The CM of an empty 1300 kg car is 2.40 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.80 m from the front? Assume that each person has a mass of 60.0 kg.
I will be happy to critique your work.
nju
To find the new position of the center of mass (CM) of the car with people sitting in it, we need to consider the mass and position of each individual, as well as the original position of the empty car's CM.
Let's start by calculating the CM of the empty car.
Given:
Mass of the empty car (m1) = 1300 kg
Position of the CM of the empty car (d1) = 2.40 m behind the front of the car
Next, let's calculate the CM of the people sitting in the car.
Number of people in the front seat (n1) = 2
Mass of each person in the front seat (m2) = 60.0 kg
Position of the front seat (d2) = 2.80 m from the front of the car
Number of people in the back seat (n3) = 3
Mass of each person in the back seat (m3) = 60.0 kg
Position of the back seat (d3) = 3.80 m from the front of the car
To find the new position of the CM, we can use the formula:
CM = (m1 * d1 + m2 * d2 + m3 * d3) / (m1 + n1 * m2 + n3 * m3)
Let's calculate the new position of the CM.
CM = (1300 kg * 2.40 m + 2 * 60.0 kg * 2.80 m + 3 * 60.0 kg * 3.80 m) / (1300 kg + 2 * 60.0 kg + 3 * 60.0 kg)
CM = (3120 kg*m + 336 kg*m + 684 kg*m) / (1300 kg + 120 kg + 180 kg)
CM = 4140 kg*m / 1600 kg
CM = 2.5875 m
Therefore, when two people sit in the front seat and three people sit in the back seat, the center of mass will be located 2.59 m from the front of the car.