If a particle of mass 5.7 kg is moving east at 10 m/s and a particle of mass 19 kg is moving west at 10 m/s, what is the velocity of the center of mass of the pair? Give answer is m/s to the west.
I tired to use: Vcm = mv/M.
I plugged in (5.7)(10) + (19)(10) / 5.7+19. = 57+190/24.7 = 10m/s. This answer is wrong. Please assist.
Of course it is wrong. Make E + direction, W - direction.
Thank you. I don't know why I was over looking that.
(19x10)-(5.7x10) / (19+5.7) = 5.38 m/s
To find the velocity of the center of mass (Vcm) of the pair, you need to calculate the total momentum of the system and divide it by the total mass of the system.
Let's use the following notation:
m1 = mass of particle 1 = 5.7 kg
v1 = velocity of particle 1 = 10 m/s (east)
m2 = mass of particle 2 = 19 kg
v2 = velocity of particle 2 = 10 m/s (west)
To calculate the total momentum of the system (Ptotal), you need to multiply the mass of each particle by its velocity and sum them up.
Ptotal = (m1 * v1) + (m2 * v2)
Ptotal = (5.7 kg * 10 m/s) + (19 kg * -10 m/s) (note: -10 m/s is used for particle 2 moving west)
Ptotal = 57 kg m/s - 190 kg m/s
Ptotal = -133 kg m/s
Next, to find the total mass of the system (M), you simply need to add the masses of both particles.
M = m1 + m2
M = 5.7 kg + 19 kg
M = 24.7 kg
Finally, divide the total momentum of the system by the total mass of the system to get the velocity of the center of mass.
Vcm = Ptotal / M
Vcm = (-133 kg m/s) / (24.7 kg)
Vcm ≈ -5.38 m/s
Therefore, the velocity of the center of mass of the pair is approximately 5.38 m/s to the west.