Answer:
A) d = 24 m
B) 50400 kg.m/s
C) v₀ = 16.8 m/s
D) 50400 kg.m/s. It's equal to the momentum found in part B.
Explanation:
We are given;
Mass of station wagon;m1 = 1200 kg Velocity; V = 12 m/s
Mass of car; m2 = 1800 kg
Velocity of car; v2 = 20 m/s
a ) Let centre of mass of car and station wagon be at a distance d from wagon
Thus,
If we take moment of weight about it, we have;
1200 x d = 1800 x ( 40 - d )
Where, d is the position of the center of mass of the system consisting of the two cars
Thus,
1200d = 72000 - 1800d
1200d + 1800d = 72000
3000 d = 72,000
d = 72,000/3000
d = 24 m
b ) Total momentum= m1•v1 + m2•v2
= (1200 x 12) + (1800 x 20)
= 14400 + 36000
= 50400 kg.m/s
c ) Let speed of centre of mass be v₀
Thus,
v₀ = (m1•v1 + m2•v2)/(m1 + m2)
v₀ = 50400/(1200 + 1800)
v₀ = 50400/3000
v₀ = 16.8 m/s
d) System Total momentum = velocity of centre mass x total mass
Thus,
Total momentum = v₀(m1 + m2)
= 16.8(3000) = 50400 kg.m/s .
This value is equal to what was calculated in part b
