Inelastic and elastic collision problems

[mdwjun]

1. An 8 g rubber bullet was fired into a 2.5 kg pendulum bob, initially at rest, and becomes embedded in it. The pendulum rises a vertical distance of 6.0 cm.Calculate the initial speed and how much kinetic energy is lost in this collision?

2. An 8 g rubber bullet was fired into a 2.5 kg pendulum bob, initially at rest, and bounces off into the opposite direction. It rises 6.0 cm vertically. (elastic case) What is the velocity of the bob after the collision? Use conservation momentum to find the change in velocity of the bullet. Use conservation of Kinetic energy to find initial velocity of bullet and final velocity of the bullet.

I heard that I needed to use the inelastic collision and the conservation of energy equation for number 1.
0.5*mass*initial velocity^2 +mass*gravitational pull* initial height=0.5*mass*final velocity^2 +mass*gravitational pull* final height.

I triedto solve but could not because i did not know the initial velocity of the bullet and the final velocity.

 

[mdwjun]

-sigh- help

 

[nlightner]

I would like to clarify that both problems involve conservation of momentum and energy, but they are different types of collisions - inelastic and elastic. In an inelastic collision, the objects stick together after the collision and move with a common velocity, while in an elastic collision, the objects bounce off each other with no loss of kinetic energy.

For the first problem, we can use the conservation of momentum equation to find the initial velocity of the bullet. Since the pendulum bob was initially at rest, its initial momentum is zero. Therefore, the initial momentum of the system is equal to the momentum of the bullet before the collision. We can write this as:

m_bullet * v_bullet = (m_bullet + m_bob) * v_final

where m_bullet is the mass of the bullet, v_bullet is its initial velocity, m_bob is the mass of the pendulum bob and v_final is the common velocity after the collision. We also know that the energy is conserved in this case, so we can use the conservation of energy equation to find the initial velocity of the bullet:

0.5 * m_bullet * v_bullet^2 = 0.5 * (m_bullet + m_bob) * v_final^2

We also know that the pendulum rises a vertical distance of 6.0 cm, so we can use the conservation of energy equation again to find the initial velocity of the bullet:

m_bullet * g * h = 0.5 * (m_bullet + m_bob) * v_final^2

where g is the gravitational acceleration and h is the height the pendulum rises. Now we have three equations and three unknowns (v_bullet, v_final, and h), so we can solve for all of them. Once we find the initial velocity of the bullet, we can use the conservation of energy equation to find the kinetic energy lost in the collision:

KE_lost = 0.5 * m_bullet * v_bullet^2 - 0.5 * (m_bullet + m_bob) * v_final^2

For the second problem, we have an elastic collision, so we can use the conservation of momentum equation to find the final velocity of the bullet. We can write this as:

m_bullet * v_bullet = (m_bullet + m_bob) * v_final

We also know that the bob rises a vertical distance of 6.0 cm, so we can use