A 1200-kg SUV is moving along a straight highway at 12.0 m/s. Another car, with

Question

A 1200-kg SUV is moving along a straight highway at 12.0 m/s. Another car, with mass 1800 kg and speed 20.0 m/s, has its center of mass 40.0 m ahead of the center of mass of the SUV

Find the position of the center of mass of the system consisting of the two cars.

Find the magnitude of the system’s total momentum, by using the given data.

Find the speed of the system’s center of mass.

Find the system’s total momentum, by using the speed of the center of mass.

Compare your results of parts B and D.

Explanation / Answer

mass of SUV m1 = 1200 kg

v1 = 12 m/s

mass of another car m2 = 1800 kg

v2 = 29 m/s

position of center of mas of car    x2 = 40 m

part(a)

position of the center of mass of the system

x = m2*x2/ (m1+m2)

x = 1800*40 / 1800+1200

x = 24 m     ahead of the SUV .

part(b)

p = m1*v1 + m2*v2

p = 1200*12 + 1800*20 = 50400 kg*m /s

part (c)

speed of center of mass

v = p /m1+m2

v = 50400 / 1200+1800

v = 16.8 m/s

part(d)

total momentum = total mass * speed of system's center of mass

total momentum = (1200+1800)*16.8

total momentum = 3000*16.8 = 50400 kg*m/s

part(e)

total momentum by using the given data is same as total momentum by using the speed of the center of mass.

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