A freight car with a mass of 10 metric tons is rolling at 108 km/h along a level track when it collides with another freight car, which is initially at rest. If the speed of the cars after they couple together is 36 km/h, what is the mass of the second car?

20 metric tons

Explanation:

Using the Principle of Conservation of Linear Momentum which states that the total momentum of a system is constant in any direction in which no external force acts.

momentum before collision = momentum after collision

mathematically expressed as

m1u1 + m2u2 = m1v1+m2v2 = 0

where:

m1 = mass of rolling freight car = 10 metric tons = 10Mg

1 ton = 1000kg = 1Mg

u1 = initial velocity of freight car = 108km/h,

m2 = mass of stationary freight car = ?, this the unknown we are finding

u2 = initial velocity of

m2 = 0, because it is at rest,

v1 = final velocity of m1,

v2 = final velocity of m2

since they move together in the same direction they share a common final velocity as such

v1=v2 = 36km/h

substituting valves in expression give

m1u1 + m2u2 = m1v1 + m2v2 = 0

10Mgx 108km/hr + m2 x 0 = 10Mg x 36km/h + m2x36km/h

1080 (Mg x km/hr) + 0 = 360 (Mg x Km/h) + 36m2 (km/h)

1080 (Mgx km/hr) - 360 (Mg x km/h) = 36m2 (km/h)

720 (Mg x km/h) = 36m2 (km/h)

divide both side by 36 (km/h) gives

m2 = 20Mg = 20 metric tons