A lead bullet of mass 50 grams is fired with a velocity of 200m/s into a lead block of mass 950 grams. Given that the lead block can move freely, calculate the kinetic energy after impact and the loss of energy.

PLEASE ANSWER THIS QUESTION.

Convert the masses in g to kg

So, 50g=0.05kg & 950g=0.95kg
Mass of bullet (Mb)=0.05kg
Mass of lead block (mB)=0.95kg
Initial vel of bullet (Ub)=200m/s
Final vel of bullet (Vb)=0m/s
Initial vel of lead block(uB)=0m/s
Final vel of lead block(vB)=vB?
The collision is linear. So, using: 1/2MbUb^2+1/2mBuB^2=1/2MbVb^2+1/2mBvB^2
1/2×0.05×200^2+1/2×0.95×0^2=1/2×0.05×0^2+1/2×0.95×vB^2
1000+0=0+0.5vB^2
1000=0.5vB^2
Therefore VB^2=1000/0.5
Hence vB=√2000
vB=45m/s (approximately)
After impact, they will move with the same velocity i.e vel of lead block
Therefore, Kinetic Energy after impact =kinetic energy of lead block=k.eB
k.eB=1/2mBvB^2
k.eB=1/2×0.95×45^2
k.eB=962Joules(approximately)
Recall; Mb=0.05kg
Ub=200m/s
Therefore, K.Eb(kinetic energy of bullet)
K.Eb=1/2MbUb^2
K.Eb=1/2×0.05×200^2
K.Eb=1000Joules
LOSS OF ENERGY =K.Eb-k.eB
=1000-962=38Joules

To calculate the kinetic energy after impact, we need to use the principle of conservation of linear momentum.

The initial momentum of the bullet is given by the product of its mass and velocity:
Momentum_before = mass_bullet * velocity_bullet
= 0.050 kg * 200 m/s
= 10 kg·m/s

The initial momentum of the block is zero, since it is initially at rest.

According to the principle of conservation of linear momentum, the total momentum before and after the impact remains the same.

The final momentum of the system is the sum of the final momenta of the bullet and the block, which can be represented as:
Momentum_after = mass_bullet * velocity_bullet_after + mass_block * velocity_block_after

Since the lead block can move freely after the impact, we can assume that the bullet and the block will have the same final velocity, denoted as v_after.

Momentum_after = (mass_bullet + mass_block) * v_after

Since the total momentum is conserved, we can equate the initial and final momenta:
10 kg·m/s = (0.050 kg + 0.950 kg) * v_after

Simplifying the equation:
10 kg·m/s = 1 kg * v_after

Dividing both sides by 1 kg, we find:
v_after = 10 m/s

Now we can calculate the final kinetic energy of the system.

The kinetic energy after impact is given by:
Kinetic_energy_after = 0.5 * (mass_bullet + mass_block) * (v_after)^2

Plugging in the values:
Kinetic_energy_after = 0.5 * (0.050 kg + 0.950 kg) * (10 m/s)^2
= 0.5 * 1 kg * 100 m^2/s^2
= 50 J

Therefore, the kinetic energy after impact is 50 Joules.

To calculate the loss of energy, we need to find the difference between the initial and final kinetic energies.

Initial kinetic energy = 0.5 * mass_bullet * (velocity_bullet)^2
= 0.5 * 0.050 kg * (200 m/s)^2
= 1000 J

Loss of energy = Initial kinetic energy - Final kinetic energy
= 1000 J - 50 J
= 950 J

Therefore, the loss of energy is 950 Joules.

To calculate the kinetic energy after impact, you can use the principle of conservation of momentum, which states that the total momentum before the impact is equal to the total momentum after the impact.

The initial momentum can be calculated using the formula:

Initial momentum = mass × velocity

For the bullet, the initial momentum is given by:

Initial momentum of bullet = mass of bullet × velocity of bullet

Plugging in the values, we have:

Initial momentum of bullet = 0.05 kg × 200 m/s = 10 kg⋅m/s

Similarly, for the block, the initial momentum is given by:

Initial momentum of block = mass of block × velocity of block

Plugging in the values, we have:

Initial momentum of block = 0.95 kg × 0 m/s (as the block is initially at rest) = 0 kg⋅m/s

Since momentum is conserved, the total momentum after the impact is equal to the initial momentum:

Total momentum after impact = Initial momentum

Therefore, we have:

Total momentum after impact = Final momentum of bullet + Final momentum of block

After the impact, both the bullet and block move with the same velocity (let's call it v). Since the block is much heavier, its contribution to the total momentum is greater. Therefore, we can rewrite the equation as:

m1v + m2v = Initial momentum

where m1 is the mass of the bullet and m2 is the mass of the block.

Plugging in the values, we have:

0.05 kg × v + 0.95 kg × v = 10 kg⋅m/s

Simplifying the equation, we get:

1 kg × v = 10 kg⋅m/s

v = 10 m/s

Now that we have the velocity after impact, we can calculate the kinetic energy after impact.

The kinetic energy can be calculated using the formula:

Kinetic energy = 0.5 × mass × (velocity)^2

For the bullet, the kinetic energy after impact is given by:

Kinetic energy of bullet = 0.5 × mass of bullet × (velocity of bullet)^2

Plugging in the values, we have:

Kinetic energy of bullet = 0.5 × 0.05 kg × (10 m/s)^2 = 2.5 J

Similarly, for the block, the kinetic energy after impact is given by:

Kinetic energy of block = 0.5 × mass of block × (velocity of block)^2

Plugging in the values, we have:

Kinetic energy of block = 0.5 × 0.95 kg × (10 m/s)^2 = 47.5 J

The total kinetic energy after impact is the sum of the kinetic energies of the bullet and the block:

Total kinetic energy after impact = Kinetic energy of bullet + Kinetic energy of block

Total kinetic energy after impact = 2.5 J + 47.5 J = 50 J

To calculate the loss of energy, subtract the initial kinetic energy from the total kinetic energy after impact:

Loss of energy = Total kinetic energy after impact - Initial kinetic energy

Loss of energy = 50 J - 10 J (initial kinetic energy of the bullet) = 40 J

Therefore, the kinetic energy after impact is 50 J, and the loss of energy is 40 J.