Just conservation of momentumx2017 said:Homework Statement
Kevin and Jake collide in the air. If Kevin undergoes a 4.2 kg*m/s change in momentum, what is Jacob’s change in velocity if he has a mass of 83.2 kg?
Homework Equations
p=mv
MV+mv=MV'+mv'
The Attempt at a Solution
I tried the simplest way possible...
p=mv
v=p/m
v=4.2/83.2
v=0.050m/s (incorrect)
I feel like conservation of momentum plays a role here, but I can't figure out how... I'm not great at questions where I'm given such little information...
SammyS said:Just conservation of momentum
MV+mv=MV'+mv'
and a little algebra, rearranging.
Which variables are for Kevin? which for Jake ?
One step at a time.x2017 said:Big letters for Kevin, small for Jake.
MV+mv=MV'+mv'
So I'm solving for:
v'=(MV+mv-MV')m
My question now is how on Earth do I get velocities for them? Or can I just plug in the 4.2 for MV'?
SammyS said:One step at a time.
You are given Kevin's change in momentum.
How do express that with your chosen variables?
That should be related in a simple way to Jake's change in momentum..
So solve the conservation of momentum equation for MV'-MV .x2017 said:If Kevin's momentum changes by 4.2, then so will Jake's?
& Kevin's change in momentum could be shown as MV'-MV=4.2?
SammyS said:So solve the conservation of momentum equation for MV'-MV .
Right.x2017 said:Alrighty,
MV'-MV=mv-mv'
4.2=mv-mv'
SammyS said:Right.
That's actually the negative of the change in Jake's momentum.
Alternatively, that could be written as:
4.2 − (mv' − mv) =0 ,
where (mv' − mv) is the change in Jake's momentum.
What does the question ask for?x2017 said:Okay, so how would one solve for v' without v? Do we assume that v is 0?
x2017 said:what is Jacob’s change in velocity
SammyS said:What does the question ask for?
x2017 said:OOOHHHHHHH
Okay I've got it now!
change in velocity = v'-v
4.2=mv-mv'
4.2/83.2=mv-mv'
0.05=v-v'
-0.05=v'-v
I was so close at the beginning!
Thanks for your help, I'm glad I just didn't try the negative answer in the beginning, now I understand how to get there! :)
Rearranging gives:x2017 said:v'=(MV+mv-MV')/m
...
Change in velocity after a collision refers to the difference in velocity of an object before and after a collision occurs. It is a measure of the object's change in speed and direction.
Change in velocity can be calculated using the formula: change in velocity = final velocity - initial velocity. The final and initial velocities are determined by measuring the speed and direction of the object before and after the collision.
The change in velocity after a collision can be affected by factors such as the mass, velocity, and angle of the objects involved in the collision. Other factors such as the elasticity of the objects and any external forces can also impact the change in velocity.
Yes, change in velocity can be negative. This indicates that the velocity of the object has decreased after the collision, either in speed or direction, compared to its initial velocity. A negative change in velocity can occur in collisions where the objects stick together or in elastic collisions where the objects move in opposite directions.
Newtons's laws of motion explain the relationship between force, mass, and acceleration. In the case of a collision, the force exerted on the objects involved can cause a change in velocity. The change in velocity is directly proportional to the force and inversely proportional to the mass of the object, as stated in Newton's second law of motion (F=ma).