A piece of modeling clay is motionless in space. Another piece of clay that is 4 times as massive moving at 10m/s collides with it and sticks to it. What is the momentum of the combined blob after the collision?
Linear momentum is conserved.
If the mass of the motionless clay piece is m, that of the other piece is 4m. The heavier piece initially has all of the momentum.
4m*10 m/s = (4m + m)*Vfinal
Vfinal = (4/5)*10 = 8 m/s
To determine the momentum of the combined blob after the collision, we need to apply the law of conservation of momentum. According to this law, the total momentum before the collision should equal the total momentum after the collision.
The momentum of an object is calculated as the product of its mass and velocity. Let's calculate the initial momentum of both pieces of clay separately.
1. The initial momentum of the motionless clay is given by:
Momentum = mass × velocity
= (mass of motionless clay) × 0 (since it is motionless)
= 0
2. The initial momentum of the moving clay is given by:
Momentum = mass × velocity
= (mass of moving clay) × (velocity of moving clay)
= (4 times mass of motionless clay) × (10 m/s)
= 40 × (mass of motionless clay) * m/s
Now, since the two clays stick together after the collision and combine into a single blob, their momenta should be equal. Let's say the final momentum of the combined blob is P.
According to the law of conservation of momentum:
Initial momentum of motionless clay + Initial momentum of moving clay = Final momentum
0 + 40 × (mass of motionless clay) m/s = P
Therefore, the momentum of the combined blob after the collision is 40 times the mass of the motionless clay, measured in kilogram-meter per second (kg·m/s).