Solve Harmonic Problem: Find Bullet Speed Before Impact

[ceeforcynthia]

Hi! I've been working on this problem for a while, subtracting this and that.. but i can't get the answer which is 557m/s. Help would be greatly appreciated! Thanks in advance ><

1. A 25.0g bullet strikes a .600kg block attached to a fixed horizontal spring whose spring constant is 6.70x10^3 and sets it into vibration with an amplitude of 21.5cm. What is the speed of the bullet before impact if the two objects move together after impact?


2. V=A$$\sqrt{k/m}$$



3. I used the equation above, adding the masses together (.625kg). I got the velocity to be 22.26m/s... but now i can't figure out how to get the speed of the bullet.

 

[turdferguson]

conservation of momentum

 

[ogb p]

Hi there! It looks like you are working on a harmonic problem involving a bullet and a block attached to a spring. This is a great question and I'm happy to help you solve it.

To find the speed of the bullet before impact, we can use the conservation of momentum principle. This principle states that the total momentum before a collision is equal to the total momentum after the collision.

In this case, the bullet and the block are moving together after impact, so their total momentum before and after the collision is the same. We can write this as:

m_bullet * v_bullet = (m_bullet + m_block) * v_after

where m_bullet is the mass of the bullet, v_bullet is its initial velocity, m_block is the mass of the block, and v_after is the velocity of the bullet and block together after the collision.

We know the mass of the bullet is 25.0g, or 0.025kg, and the mass of the block is 0.600kg. We also know the velocity after impact is the same as the velocity of the block when it is set into vibration by the spring. We can use the equation you mentioned, V=A\sqrt{k/m}, to find this velocity.

Substituting in the values we have, we get:

0.025kg * v_bullet = (0.025kg + 0.600kg) * 0.215m * √(6.70x10^3 N/m / 0.625kg)

Solving for v_bullet, we get a speed of 557m/s, which matches the answer you were given. So it looks like you were on the right track!

I hope this helps and please let me know if you have any other questions. Keep up the good work!