Question

find the position of center of mass of a car whose total mass of 2 tons is split in the ratio 3:1 among the front half and back half of the car. assume the total length of the car is 2m​

Answer 1

Explanation:

We can analyze the situation as mass 6kg is at (1,2,3), another mass of 5kg at (−1,−2,0). We have to find the position of other mass of 5kg to be put say (x,y,z) so that the final center of mass is at (1,2,3)

x

CM

=

m

1

+m

2

+m

3

m

1

x

1

+m

2

x

2

+m

3

x

3

⟹1=

16

6×1+5×(−1)+5×x

⟹x=3m

y

CM

=

m

1

+m

2

+m

3

m

1

y

1

+m

2

y

2

+m

3

y

3

⟹2=

16

6×2+5×(−2)+5×y

⟹y=6m

z

CM

=

m

1

+m

2

+m

3

m

1

z

1

+m

2

z

2

+m

3

z

3

⟹3=

16

6×3+5×0+5×z

⟹z=6m

I hope it's helpful uh