# Bullet is fired and hits a block. find KE and Speed?

• physics1007
In summary, the bullet has a kinetic energy of .5mv^2-.5mv0^2 after it is embedded in the block. The block and the bullet then slide across the surface with a speed of 1000 m/s.
physics1007
A 2.0-kg pistol fires a 1.0-kg bullet with a muzzle speed of 1000 m/s. The bullet then strikes a 10-kg wooden block resting on a horizontal frictionless surface. The block and the embedded bullet then slide across the surface.
A) what is the kinetic energy of the bullet as it travels toward the block?
B) what is the speed of the "bullet+block" system immediately afer the bullet is embedded in the block?

I have the KE=.5mv^2-.5mv0^2 equation and substituted my numbers and am unsure how to solve part B. Also could someone explain part a for me. Thanks.

To determine the velocity of the system in part B keep in mind that momentum will be conserved. Muzzle velocity is the speed of the bullet relative to the gun, the gun shoots the bullet and recoils so the velocity of the bullet in the frame of reference of the block will be lower than 1000 m/s. Again, momentum will be conserved after the gun shoots the bullet.

^I don't think they want you to go that deep into it. This is a simple inelastic collision in which momentum is conserved. The mass of the system increases, so what happens to the velocity?

Some textbooks classify this type of a problem as a perfectly inelastic collision. For this type of collision, two objects, intially separate, collide and stick together. The momentum of the system is conserved, but the kinetic energy of the system isn't. In fact, it can't be conserved for such a scenario, so energy conservation won't help.

The last part of your question says, "The block and the embedded bullet then slide across the surface". Seems that the new system is the sum of the masses of the block and the bullet. Momentum conservation says the initial momentum of the system should be equal to the final momentum of the system.

Simply equate your initial and final momentums and solve for the final velocity of the system as a whole.

## 1. What is the equation for calculating kinetic energy?

The equation for calculating kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

## 2. How do you determine the speed of an object using its kinetic energy?

To determine the speed of an object using its kinetic energy, you can rearrange the kinetic energy equation to solve for v. The equation becomes v = √(2 * KE / m).

## 3. What is the unit of measurement for kinetic energy?

The unit of measurement for kinetic energy is joules (J).

## 4. How does the mass of the object affect its kinetic energy and speed?

The mass of an object directly affects its kinetic energy and speed. The greater the mass, the greater the kinetic energy and speed will be, assuming the velocity remains constant.

## 5. Can you calculate the kinetic energy and speed of the bullet if you know the mass and velocity of the block it hit?

Yes, you can calculate the kinetic energy and speed of the bullet if you know the mass and velocity of the block it hit. You can use the conservation of momentum equation, which states that the momentum of the bullet before impact is equal to the momentum of the bullet and block after impact. By rearranging this equation and substituting in the mass and velocity of the block, you can solve for the velocity of the bullet, which can then be used to calculate its kinetic energy and speed using the equations mentioned in the previous questions.

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