A bullet of mass 0.01kg is fired into a sandbag of mass 0.49 kg hanging from a tree. Swings away at 10 m/s. Find
A) the momentum after the collision.
B) the momentum before the collision.
C) the velocity of the bullet.
(A and B) the momentum after is exactly the same as the momentum before
P = momentum = m v = (0.01 + 0.49) * 10 = 5 kg m/s
(C) 5 kg m/s = 0.01 kg u
u = 5 / 0.01 = 500 m/s
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided that there are no external forces acting on the system.
A) To find the momentum after the collision, we need to calculate the net momentum of the system, which includes both the bullet and the sandbag. The equation for momentum is:
momentum = mass × velocity
The momentum of the bullet after the collision is given by:
momentum of the bullet = mass of the bullet × velocity of the bullet
Substituting the given values:
mass of the bullet = 0.01 kg
velocity of the bullet = 10 m/s
momentum of the bullet = 0.01 kg × 10 m/s = 0.1 kg·m/s
B) To find the momentum before the collision, we can assume that there are no external forces acting on the system before the collision, so the total momentum is zero. Therefore, the momentum before the collision is also zero.
momentum before the collision = 0 kg·m/s
C) To find the velocity of the bullet, we can use the equation for momentum:
momentum = mass × velocity
Rearranging the equation, we can solve for the velocity:
velocity = momentum / mass
Using the given values:
momentum of the bullet = 0.1 kg·m/s
mass of the bullet = 0.01 kg
velocity of the bullet = 0.1 kg·m/s / 0.01 kg = 10 m/s
So, the velocity of the bullet is 10 m/s.
To find the answers, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
A) To find the momentum after the collision, we need to know the final velocity of the bullet and sandbag system. From the problem, we know that the sandbag swings away at 10 m/s after the collision. Since the bullet is embedded in the sandbag, the final velocity of the system is the same as the sandbag's velocity.
The momentum after the collision is given by the equation: momentum = mass × velocity. Therefore,
momentum_after = (mass of bullet + mass of sandbag) × velocity_after
= (0.01 kg + 0.49 kg) × 10 m/s
= 0.5 kg × 10 m/s
= 5 kg·m/s
So, the momentum after the collision is 5 kg·m/s.
B) To find the momentum before the collision, we need to know the initial velocity of the bullet. Unfortunately, the problem does not provide any information about the initial velocity. Without this information, we cannot directly calculate the momentum before the collision.
C) Without the initial velocity of the bullet, we cannot determine its velocity. The problem does not provide any information about the initial velocity of the bullet, so we cannot find its velocity using the given data.
In summary:
A) The momentum after the collision is 5 kg·m/s.
B) The momentum before the collision cannot be determined without the initial velocity of the bullet.
C) The velocity of the bullet cannot be determined without the initial velocity.