What is the momentum of a two-particle sys-
tem composed of a 1300 kg car moving east at
60 m/s and a second 1500 kg car moving west
at 95 m/s? Let east be the positive direction.
Answer in units of kg · m/s.
To find the momentum of a two-particle system, we need to find the individual momentum of each particle and then add them together since momentum is a vector quantity.
Momentum (p) is defined as the product of mass (m) and velocity (v). Mathematically, it can be expressed as:
p = m * v
For the first car:
Mass (m1) = 1300 kg
Velocity (v1) = 60 m/s
p1 = m1 * v1
Similarly, for the second car:
Mass (m2) = 1500 kg
Velocity (v2) = -95 m/s (since it's moving in the opposite direction, we use a negative sign)
p2 = m2 * v2
Now, we can calculate the momentum of each car:
p1 = 1300 kg * 60 m/s = 78000 kg·m/s (eastward direction)
p2 = 1500 kg * (-95 m/s) = -142500 kg·m/s (westward direction)
To find the total momentum of the system, we add the individual momenta:
Total momentum (ptotal) = p1 + p2
ptotal = 78000 kg·m/s + (-142500 kg·m/s)
Simplifying:
ptotal = -64500 kg·m/s
Therefore, the momentum of the two-particle system, composed of a 1300 kg car moving east at 60 m/s and a 1500 kg car moving west at 95 m/s, is -64500 kg·m/s.