How to Find the Speed of a Bullet at Impact with a Block
What was the speed of the bullet at impact with the block?
How can we determine the velocity of the bullet when it impacts a block?
Steps to Find the Speed of the Bullet at Impact:
By following these steps, you can determine the speed of the bullet at impact with the block:
1. Calculate the initial velocity of the bullet:The wooden block is initially at rest, so the initial velocity of the bullet is zero.
2. Calculate the change in potential energy of the spring:Use the formula ΔPE = (1/2)kx^2 with the given spring constant and compression of the spring.
3. Calculate the kinetic energy of the bullet-block system at impact:Use the formula KE = (1/2)mv^2 with the combined mass of the bullet-block system.
4. Set the change in potential energy equal to the kinetic energy to find the velocity:Equating the two energies will give you the velocity of the bullet at impact.
The speed of the bullet at impact with the block can be determined by using the principles of conservation of momentum and energy. First, let's identify the relevant information given in the question:
- Mass of the bullet: 12.0 g (or 0.012 kg)
- Mass of the wooden block: 104 × 10^(-9) kg
- Spring constant: 148 N/m
- Compression of the spring: 76.0 cm (or 0.76 m)
Now, let's go through the steps to find the speed of the bullet at impact:
1. Calculate the initial velocity of the bullet:- The wooden block is initially at rest, so the initial velocity of the bullet is also the velocity of the bullet-block system.
- We can use the principle of conservation of momentum to find the initial velocity of the bullet.
- The momentum before the collision is zero because the block is initially at rest.
- The momentum after the collision is given by the mass of the bullet-block system multiplied by the final velocity of the bullet.
- Therefore, the initial velocity of the bullet is zero.
2. Calculate the change in potential energy of the spring:- The compression of the spring is 0.76 m.
- The change in potential energy of the spring can be calculated using the formula: ΔPE = (1/2)kx^2, where k is the spring constant and x is the compression of the spring.
- Substituting the given values, we get: ΔPE = (1/2)(148 N/m)(0.76 m)^2.
3. Calculate the kinetic energy of the bullet-block system at impact:- The final kinetic energy of the bullet-block system can be calculated using the formula: KE = (1/2)mv^2, where m is the mass of the bullet-block system and v is the velocity of the bullet at impact.
- The mass of the bullet-block system is the sum of the mass of the bullet and the mass of the wooden block.
- Substituting the given values, we get: KE = (1/2)(0.012 kg + 104 × 10^(-9) kg)v^2.
4. Set the change in potential energy equal to the kinetic energy to find the velocity:- Equating the change in potential energy of the spring to the kinetic energy of the bullet-block system, we get: (1/2)(148 N/m)(0.76 m)^2 = (1/2)(0.012 kg + 104 × 10^(-9) kg)v^2.
- Simplifying the equation and solving for v, we find the velocity of the bullet at impact.
By following these steps, you can find the speed of the bullet at impact with the block.