Question

You are holding a shopping basket at the grocery store with two 0.64-kg cartons of cereal at the left end of the basket. The basket is 0.91 m long. Part A Where should you place a 1.9-kg half gallon of milk, relative to the left end of the basket, so that the center of mass of your groceries is at the center of the basket? Express your answer using two significant figures.

Answer 1

Mass of each carton of cereal = m₁ = 0.64 kg

Number of cartons of cereal = n = 2

Position of the cartons of cereal from the left end = X₁ = 0 m

Mass of the half gallon of milk = m₂ = 1.9 kg

Position of the half gallon of milk from the left end = X₂

Length of the basket = L = 0.91 m

The center of mass of the groceries is maintained at the center of the basket.

Center of mass of the groceries from the left end = X_cm = L/2 = 0.91/2 = 0.455 m

A) Position of the 1.9 kg half gallon of milk relative to the left end of the basket = 0.762 m