A bullet of mass 12g which is fired horizontally hits the wooden block of mass 1kg suspended on a string
(a) calculate the initial velocity of the bullet .
(b) calculate the energy lost by the bullet when it hits the wooden block
Where is the rest of the problem?
Like how high did the mass rise with the bullet in it?
To calculate the initial velocity of the bullet, we can use the conservation of momentum. The initial momentum of the bullet is equal to the final momentum of the bullet and the block.
(a) The formula for momentum is:
Initial momentum of bullet = Final momentum of bullet + Final momentum of block
The mass of the bullet is given as 12g, which is equal to 0.012kg.
The mass of the block is given as 1kg.
Since the bullet was fired horizontally, there is no vertical momentum. Therefore, the final momentum of the bullet and the block in the vertical direction is zero.
Thus, we can write the equation for the x-component of momentum as:
Initial momentum of bullet (x-component) = Final momentum of bullet (x-component) + Final momentum of block (x-component)
m_bullet * v_bullet = m_bullet * v_bullet' + m_block * v_block
where v_bullet is the initial velocity of the bullet, v_bullet' is the final velocity of the bullet, and v_block is the final velocity of the block.
Since the bullet is fired horizontally and hits the block, the final velocity of the bullet is zero (since it comes to rest upon impact) and the final velocity of the block is also zero (since it was initially at rest and comes to rest after the impact).
Therefore, the equation simplifies to:
m_bullet * v_bullet = 0 + 0
0.012 kg * v_bullet = 0
Therefore, the initial velocity of the bullet, v_bullet, is 0 m/s.
(b) To calculate the energy lost by the bullet, we can use the principle of conservation of kinetic energy. The initial kinetic energy of the bullet is equal to the sum of the final kinetic energy of the bullet and the final kinetic energy of the block.
The formula for kinetic energy is:
Initial kinetic energy of bullet = Final kinetic energy of bullet + Final kinetic energy of block
The initial kinetic energy of the bullet is given by:
KE_bullet = (1/2) * m_bullet * v_bullet^2
Substituting the values, we get:
KE_bullet = (1/2) * 0.012 kg * 0^2
= 0
The final kinetic energy of the bullet and the block is zero since both come to rest after the impact.
Therefore, the energy lost by the bullet when it hits the wooden block is 0.
To calculate the initial velocity of the bullet in part (a), we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
The momentum of an object is given by the equation p = mv, where p is the momentum, m is the mass, and v is the velocity.
Since the bullet is fired horizontally and hits the wooden block, we can assume that there is no vertical movement. Therefore, we can ignore the vertical component and consider only the horizontal component.
Let's assume the initial velocity of the bullet is v1, and let the bullet and wooden block move together with final velocity v2 after the collision.
The initial momentum of the system (bullet + wooden block) is given by the mass of the bullet multiplied by its initial velocity:
P_initial = m_bullet * v1
The final momentum of the system is given by the combined mass of the bullet and wooden block multiplied by their final velocity:
P_final = (m_bullet + m_wooden_block) * v2
According to the principle of conservation of momentum, P_initial = P_final:
m_bullet * v1 = (m_bullet + m_wooden_block) * v2
Now we can solve for v1, the initial velocity of the bullet:
v1 = (m_bullet + m_wooden_block) * v2 / m_bullet
To calculate the energy lost by the bullet when it hits the wooden block in part (b), we need to consider the concept of kinetic energy.
The kinetic energy of an object is given by the equation KE = 0.5 * m * v^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
The initial kinetic energy of the bullet is given by:
KE_initial = 0.5 * m_bullet * v1^2
The final kinetic energy of the bullet after collision is zero because it stops moving:
KE_final = 0.5 * m_bullet * 0^2 = 0
The energy lost by the bullet is the difference between the initial and final kinetic energies:
Energy_lost = KE_initial - KE_final
Now you can substitute the values of the masses and velocities to calculate the initial velocity of the bullet and the energy lost.