Bullet Velocity: Calculate Speed of Bullet Before Hitting Wood

In summary, a bullet with mass 3.10×10-2kg is fired and imbeds itself into a block of wood with mass 1.35kg. The block and bullet slide up an incline, assumed to be frictionless, and rise a height of 1.25m before stopping. The final velocity of the block and bullet is 0 and the equation for conservation of energy can be used to find the velocity of the bullet just before it hits the block. The equation used is v_2 = \sqrt{2gy}, where v_2 is the speed of the block and bullet immediately after the collision. The initial velocity of the bullet can then be calculated using the conservation of momentum equation v_
  • #1
am08
44
0
A bullet of mass m= 3.10×10-2kg is fired along an incline and imbeds itself quickly into a block of wood of mass M= 1.35kg. The block and bullet then slide up the incline, assumed frictionless, and rise a height H= 1.25m before stopping. Calculate the speed of the bullet just before it hits the wood.

What equation do I need?

I was thinking mgh = 1.2mv^2 but that wasn't it.
 
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  • #2
am08 said:
I was thinking mgh = 1.2mv^2 but that wasn't it.
That's part of what you need. Conservation of energy applies after the collision.

What applies during the collision?
 
  • #3
am08 said:
AI was thinking mgh = 1.2mv^2 but that wasn't it.

You're nearly there. But you haven't used M, have you?

Try again … :smile:
 
  • #4
Conservation of Momentum.
 
  • #5
So i used v2 = squareroot (2gy) and found the final velocity to be 5 m/s

then i used v1 = (mass bullet + mass block / mass bullet) * v2

is this right? I'm using conservation of momentum..
 
  • #6
Looks good.
 
  • #7
am08 said:
So i used v2 = squareroot (2gy) and found the final velocity to be 5 m/s

then i used v1 = (mass bullet + mass block / mass bullet) * v2

is this right? I'm using conservation of momentum..

I'm not convinced.

Don't forget - the "final velocity" is zero - you're looking for the initial velocity (the velocity of the bullet just before everything happens).

Your "v = √(2gy)" is wrong - the mass that should be on the left is not the same as on the mass on the right, and so you must put them both in.

(btw, if you type alt-v, it prints √ for you)

Try the √2gy equation (conservation of energy) again! :smile:
 
  • #8
tiny-tim said:
Your "v = √(2gy)" is wrong - the mass that should be on the left is not the same as on the mass on the right, and so you must put them both in.
Huh? :confused: (Mass cancels out.)
 
  • #9
Doc Al said:
Huh? :confused: (Mass cancels out.)

No - the inital KE is in the bullet (and the final KE is zero).

The PE involves the block also.
 
  • #10
tiny-tim said:
No - the inital KE is in the bullet (and the final KE is zero).

The PE involves the block also.
Energy is conserved after the collision:

[tex]1/2 (M + m)v_2^2 = (M + m)gy[/tex]

Thus:
[tex]v_2 = \sqrt{2gy}[/tex]
is perfectly correct. (Note that v_2 is the speed of block + bullet immediately after the collision.
 
  • #11
woohooo tiny-tim managed to force the answer out of Doc AI!
 

1. What is bullet velocity and why is it important?

Bullet velocity is the speed at which a bullet travels. It is important because it determines the force and impact of the bullet when it hits a target, and can also affect accuracy and range.

2. How is bullet velocity calculated?

Bullet velocity is typically calculated by measuring the distance the bullet travels over a known time frame. This can be done using specialized equipment such as a chronograph or by using mathematical formulas that take into account factors such as bullet weight, muzzle velocity, and air resistance.

3. What factors can affect bullet velocity?

Several factors can affect bullet velocity, including the type and weight of the bullet, the type of gun and ammunition used, the length of the barrel, and environmental conditions such as temperature and air density.

4. Why is it important to calculate the speed of a bullet before it hits wood?

Calculating the speed of a bullet before it hits wood can provide important information for forensic investigations, such as determining the distance between the shooter and the target, the type of gun used, and the angle at which the bullet entered the wood.

5. Can bullet velocity be used to determine the caliber of a bullet?

While bullet velocity can provide some information about the bullet, it is not a reliable method for determining the caliber. Other factors such as bullet weight and shape, as well as the gun and ammunition used, must also be taken into account.

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