A mass of 1.50 kg is at
(−2.55 m, 0)
and a 2.04-kg mass at
(4.00 m, 4.00 m).
Find the center of mass of the system.
m, m
To find the center of mass of a system, we need to take into account the masses and positions of the objects in the system.
The center of mass of a system is the point at which the total mass of the system is evenly distributed. Mathematically, it can be calculated using the following formula:
x_cm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)
y_cm = (m1y1 + m2y2 + ... + mnyn) / (m1 + m2 + ... + mn)
Where x_cm and y_cm are the x and y coordinates of the center of mass, m1, m2, ..., mn are the masses of the objects, and x1, x2, ..., xn and y1, y2, ..., yn are their respective positions.
In this case, we have two masses with their respective positions:
m1 = 1.50 kg
x1 = -2.55 m
y1 = 0
m2 = 2.04 kg
x2 = 4.00 m
y2 = 4.00 m
Let's calculate the center of mass using the formula:
x_cm = (m1x1 + m2x2) / (m1 + m2)
y_cm = (m1y1 + m2y2) / (m1 + m2)
Substituting the given values:
x_cm = (1.50 kg * -2.55 m + 2.04 kg * 4.00 m) / (1.50 kg + 2.04 kg)
y_cm = (1.50 kg * 0 + 2.04 kg * 4.00 m) / (1.50 kg + 2.04 kg)
Calculating further:
x_cm = (-3.825 kg * m + 8.16 kg * m) / 3.54 kg
y_cm = (0 + 8.16 kg * m) / 3.54 kg
x_cm = 4.335 m
y_cm = 2.305 m
Therefore, the center of mass of the system is at approximately (4.335 m, 2.305 m).