Motion of a system of particles

  • #1

Homework Statement


The vector position of a 3.15 g particle moving in the xy plane varies in time according to the following equation.
r1 = (3i+3j)t + 2jt^2


At the same time, the vector position of a 5.00 g particle varies according to the following equation.
r2= 3i-2it^2 -6jt

For each equation, t is in s and r is in cm. Solve the following when t = 2.50:
(a) Find the vector position of the center of mass.

i cm
j cm

(b) Find the linear momentum of the system.
i g-cm/s
j g-cm/s

(c) Find the velocity of the center of mass.
i cm/s
j cm/s

(d) Find the acceleration of the center of mass.
i cm/s2
j cm/s2

(e) Find the net force exerted on the two-particle system.
i μN
j μN


Homework Equations


im really not sure about this
i think for some of them you would use p=mv
and for the center of mass you use 1/M integral of r??


The Attempt at a Solution


im not sure what to do first
am i plugging in for t first? and then what do i do?
 

Answers and Replies

  • #2
LowlyPion
Homework Helper
3,090
4
Yes you will need to evaluate the vector function at the time given and determine position.

Basically your center of mass is a function of the motion of both particles, so you will need to develop the answers from the vector form of the Center of Mass equation.

The acceleration will let you find the net force by ordinary means.
 
  • #3
ok im still a bit confused
so i plug in the value of t into both equations and then what..im not getting it right
 
  • #4
LowlyPion
Homework Helper
3,090
4
OK, for the first one you have the values of R1 and R2 @ t=2.5 in terms of i,j.

The weighted average of their positions then means that you multiply each by the mass of the appropriate particle and then divide by the total mass of the particles. These are all scalar operations on the i,j dimensions of each vector @ 2.5.
 
  • #5
o so by doing this
it'll give me the vector position of each?
 
  • #6
LowlyPion
Homework Helper
3,090
4
o so by doing this
it'll give me the vector position of each?
Each R vector is a function in t.

But at any t, you have a value for R, and hence the displacement vector for each particle.

You are simply evaluating the vector at that time and applying the rules for determining the center of mass.
 
  • #7
oo so by evaluating each at t..then i just multiply by the masses
and add them up..and then divide everything by the total mass?
 
  • #8
LowlyPion
Homework Helper
3,090
4
oo so by evaluating each at t..then i just multiply by the masses
and add them up..and then divide everything by the total mass?
Yes, that's what the center of mass is.

In this case though they give you the i,j components, but they can be dealt with independently.
 
  • #9
7
0
nevermind- just added the vectors
 
Last edited:
  • #10
7
0
(e) Find the net force exerted on the two-particle system.
i μN
j μN


Shouldn't the net force exerted for i and j just be the :

acceleration i-hat * (m1 + m2)
and
acceleration j-hat * (m1 + m2)

I have part D for acceleration as
r1 : 4 j
r2 : -4 i

I'm doing this and am getting the wrong answer.
 
  • #11
7
0
bump for question due today.
 
  • #12
so i figured out the vector position of the center of mass

now im trying to find the velocity of the center of mass
i have no idea how to do this..i know its going to be P/M but how do i get the velocities?
 
  • #13
7
0
take the derivative of the position vectors and to find the velocity vectors.
 
  • #14
yea i figured it out
thanks a lot guys for your help :)
 

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