1) A 1 kg moving at 1 m/s ha s a totally inelastic collision with a 0.7 kg mass. What is the speed of the resulting combined mass after the collision?
2) A 0.010n kg bullet is shot from a 0.500 kg gun at speed of 230 m/s. Find the speed of the gun.
1. conservation of momentum
1kg*1m/s=(1.7kg)V solve for v
2. initial momentum=0=.010(230)+.500V
solve for V. Notice is is negative.
1) To find the speed of the resulting combined mass after a totally inelastic collision, we can use the principle of conservation of momentum. The equation for momentum is:
Momentum (p) = mass (m) × velocity (v)
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision. In this case, the total momentum before the collision is:
Initial momentum = (mass1 × velocity1) + (mass2 × velocity2)
Given:
mass1 (m1) = 1 kg
velocity1 (v1) = 1 m/s
mass2 (m2) = 0.7 kg (mass of the object colliding with the 1 kg mass)
velocity2 (v2) = unknown (speed of the resulting combined mass after the collision)
Hence, the initial momentum is:
Initial momentum = (1 kg × 1 m/s) + (0.7 kg × 0 m/s) = 1 kg·m/s
The total momentum after the collision is:
Final momentum = (combined mass after collision × velocity after collision)
Since the collision is totally inelastic, the two objects stick together after the collision, becoming a single combined mass. Therefore, the combined mass after the collision is the sum of the individual masses, which is 1 kg + 0.7 kg = 1.7 kg.
We can now solve for the velocity after the collision:
Final momentum = (1.7 kg × velocity after collision)
Using the conservation of momentum principle, we can equate the initial and final momentum:
1 kg·m/s = 1.7 kg × velocity after collision
Dividing both sides by 1.7 kg:
velocity after collision = (1 kg·m/s) / 1.7 kg = 0.59 m/s
Therefore, the speed of the resulting combined mass after the collision is approximately 0.59 m/s.
2) To find the speed of the gun, we can again use the principle of conservation of momentum. The equation for momentum is the same as mentioned above:
Momentum (p) = mass (m) × velocity (v)
According to the conservation of momentum, the total momentum should be conserved before and after the event.
Before the event, the momentum is zero because the gun is at rest.
Final momentum = (bullet mass × bullet speed) + (gun mass × gun speed)
Given:
bullet mass = 0.010 kg
bullet speed = 230 m/s
gun mass = 0.500 kg
gun speed = unknown (speed of the gun)
We can rewrite the equation for the final momentum as:
Final momentum = (0.010 kg × 230 m/s) + (0.500 kg × gun speed)
Since the initial momentum is zero, the final momentum must also be zero to satisfy the conservation of momentum.
0 = (0.010 kg × 230 m/s) + (0.500 kg × gun speed)
Now we can solve for the speed of the gun:
0 = 2.3 kg·m/s + (0.500 kg × gun speed)
Rearranging the equation:
(0.500 kg × gun speed) = -2.3 kg·m/s
Dividing both sides by 0.500 kg:
gun speed = (-2.3 kg·m/s) / 0.500 kg = -4.6 m/s
Note that the negative sign indicates that the gun is moving in the opposite direction of the bullet.
Therefore, the speed of the gun is approximately 4.6 m/s in the opposite direction of the bullet.