a bullet of mass 40g strikes a stationary wooden block of mass 6kg horizontally at 500m per second.the bullet goes through the block,and emerges from the other side at 200m per second.a)Calculate the velosity of the block once the bullet emerges from it?
Take the direction of bullet to a block as postive
M1vi1+m2vi2=m1vf1+m2vf2
(0,04)(500)+(6)(0)=(0.04)(200)+(6)(vf2)
20=8+6(vf2)
20-8=6(vf2)
6(vf2)=12
.:vf2=2m.s
2m/second in the original direction of the bullet
To calculate the velocity of the block once the bullet emerges from it, we can use the principle of conservation of momentum. According to this principle, in the absence of external forces, the total momentum before and after a collision remains constant.
The momentum of an object is given by the product of its mass and velocity. Thus, we can express the initial momentum of the bullet as:
Initial momentum of bullet = mass of bullet * initial velocity of bullet
Given that the mass of the bullet is 40 grams and its initial velocity is 500 m/s, we need to convert the mass to kilograms:
Mass of bullet = 40 g = 40/1000 kg = 0.04 kg
Initial momentum of bullet = 0.04 kg * 500 m/s = 20 kg·m/s
Similarly, we can calculate the initial momentum of the block. Since the block is initially stationary, its initial velocity is zero. Therefore:
Initial momentum of block = mass of block * initial velocity of block
= 6 kg * 0 m/s
= 0 kg·m/s
Using the principle of conservation of momentum, the total initial momentum before the collision is equal to the total momentum after the collision:
Total initial momentum = Total final momentum
(Initial momentum of bullet) + (Initial momentum of block) = (Final momentum of bullet) + (Final momentum of block)
Substituting the known values:
20 kg·m/s + 0 kg·m/s = (final momentum of bullet) + (final momentum of block)
Since the bullet passes through the block and continues moving after the collision, the final momentum of the bullet is:
Final momentum of bullet = mass of bullet * final velocity of bullet
Given that the mass of the bullet remains the same (0.04 kg) and its final velocity is 200 m/s:
Final momentum of bullet = 0.04 kg * 200 m/s = 8 kg·m/s
To find the final momentum of the block, we subtract the final momentum of the bullet from the total initial momentum:
Final momentum of block = Total initial momentum - Final momentum of bullet
= 20 kg·m/s - 8 kg·m/s
= 12 kg·m/s
Finally, we can determine the final velocity of the block by dividing its final momentum by its mass:
Final velocity of block = Final momentum of block / mass of block
= 12 kg·m/s / 6 kg
= 2 m/s
Therefore, the velocity of the block once the bullet emerges from it is calculated to be 2 m/s.