a bullet of mass 20g is fired into a block of wood of mass 400g . if the bullut and wood move together with speed of 20ms-1 calclate(i) speed with the bullet hits the wood ii the kinetic energy lost iii state the energy changes involed
bullet momentum = m v = .020 v
final momentum = (.020 + .400)(20)
so
v of bullet = (.020 + .400)(20) / (.020)
initial Ke = (1/2) (.020) v^2
final Ke = (1/2)(.420)(400) It better be less :)
so loss to heat = final Ke - initial Ke
To calculate the speed at which the bullet hits the wood, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision. The formula for momentum is:
momentum = mass x velocity
Given:
Mass of the bullet (m1) = 20g = 0.02 kg
Mass of the wood block (m2) = 400g = 0.4 kg
Final velocity after collision (v) = 20 m/s
Using conservation of momentum, we can write:
momentum before collision = momentum after collision
(mass of bullet x velocity of bullet) + (mass of wood x velocity of wood) = (mass of bullet + mass of wood) x final velocity
(0.02 kg x velocity of bullet) + (0.4 kg x 0) = (0.02 kg + 0.4 kg) x 20 m/s
0.02 kg x velocity of bullet = 8.4 kg m/s
velocity of bullet = 8.4 kg m/s / 0.02 kg
velocity of bullet = 420 m/s
So, the speed at which the bullet hits the wood is 420 m/s.
Now, to calculate the kinetic energy lost, we need to find the initial kinetic energy of the bullet before the collision and subtract the final kinetic energy of the bullet and wood after the collision.
The formula for kinetic energy is:
kinetic energy = (1/2) x mass x velocity^2
Initial kinetic energy of the bullet = (1/2) x mass of bullet x (velocity of bullet)^2
Initial kinetic energy of the bullet = (1/2) x 0.02 kg x (420 m/s)^2
Initial kinetic energy of the bullet = 1764 J
Final kinetic energy of the bullet and wood = (1/2) x (mass of bullet + mass of wood) x (velocity)^2
Final kinetic energy of the bullet and wood = (1/2) x (0.02 kg + 0.4 kg) x (20 m/s)^2
Final kinetic energy of the bullet and wood = 220 J
Kinetic energy lost = Initial kinetic energy - Final kinetic energy
Kinetic energy lost = 1764 J - 220 J
Kinetic energy lost = 1544 J
So, the kinetic energy lost is 1544 Joules.
The energy changes involved in this scenario are:
1. The bullet initially has kinetic energy, which is transferred to the bullet and wood as they move together.
2. The kinetic energy of the bullet and wood is lost during the collision.
3. Some of the kinetic energy is converted into other forms such as heat, sound, and deformation of the wood block.