AN INTERACTING SYSTEM OF TO OBJECTS HAS NO EXTERRNAL FORCE ACTING ON THE SYSTEM.

Question

AN INTERACTING SYSTEM OF TO OBJECTS HAS NO EXTERRNAL FORCE ACTING ON THE SYSTEM. THE FIRST OBJECT HAS A MASS 2.0 KG AND IS MOVING WITH A VELOCITY (2.0 M/S)i + (1.0 M/S)j at a time t=0.00 seconds. the second object has a mass 3.00jg and is moving with a velocity (-1.0 m/s)i + (1.0 m/s)j at a time t=0.00 seconds. the second object is moving with a object with a velocity (2.0 m/s)i + (-1.0 m/s)j at time t= 1.00 seconds. a) what is the total momentum of the system at time t=0.00 seconds? b) what is the velocity of the first object at t=1.00 seconds? THANK YOU!!!

Explanation / Answer

velocity of center of mass Vcm = (m1v1 + m2v2)/(m1+m2)

m1 = 2Kg

m2 = 3Kg

at t = 0s

v1 = (2.0 m/s)i + (1.0 m/s)j

v2 = (-1.0 m/s)i + (1.0 m/s)j

Vcm(0) = (m1v1 + m2v2)/(m1+m2) = (0.2 m/s) i + (1 m/s) j

a) Total momentum

P = m1v1 + m2v2 = (1 Kg-m/s) i + (5 Kg-m/s)J

b)

since no external forces

Vcm is constant

at t = 1s

v2 = (2.0 m/s)i + (-1.0 m/s)j

using Vcm(1) = (m1v1 + m2v2)/(m1+m2) = Vcm(0) = (0.2 m/s) i + (1 m/s) j

we have

v1 = (-2.5 m/s) i + (4 m/s )j

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