Question

Object A has mass m_A = 10 kg and initial momentum _A,i = < 20, -5, 0 > kg · m/s, just before it strikes object B, which has mass m_B = 14 kg. Just before the collision object B has initial momentum _B,i = < 3, 5, 0 > kg · m/s.

Consider a system consisting of both objects A and B. What is the total initial momentum of this system, just before the collision?
_{P sys,i} =

The forces that A and B exert on each other are very large but last for a very short time. If we choose a time interval from just before to just after the collision, what is the approximate value of the impulse applied to the two-object system due to forces exerted on the system by objects outside the system?
_FnetΔt =    

Therefore, what does the momentum principle predict that the total final momentum of the system will be, just after the collision?
_Psys,f =  
Just after the collision, object A is observed to have momentum _A,f = < 18, 3, 0 > kg · m/s. What is the momentum of object B just after the collision?
_PB,f =  

At this point we've learned all that we can from applying the momentum principle. Next we'll see what additional information we can obtain by using the energy principle.

Before the collision, what was the magnitude of the momentum of object A?
P|_A,i| =  
Before the collision, what was the kinetic energy of object A? Remember that you can calculate kinetic energy not only from K = (1/2)m||² but more directly from K = (1/2)||²/m.
K_A,i =  
Before the collision, what was the magnitude of the momentum of object B?
P|_B,i| =  
Before the collision, what was the kinetic energy of object B?
K_B,i =  
After the collision, what was the magnitude of the momentum of object A?
P|_A,f| =
After the collision, what was the kinetic energy of object A?
K_A,f =  
After the collision, what was the magnitude of the momentum of object B?
P|_B,f| =  
After the collision, what was the kinetic energy of object B?
K_B,f =
Before the collision, what was the total kinetic energy of the system?
K_sys,i = K_A,i + K_B,i =
After the collision, what was the total kinetic energy of the system?
K_sys,f = K_A,f + K_B,f =  

What kind of collision was this? (Remember that an "elastic" collision is one where the final value of the total kinetic energy is equal to the initial value of the total kinetic energy.)

Assume that all of the energy is either kinetic energy or thermal energy. Calculate the increase of thermal energy of the two objects.
ΔE_A,thermal + ΔE_B,thermal =  

Answer 1

_{P sys,i} = < 20, -5, 0 > + < 3, 5, 0 >

_{P sys,i} = < 23, 0 , 0>

______________________

_FnetΔt = 0

because there is no external force

_________________

_Psys,f =  < 23, 0 , 0>

________________

_PB,f =  < 23, 0 , 0> -  < 18, 3, 0 >

_PB,f = < 5, -3, 0 >

______________

P|_A,i| = sqrt ( 20² + 5² + 0²)

P|_A,i| = 20.615 Kg.m/s

______________

K_A,i =  20.615² / (2 * 10)

K_A,i = 21.25 J

_____________

P|_B,i| = sqrt ( 3² + 5²)

P|_B,i| = 5.83 Kg.m/s

____________

K_B,i = 1.214 J

___________

P|_A,f| = sqrt ( 18² + 3² )

P|_A,f| = 18.248 Kg.m/s

____________

K_A,f = 16.7 J

____________

P|_B,f| = 5.83 Kg.m/s

____________

K_B,f = 1.214 J

___________

K_sys,i = K_A,i + K_B,i = 22.464 J

____________

K_sys,f = K_A,f + K_B,f = 17.914 J

____________

What kind of collision was this

Inelastic collision

___________

ΔE_A,thermal + ΔE_B,thermal = 4.55 J