How Does a Frictionless Surface Affect Bullet Penetration Depth?

[Oerg]

Homework Statement

A 7.00g bullet, when fired from a gun into a 1:00-kg block of wood held
in a vise, penetrates the block to a depth of 8.00 cm. This block of wood
is placed on a frictionless horizontal surface, and a second 7.00g bullet is
fired from the gun into the block. To what depth will the bullet penetrate
the block in this case?

Homework Equations

The Attempt at a Solution

It looks deceptively simple, but I thought the answer was the same at 8 cm. I think it is wrong? Am I?

 

[LowlyPion]

Homework Statement

A 7.00g bullet, when fired from a gun into a 1:00-kg block of wood held
in a vise, penetrates the block to a depth of 8.00 cm. This block of wood
is placed on a frictionless horizontal surface, and a second 7.00g bullet is
fired from the gun into the block. To what depth will the bullet penetrate
the block in this case?

Homework Equations

The Attempt at a Solution

It looks deceptively simple, but I thought the answer was the same at 8 cm. I think it is wrong? Am I?

Yes, you are wrong.

In the first case all of the Kinetic Energy is absorbed in the block decelerating the bullet.

In the second case since there is no friction your kinetic energy will go into moving the block AND being stopped within the wooden block.

You know from the first case that the stopping power of the wood in terms of the velocity of the bullet.

If you construct your equations to conserve Kinetic Energy - including the deceleration times mass times the unknown distance - and Momentum conservation, you should expect to be able to solve for the depth in the free moving block.

 

[baba89]

I can confirm that the answer is indeed not the same at 8 cm. When a bullet is fired at a block, the depth of penetration depends on various factors such as the velocity of the bullet, the density and composition of the block, and the surface area of impact. In this case, we have all the necessary information to calculate the depth of penetration for the second bullet.

Based on the given information, we can assume that the second bullet will have the same mass and velocity as the first bullet. However, the block now has a hole from the first bullet, which may affect the second bullet's penetration depth. Additionally, the block is now resting on a frictionless surface, which may also impact the bullet's penetration.

To accurately calculate the depth of penetration, we would need to consider the conservation of momentum and energy, as well as the forces acting on the bullet and the block. We would also need to take into account the deformation of the block and the bullet upon impact.

In conclusion, the depth of penetration for the second bullet cannot be determined without further information and calculations. It is not safe to assume that the depth will be the same as the first bullet. As scientists, we must always consider all factors and use scientific principles to accurately predict and explain phenomena.