An old Chrysler with mass 1900 kg is moving along a straight stretch of road at 48 km/h. It is followed by a Ford with mass 1500 kg moving at 65 km/h. How fast is the center of mass of the two cars moving?
m1v1 + m2v2= (m1+m2)vcm
solve for vcm
55.5
98998
To find the speed of the center of mass (vcm) of the two cars, we can use the equation:
m1v1 + m2v2 = (m1 + m2)vcm
where m1 and m2 are the masses of the Chrysler and the Ford, v1 and v2 are their respective velocities, and vcm is the velocity of the center of mass.
Given:
m1 = 1900 kg (mass of the Chrysler)
v1 = 48 km/h (velocity of the Chrysler)
m2 = 1500 kg (mass of the Ford)
v2 = 65 km/h (velocity of the Ford)
Substituting these values into the equation:
(1900 kg)(48 km/h) + (1500 kg)(65 km/h) = (1900 kg + 1500 kg)vcm
91400 kg·km/h + 97500 kg·km/h = 3400 kg·vcm
188900 kg·km/h = 3400 kg·vcm
Now, to solve for vcm, we divide both sides of the equation by the total mass of the system (m1 + m2):
vcm = (188900 kg·km/h) / (3400 kg)
vcm ≈ 55.5 km/h
Therefore, the center of mass of the two cars is moving at approximately 55.5 km/h.