 #1
 242
 25
 Homework Statement:

Hello I have been revising momentum and collisions and have found the question below focusing on an elastic collision. I have answered all of the questions but I am struggling particularly with question 3 and would appreciate if anyone could offer any guidance
A hydrogen atom has a mass 1.7x10^27 kg and moves at 500 m/s. It collides elastically with a stationary carbon atom of mass 2.0x10^26 kg and rebounds with a speed of 420 m/s in the opposite direction to its original motion.
Question 1; Use a momentum equation to find the speed of the carbon atom after collision. Question 2; Verify that the collision is perfectly elastic, within the number of significant figures given.
Question 3; If the collision takes 3.0 ms, what is the average force acting in this time interval?
 Relevant Equations:

p=mv
Ek=1/2mv^2
F=ma
1.p=mv
Before the collision:
p hydrogen = 1.7x10^27 * 500 =8.5*10^25 kg ms^1
p carbon = 2.0x10^26 * 0 = 0 kg ms^1
p total before = 8.5*10^25 kg ms^1
The sum of momentum prior to the collision is equal to the total momentum after a collision, momentum is constant, therefore;
p before = p after
After:
p hydrogen = 1.7x10^27 * 420 =7.14*10^25 kg ms^1
p carbon = 8.5*10^25  7.14*10^25 kg ms^1 = 1.564*10^24 kgms^1
Rearrange p=mv in terms of the speed of the carbon atom after the collision;
v=p/m
v=1.564*10^24/2.0x10^26
v=78.2 ms^1
2.In an elastic collision, total kinetic energy is conserved.
KE before=KE after
Before;
Ek hydrogen = 1/2*1.7x10^27*500^2=2.125 *10^22 J
Ek carbon = 1/2*2.0x10^26*0^2=0J
Ek total before = 2.125 *10^22 J~ 2.1*10^22 J
After;
Ek hydrogen = 1/2*1.7x10^27*420^2=1.4994*10^22J
Ek carbon = 1/2*2.0x10^26*78.2^2=6.11524*10^23 J
Ek total after = 1.4994*10^22 + 6.11524*10^23 = 2.110924*10^22 J ~ 2.1 *10^22J
KE before=KE after
Thus, 2.1 *10^22J = 2.1 *10^22J
3. This is where I am most confused, I do not know whether the equations I have used are correct here nor am I entirely sure which force it is referring to? Would this be the force acting on the hydrogen atom in the collision? Also, would I take the velocity to be 500ms^1 during the 3 seconds of this collision?
In yes then;
Force=ma=mv/t
Force = 1.7x10^27 *500/3
Force = 2.83 * 10^25 N
Or would I use;
Force=change in momentum/time
Change in momentum = mvfmvi=(1.7x10^27 *420) (1.7x10^27 *500)= 7.14*10^25  8.5*10^25=  1.564 *10^24
Force =  1.564 *10^24 / 3
Force =  5.21 *10^25 N
I am rather confused on this last section, also would the negative sign be applicable here? Sorry I think I have confused myself!
Before the collision:
p hydrogen = 1.7x10^27 * 500 =8.5*10^25 kg ms^1
p carbon = 2.0x10^26 * 0 = 0 kg ms^1
p total before = 8.5*10^25 kg ms^1
The sum of momentum prior to the collision is equal to the total momentum after a collision, momentum is constant, therefore;
p before = p after
After:
p hydrogen = 1.7x10^27 * 420 =7.14*10^25 kg ms^1
p carbon = 8.5*10^25  7.14*10^25 kg ms^1 = 1.564*10^24 kgms^1
Rearrange p=mv in terms of the speed of the carbon atom after the collision;
v=p/m
v=1.564*10^24/2.0x10^26
v=78.2 ms^1
2.In an elastic collision, total kinetic energy is conserved.
KE before=KE after
Before;
Ek hydrogen = 1/2*1.7x10^27*500^2=2.125 *10^22 J
Ek carbon = 1/2*2.0x10^26*0^2=0J
Ek total before = 2.125 *10^22 J~ 2.1*10^22 J
After;
Ek hydrogen = 1/2*1.7x10^27*420^2=1.4994*10^22J
Ek carbon = 1/2*2.0x10^26*78.2^2=6.11524*10^23 J
Ek total after = 1.4994*10^22 + 6.11524*10^23 = 2.110924*10^22 J ~ 2.1 *10^22J
KE before=KE after
Thus, 2.1 *10^22J = 2.1 *10^22J
3. This is where I am most confused, I do not know whether the equations I have used are correct here nor am I entirely sure which force it is referring to? Would this be the force acting on the hydrogen atom in the collision? Also, would I take the velocity to be 500ms^1 during the 3 seconds of this collision?
In yes then;
Force=ma=mv/t
Force = 1.7x10^27 *500/3
Force = 2.83 * 10^25 N
Or would I use;
Force=change in momentum/time
Change in momentum = mvfmvi=(1.7x10^27 *420) (1.7x10^27 *500)= 7.14*10^25  8.5*10^25=  1.564 *10^24
Force =  1.564 *10^24 / 3
Force =  5.21 *10^25 N
I am rather confused on this last section, also would the negative sign be applicable here? Sorry I think I have confused myself!