The CM of an empty 1200-kg car is 2.50 mbehind the front of the car. Part A How

Question

The CM of an empty 1200-kg car is 2.50 mbehind the front of the car.

Part A

How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.70 m from the front? Assume that each person has a mass of 80.0 kg .

Express your answer to three significant figures and include the appropriate units.

The CM of an empty 1200-kg car is 2.50 mbehind the front of the car.

Part A

How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.70 m from the front? Assume that each person has a mass of 80.0 kg .

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

the position of the center of mass, xcm, is given by

x cm = (x1 m1 + x2 m2 + x3 m3)/total mass

m1, m2, m3 are the different masses
x1,x2,x3 are the positions of the three masses

Here n=3, X1=2.5 m, X2=2.8 m, X3=3.7 m

M1=1200 kg, M2=2*80 kg, M3=3*80 kg

for this case, we will treat the two people in the front seat as one person of 160kg 2.80 m from the front of the car, and the back seat has one person of 240 kg who is 3.70m from the front of the car

we will set x=0 to coincide with the front of the car, so we have

x cm = (1200kg x 2.50 m + 160kg x 2.80m + 240 kg x 3.70 m)/(1200kg + 160 kg+ 240kg)

x = 2.71cm

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