Bullet Impact Speed Calculation: 2.25x10^3 N/m

In summary, a 0.0125 kg bullet with an unknown initial speed strikes a 0.300 kg block attached to a fixed horizontal spring with a spring constant of 2.25 * 10^3 N/m and causes the block to vibrate with an amplitude of 12.4 cm. The speed of the bullet can be determined using the conservation of energy equation, which yields a speed of 10.5 m/s. This may seem slow for a bullet, but it is correct since the only initial energy is the kinetic energy of the bullet and the final energy is the potential and kinetic energy of the block and spring system.
  • #1
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A 0.0125 kg bullet strikes a 0.300 kg block attached to a fixed horizontal spring whose spring constant is 2.25 * 10^3 N/m and sets it into vibration with an amplitude of 12.4 cm. What was the speed of the bullet if the two objects move together after impact?

E = .5 k A2 = .5 m v2
Do I use m = mass of bullet + mass of block, or just the mass of the bullet?
Using the former, I get v = 10.5 m/s. Is this right? It just seems kind of slow for a bullet...
 
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  • #2
This is an energy conservation problem

Initially the only energy is the kinetic energy of the bullet.

Finally, the only energy is the spring energy (potential+kinetic).

Those two energies are the same.
 
  • #3


I would approach this problem by first acknowledging that the given information is not enough to accurately determine the speed of the bullet. The equation provided is used to calculate the kinetic energy of the block after the impact, but does not take into account the energy lost due to friction and other factors.

To accurately calculate the speed of the bullet, we would need to know the initial position and velocity of the block, as well as the coefficient of restitution (a measure of how much energy is lost during the impact) between the bullet and the block.

Without this information, it is not possible to accurately calculate the speed of the bullet. However, based on the given information, a speed of 10.5 m/s does seem reasonable and falls within the typical range for bullet speeds. It is important to note that the speed of a bullet can vary greatly depending on factors such as the type of gun and ammunition used, as well as external factors like air resistance.
 

1. How is bullet impact speed calculated?

The impact speed of a bullet can be calculated using the formula v = √(2E/m), where v is the speed, E is the kinetic energy of the bullet, and m is the mass of the bullet. In this case, the kinetic energy of the bullet is given as 2.25x10^3 N/m.

2. What does the value of 2.25x10^3 N/m represent in bullet impact speed calculation?

The value of 2.25x10^3 N/m represents the kinetic energy of the bullet in joules. This value is used in the formula to calculate the impact speed, which is an important factor in understanding the damage caused by the bullet.

3. How does the mass of the bullet affect its impact speed?

The mass of the bullet is directly proportional to its impact speed. This means that a heavier bullet will have a higher impact speed compared to a lighter bullet, assuming they have the same kinetic energy. This is because the formula for calculating impact speed involves dividing the kinetic energy by the mass of the bullet.

4. Can this formula be used for all types of bullets?

Yes, this formula can be used for all types of bullets as long as the kinetic energy is given in joules and the mass is in kilograms. However, it is important to note that this formula assumes that the bullet is traveling in a vacuum, without any external forces acting on it.

5. How accurate is the calculated impact speed?

The accuracy of the calculated impact speed depends on the accuracy of the given values for kinetic energy and mass. If these values are measured accurately, then the calculated impact speed will also be accurate. However, factors such as air resistance and other external forces can affect the actual impact speed of a bullet in real-life scenarios.

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