Question

Alice is going on a picnic and is aware that it will be easier to carry the picnic basket if it balances at the center where the handle is attached. She has placed a 1.65-kg container of potato salad at one end and a 0.675-kg package of hot dogs at the other end of a 52.0-cm long basket. Determine where she should place a 2.35-kg container of lemonade so that the basket balances at its center.

Answer 1

Answer:

10.787 cm towards the 0.675 kg mass or 41.213 cm from the 1.65 kg mass.

Explanation:

$m_1$ = Mass of potato salad container = 1.65 kg

$m_2$ = Mass of lemonade container = 2.35 kg

$m_3$ = 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

$-m_1\frac{l}{2}+m_2x+m_3\frac{l}{2}=0\\\Rightarrow x=\frac{m_1\frac{l}{2}-m_3\frac{l}{2}}{m_2}\\\Rightarrow x=\frac{1.65\frac{0.52}{2}-0.675\frac{0.52}{2}}{2.35}\\\Rightarrow x=0.10787\ m$

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.