Answer:
10.787 cm towards the 0.675 kg mass or 41.213 cm from the 1.65 kg mass.
Explanation:
[tex]m_1[/tex] = Mass of potato salad container = 1.65 kg
[tex]m_2[/tex] = Mass of lemonade container = 2.35 kg
[tex]m_3[/tex] = Mass of hot dog package = 0.675 kg
l = Length of basket = 52 cm
x = Location of lemonade container
When the mass is balanced along the center of mass the following equation applies
[tex]-m_1\frac{l}{2}+m_2x+m_3\frac{l}{2}=0\\\Rightarrow x=\frac{m_1\frac{l}{2}-m_3\frac{l}{2}}{m_2}\\\Rightarrow x=\frac{1.65\frac{0.52}{2}-0.675\frac{0.52}{2}}{2.35}\\\Rightarrow x=0.10787\ m[/tex]
The lemonade container should be placed at 10.787 cm towards the 0.675 kg mass or 41.213 cm from the 1.65 kg mass.
The place she should place the 2.35-kg container of lemonade so that the basket balances at its center is = 10.787 cm towards the mass of 0.675kg.
The length of the basket= 52 cm= 0.52m
The center of gravity length= 26cm = 0.26m
Mass of the container of potatoes (M1)= 1.65kg
Mass of hot dogs (M2)= 0.675kg
Additional mass of lemonade (M3) = 2.35kg
Click wise rotation= Anticlockwise rotation
Fcw(m× d) = Facw (m ×d)
The distance to place the additional mass would be calculated from the part with a smaller mass,
(0.675× 0.26) + ( 2.35 × ?) = 1.65× 0.26
0.1755 + 2.35x = 0.429
2.35x = 0.429 - 0.1755
2.35x = 0.2535
X = 0.2535/2.35
X = 0.10787m = 10.787cm
Therefore, she should place the 2.35-kg container of lemonade so that the basket balances at its center is = 10.787 cm towards the mass of 0.675kg.
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