What Velocity Must the Bullet Have to Swing a Block to 40 Degrees?

In summary: If so, then you know what the rise in the height of the block when the bullet is embedded in it is. That is what s represents. Can you use that information to solve for the bullet velocity?In summary, the problem involves a bullet of unknown initial velocity striking a wooden block suspended by a string. By using the conservation of energy, the speed of the bullet can be calculated by equating the kinetic energy of the bullet to the potential energy gained by the block after the collision. The rise in height of the block can be calculated using the given angle and length of the string, and solving for the bullet velocity yields an answer of 24.5 m/s. However, it is important to note that this solution
  • #1
Ry122
565
2

Homework Statement


A bullet leaves the muzzle of a rifle at an unknown velocity and strikes a wooden block that is suspended by a piece of string.
If the block swings backwards to make an angle of 40 degrees, at what velocity must have the bullet been traveling when it struck the block?
mass of the bullet and the wood are, respectively, m=0.05 kg and M=2 kg, and the length of the string is L=1 m. Theta = 40 degrees
[PLAIN]http://img810.imageshack.us/img810/5295/bullet.jpg

Homework Equations


The Attempt at a Solution


The block is given kinetic energy equal to the kinetic energy the bullet had.
Since the block experiences no friction, all of this kinetic energy is used up by moving against gravity.
s and f can be determined and so the energy can be calculated
with f x s = energy
Then use (1/2)mv^2 = energy to calculate the speed of the bullet

The problem is that I'm unsure how to calculate s. How can this be done? (s = vertical displacement of the block)
 
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  • #2
Ry122 said:
The block is given kinetic energy equal to the kinetic energy the bullet had.
Incorrect. See below.
Since the block experiences no friction, all of this kinetic energy is used up by moving against gravity.
The block experiences no friction only after the bullet comes to rest inside it. While the bullet is slowing down inside the block there is a lot of friction. So some of the initial kinetic energy of the bullet goes into heat generated by friction.
The problem is that I'm unsure how to calculate s. How can this be done? (s = vertical displacement of the block)
Can you find how fast the bullet+block system is moving after the bullet becomes fully embedded?
 
  • #3
@ kuruman, i think at a high school/ introductory physics level we're allowed to assume that energy is conserved within the bullet-block system.

The solution is simple. It is a mere calculation using the conservation of energy.

0.5*m*v^2 = m*g*h

Theta is given to be 40 degrees. So in order to calculate the rise in the height of the block,
Lcos40 = h
g is a constant. The rest are all given.
working that out you should get
V = 24.5 m/s ( 3sf )
 
  • #4
leucocyte said:
@ kuruman, i think at a high school/ introductory physics level we're allowed to assume that energy is conserved within the bullet-block system.
Absolutely not! You've missed a key point of the exercise.

The solution is simple. It is a mere calculation using the conservation of energy.
Simple, but incorrect. Listen to kuruman!

0.5*m*v^2 = m*g*h

Theta is given to be 40 degrees. So in order to calculate the rise in the height of the block,
Lcos40 = h
g is a constant. The rest are all given.
working that out you should get
V = 24.5 m/s ( 3sf )
Let the OP do their own work please.
 
  • #5
Ry122, do you know what the answer to the question is?
 

FAQ: What Velocity Must the Bullet Have to Swing a Block to 40 Degrees?

1. How does a bullet penetrate a block of wood?

When a bullet hits a block of wood, it transfers its kinetic energy to the wood. This energy causes the wood fibers to break apart and create a hole, allowing the bullet to penetrate the block.

2. What factors affect how deeply a bullet penetrates into wood?

The velocity and mass of the bullet, as well as the type and density of the wood, can all affect the depth of penetration. A faster and heavier bullet will typically penetrate deeper, while a denser wood will provide more resistance and result in less penetration.

3. Can a bullet get stuck in a block of wood?

Yes, a bullet can get stuck in a block of wood depending on the angle and velocity at which it hits the wood. If the bullet is traveling at a low velocity or hits the wood at a shallow angle, it may not have enough energy to fully penetrate the block and can become lodged in the wood.

4. What happens to the bullet after it enters the wood?

After entering the wood, the bullet may continue to travel through the block, lose its momentum and fall to the ground, or get stuck in the wood. It may also fragment or deform upon impact, depending on the type of bullet and the density of the wood.

5. Can a bullet shatter a block of wood?

Yes, a bullet can potentially shatter a block of wood if it has enough kinetic energy and hits the wood at a perpendicular angle. However, the wood's density and type will also play a significant role in determining whether or not it will shatter upon impact.

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