Ballistic Pendulum Problem: Solving for Bullet and Block Speeds

AI Thread Summary
To solve the ballistic pendulum problem, the conservation of mechanical energy and momentum principles are crucial. The bullet's initial speed can be determined using the conservation of momentum, while the speed of the block after the bullet passes through can be calculated using the potential energy at the maximum height. The kinetic energy of the bullet after passing through the block is found using the formula ½mv², while the potential energy of the block at its peak height is calculated using mgh. The discussion emphasizes the need to correctly identify the types of energy involved and the appropriate formulas to use. Understanding these concepts will lead to the correct calculations for both the bullet's initial speed and the block's speed post-collision.
lando45
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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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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.
 
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?
 
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
 
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.
 
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?
 
Chi Meson said:
OK, you got PE. This is PE at the top. What kind of energy was it at the bottom?

Kinetic energy?
 
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)?
 

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