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.
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To find the new position of the center of mass (CM) when people sit in the car, we need to calculate the total mass and the combined moments of the car and the people.
Let's start by finding the total mass. The empty car has a mass of 1300 kg. Additionally, we have two people in the front seat and three people in the back seat, each with a mass of 60 kg. Therefore, the total mass of the people is 2 * 60 kg (front seat) + 3 * 60 kg (back seat) = 240 kg.
The next step is to calculate the combined moments of the car and the people. We know that the CM of the empty car is 2.40 m behind the front of the car. We can calculate the moment of the car by multiplying its mass by the distance from the front of the car to its CM:
Moment of car = 1300 kg * 2.40 m = 3120 kg·m
Now, let's find the combined moment of the people. Since there are two people in the front seat, their combined moment is the sum of their individual moments:
Moment of people in front seat = 2 * 60 kg * 2.80 m = 336 kg·m
For the people in the back seat, we have three individuals. Therefore, their combined moment is the sum of their individual moments:
Moment of people in back seat = 3 * 60 kg * 3.80 m = 684 kg·m
Finally, we can find the new position of the CM by dividing the sum of the moments by the total mass:
New position of CM = (Moment of car + Moment of people) / (Mass of car + Mass of people)
= (3120 kg·m + 336 kg·m + 684 kg·m) / (1300 kg + 240 kg)
= 4140 kg·m / 1540 kg
≈ 2.688 m
Therefore, 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, the new position of the CM will be approximately 2.688 m from the front of the car.