i need help with a momemtnum problem on my homework

Question

a 2kg blob of putty moving at 3 m/s slams into a 2 kg of putty at rest. what is the initial momentum of the two blobs? what must be the final momentum of the two blobs? Also, calculate the velocity of the two stuck together blobs of putty after the collision.

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Answer 1

Whenever you have two masses that stick together after a collision, the collision is called 'perfectly inelastic.' During an any inelastic collision kinetic energy will be converted into internal energy in the objects. Thus, even though the system energy is conserved (there are no external forces doing work), the internal energy changes in a way that is unknown and unpredictable. This means that conservation of energy during an inelastic collisions is completely useless to us. The conserved quantity that we can track however is the momentum. Kirill Z. did this problem correctly and I defer to his solution. Grigori S. didn't read the problem carefully. He's describing a 'perfectly elastic' collision between two equal masses. In a perfectly elastic collision there is no transfer of kinetic energy to internal energy, thus the mechanical energy (kinetic plus potential) of the system will be conserved.

Answer 2

Momentum is conserved:

 

m_i v_i = m_f v_f

The initial momentum is 6kg-m/s  {2kg X 3m/s}

 

When the first ball of putty sticks to the second the momentum remains the same {6kg-m/s}, but the mass is now 4 kg.  The new velocity would be 1.5 m/s for the 4 kg combined blob.

 

Answer 3

Hey Silvia -- the "sticking-together" collision is much like a "piggy-back ride" where we have twice the mass and half the speed ==> 4kg at 1.5m/s with unchanged momentum 6 kg-m/s ... Regards :)

Answer 4

In the closed system,if the colision is perect, then the total momentum and kinetic energy are consertved (they are the same before and after the collision). If both masses are equal, they simply exchange the velocities: the frst one will stop while the second one (at rest) will start moving with the same velocity as the first one before the collision.

Answer 5

The initial momentum is p=m₁v₁+m₂v₂, where by boldfaced letters I denote vector quantities. Since the second blob is at rest, v₂=0. Then

p=m₁v₁; |p|=m₁|v₁|=2*3=6 kg*m/s;

 

In the closed system the total momentum is conserved. Therefore, the final momentum is also 6 kg*m/s, directed the same way as the initial momentum. However, since two blobs are now stuck together, the total mass is now M=m₁+m₂=2+2=4 kg. Therefore, 

p=Mv=6=4v; From this v=6/4=1.5 m/s, directed the same way as the initial velocity of the first blob.