The CM of an empty 1170 kg car is 2.50 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 2.8 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 73 kg.
CM*totalmass=CM1*m1+CM2*m1+CM2*m3
CM(1170+2*73+2*73)=1170*2.5+2*73*2.8+2.&3*3.9
solve for CM.
thank you so much!
2.6cm
To find the new position of the center of mass (CM) of the car after two people sit in the front seat and three people sit in the back seat, we can follow these steps:
Step 1: Find the current position of the car's center of mass (CM):
Given:
- Mass of the empty car (m_car) = 1170 kg
- Distance of the empty car's CM from the front (x_car) = 2.50 m
Step 2: Find the total mass of the people sitting in the car:
Given:
- Mass of each person (m_person) = 73 kg
Total mass of two people sitting in the front seat (m_front) = m_person * 2
Total mass of three people sitting in the back seat (m_back) = m_person * 3
Step 3: Find the center of mass for the two groups of people:
Given:
- Distance of the front seat from the front of the car (x_front) = 2.8 m
- Distance of the back seat from the front of the car (x_back) = 3.90 m
Center of mass for the two people in the front seat (CM_front) = (m_person * 2 * x_front) / (m_person * 2)
Center of mass for the three people in the back seat (CM_back) = (m_person * 3 * x_back) / (m_person * 3)
Step 4: Find the total mass and new center of mass of the car:
Total mass of the car with people (m_total) = m_car + m_front + m_back
New center of mass (CM_total) = (m_car * x_car + m_front * CM_front + m_back * CM_back) / m_total
Now, let's substitute the given values into the equations and calculate the answer:
Step 1:
m_car = 1170 kg
x_car = 2.50 m
Step 2:
m_person = 73 kg
m_front = 73 kg * 2 = 146 kg
m_back = 73 kg * 3 = 219 kg
Step 3:
x_front = 2.8 m
x_back = 3.90 m
CM_front = (73 kg * 2 * 2.8 m) / (73 kg * 2)
CM_back = (73 kg * 3 * 3.90 m) / (73 kg * 3)
Step 4:
m_total = 1170 kg + 146 kg + 219 kg
CM_total = (1170 kg * 2.50 m + 146 kg * CM_front + 219 kg * CM_back) / (1170 kg + 146 kg + 219 kg)
After performing the calculations, the final answer will be the value of CM_total, which represents the new distance from the front of the car where the center of mass will be located.