A gun of mass 0.1kg has a bullet of mass 0.1kg,the bullet laves the piston when fired at a velocity of 200m/s. Find the final velocity.
(a) 20m/s (b) 23m/s (c) 30m/s (d) 45m/s (e) 15 m/s
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The answer is A : 20m/s
Solve the question
To find the final velocity, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired should be equal to the total momentum after it is fired.
The equation for momentum is given by:
momentum = mass × velocity
Let the velocity of the gun be v1, and the velocity of the bullet be v2. Since the gun and bullet move in opposite directions, we can define their velocities as:
v1 = -v (where v is the velocity of the bullet, 200 m/s)
v2 = u (where u is the final velocity we want to find)
The total momentum before the bullet is fired is:
momentum_before = (mass of gun × velocity of gun) + (mass of bullet × velocity of bullet)
= (0.1 kg × -v) + (0.1 kg × 200 m/s)
= -0.1v + 20 kg m/s
The total momentum after the bullet is fired is:
momentum_after = (mass of gun × velocity of gun) + (mass of bullet × velocity of bullet)
= (0.1 kg × u) + (0.1 kg × 0 m/s)
= 0.1u kg m/s
Since the total momentum before and after the bullet is fired should be equal, we can set up an equation:
-0.1v + 20 = 0.1u
Simplifying the equation:
-0.1v = -0.1u + 20
v = u - 200
Substituting v = 200 m/s:
200 = u - 200
400 = u
Therefore, the final velocity (u) is 400 m/s.
None of the options provided match 400 m/s, so none of the given options are correct.
To find the final velocity, we can use the principle of conservation of momentum.
The momentum before firing the bullet is equal to the momentum after firing.
The momentum of an object is given by the product of its mass and velocity, represented by the equation:
momentum = mass x velocity
For the gun-bullet system, the total initial momentum is:
P_initial = (mass of gun + mass of bullet) x velocity of the gun
The final momentum is given by:
P_final = (mass of bullet) x final velocity of the bullet
Since the principle of conservation of momentum tells us that P_initial = P_final, we can set up the equation:
(mass of gun + mass of bullet) x velocity of the gun = (mass of bullet) x final velocity of the bullet
Given:
Mass of gun = 0.1 kg
Mass of bullet = 0.1 kg
Velocity of the gun = 0 m/s (assume the gun is initially at rest)
Let's substitute the values into the equation and solve for the final velocity.
(0.1 kg + 0.1 kg) x 0 m/s = (0.1 kg) x final velocity
0.2 kg x 0 m/s = 0.1 kg x final velocity
Since anything multiplied by 0 is 0, we can disregard the left side of the equation.
0 = 0.1 kg x final velocity
Dividing both sides of the equation by 0.1 kg, we get:
0 / 0.1 kg = final velocity
Therefore, the final velocity of the bullet is 0 m/s.
None of the provided options (a) 20m/s, (b) 23m/s, (c) 30m/s, (d) 45m/s, or (e) 15m/s are correct.