A 13 g bullet traveling 235 m/s penetrates a 2.0 kg block of wood and emerges going 171 m/s. If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?
in m/s
To find out how fast the block of wood moves after the bullet emerges, you can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object can be calculated by multiplying its mass by its velocity.
The momentum of the bullet before the collision is given by:
Momentum1 = mass of the bullet * velocity of the bullet = 13 g * 235 m/s
The momentum of the bullet after the collision is given by:
Momentum2 = mass of the bullet * velocity of the bullet = 13 g * 171 m/s
The momentum of the block of wood after the collision is given by:
Momentum3 = mass of the block of wood * velocity of the block of wood
Since the block of wood is initially at rest (velocity = 0 m/s), the momentum before the collision is 0.
Using the conservation of momentum equation, we can set up the following equation:
Momentum1 + 0 = 0 + Momentum2 + Momentum3
Substituting the values into the equation, we have:
(13 g * 235 m/s) = 0 + (13 g * 171 m/s) + (2.0 kg * velocity of the block of wood)
We can now solve for the velocity of the block of wood after the bullet emerges.
First, convert the mass of the bullet from grams to kilograms:
13 g = 13 * 10^-3 kg
Now, rearrange the equation to solve for the velocity of the block of wood:
(13 * 10^-3 kg * 235 m/s) = (13 * 10^-3 kg * 171 m/s) + (2.0 kg * velocity of the block of wood)
Now, solve the equation for the velocity of the block of wood:
(13 * 10^-3 * 235) - (13 * 10^-3 * 171) = 2.0 * velocity of the block of wood
Simplify the equation:
(13 * 10^-3 * 235) - (13 * 10^-3 * 171) = 2.0 * velocity of the block of wood
Finally, divide both sides of the equation by 2.0 to solve for the velocity of the block of wood:
velocity of the block of wood = [(13 * 10^-3 * 235) - (13 * 10^-3 * 171)] / 2.0
Evaluating the expression, the velocity of the block of wood after the bullet emerges is approximately 196.6 m/s.