A bullet with a mass of 55 grams moving with a speed of 100 m/s slams into and wedges in a 1.9 kilogram block of wood supported by a string initially at rest. Which one, conservation of energy or conservation of momentum, can be applied to this situation? Why?
I think it's conservation of momentum because kinetic energy is not conserved in inelastic collisions. Correct?
Also, how high does the block swing after being hit by the bullet?
Actually, you can use the conservation of momentum first to find the initial velocity of the bullet-block system, and then you can plug that velocity into 1/2mv^2=mgh and solve for the height that the block swings, which gives a value of 0.403 m.
Correct?
Yes, that is exactly how to do the problem.
You are also correct that mechanical energy is not conserved.
Eureka!
You are correct! In this situation, conservation of momentum is the principle that can be applied.
Conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided there are no external forces acting on the system. In this case, we have an inelastic collision between the bullet and the block of wood.
During an inelastic collision, the two objects stick together after the collision and move as a single system. As a result, kinetic energy is not conserved. Instead, some of the initial kinetic energy is lost in the form of heat, sound, or deformation of the objects.
However, momentum is still conserved, which means the total momentum of the bullet and the block of wood before the collision must be equal to the total momentum after the collision. This is because there are no external forces acting on the system, so the total momentum remains constant.
To calculate the momentum before and after the collision, you need to know the masses and velocities of the objects involved. In this case, the mass of the bullet is given as 55 grams (0.055 kg) and its velocity as 100 m/s. The mass of the block of wood is given as 1.9 kilograms.
To find the momentum before the collision, you multiply the mass of the bullet by its velocity:
Momentum(before) = mass(bullet) x velocity(bullet)
= 0.055 kg x 100 m/s
After the collision, the bullet and block of wood are stuck together, so they have a combined mass. The momentum after the collision is the mass of the bullet-block system multiplied by its velocity:
Momentum(after) = mass(bullet + block) x velocity(final)
You can solve for the final velocity by applying conservation of momentum:
Momentum(before) = Momentum(after)
0.055 kg x 100 m/s = (0.055 kg + 1.9 kg) x velocity(final)
Solving this equation will give you the final velocity of the bullet-block system after the collision. Remember, in an inelastic collision, the objects stick together, so their final velocity will be the same.
So, in summary, conservation of momentum can be applied in this situation because the total momentum before and after the collision remains constant, even though kinetic energy is not conserved.