4.0 cm.

Determine the speed of the block of wood after the bullet has passed through it, and the initial speed of the bullet.

Much thanks
 
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  • #2
Conservation of mechanical energy (PE and KE) tells you how fast the block was going after the collision.

Conservation of momnetum tells you how fast the bullet was going before the collision.
 
  • #3
So I should be using ½mv² and mgh? The mass of what though? The bullet or the block of wood? Or both? Also, what does the question mean when it says: "with a speed of vf = 40.0 m/s" - what is vf?
 
  • #4
OK, I worked out the Kinetic Energy of the bullet, having passed through the block, using ½mv², and I got a value of 20J, having converted everything into m and kg. Then I calculated the Potential Energy of the block, using mgh, and I got 1.1172J, but I don't see how this helps me...I thought I need to use theta and sine/cosine to answer this? Or is it all to do with energy? Thanks
 
  • #5
The ballistic pendulum stuff generally works this way:
There is a perfectly inelastic collision between the bullet and the target, and then the swing up has conserved energy.
 
  • #6
lando45 said:
OK, I worked out the Kinetic Energy of the bullet, having passed through the block, using ½mv², and I got a value of 20J, having converted everything into m and kg. Then I calculated the Potential Energy of the block, using mgh, and I got 1.1172J, but I don't see how this helps me...I thought I need to use theta and sine/cosine to answer this? Or is it all to do with energy? Thanks

OK, you got PE. This is PE at the top. What kind of energy was it at the bottom?
 
  • #7
Chi Meson said:
OK, you got PE. This is PE at the top. What kind of energy was it at the bottom?

Kinetic energy?
 
  • #8
yes. what is the formula for KE. Can you fid the speed of the block at the bottom (right after the collision with the bullet)?
 

1. What is the ballistic pendulum problem?

The ballistic pendulum problem is a physics problem that involves a bullet being fired into a hanging block of wood or other material. The goal is to calculate the speed of the bullet and the block after the collision.

2. How do you solve the ballistic pendulum problem?

To solve the ballistic pendulum problem, you need to use conservation of momentum and conservation of energy equations. You will also need to know the mass and height of the block, as well as the mass and speed of the bullet.

3. What are the assumptions made in solving the ballistic pendulum problem?

Some of the assumptions made in solving the ballistic pendulum problem include the assumption that the collision between the bullet and the block is perfectly elastic, meaning there is no loss of energy due to friction or other factors. Additionally, it is assumed that the only forces acting on the system are gravity and the force of the bullet on the block.

4. How accurate is the solution to the ballistic pendulum problem?

The accuracy of the solution to the ballistic pendulum problem depends on the accuracy of the initial measurements and the assumptions made. In real-life situations, there may be additional factors that affect the outcome, such as air resistance or imperfections in the materials used. However, the solution can still provide a good estimate of the bullet and block speeds.

5. What are some real-life applications of the ballistic pendulum problem?

The ballistic pendulum problem has practical applications in forensic science, where it can be used to determine the speed and direction of a bullet based on the damage it causes to a target. It is also used in the design and testing of bulletproof vests and other protective gear. Additionally, the principles involved in solving this problem are important in understanding the dynamics of collisions and impacts in various fields, such as engineering and sports.

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