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 the system, you need to calculate the weighted average position of the two masses. The center of mass can be found using the following formula:
x_cm = (m1 * x1 + m2 * x2) / (m1 + m2)
y_cm = (m1 * y1 + m2 * y2) / (m1 + m2)
Where:
- x_cm and y_cm are the x and y coordinates of the center of mass respectively.
- m1 and m2 are the masses of the two objects.
- (x1, y1) and (x2, y2) are the positions of the two objects respectively.
Let's plug in the given values:
m1 = 1.50 kg
(x1, y1) = (-2.55 m, 0)
m2 = 2.04 kg
(x2, y2) = (4.00 m, 4.00 m)
Calculating the x-coordinate of the center of mass:
x_cm = (1.50 kg * -2.55 m + 2.04 kg * 4.00 m) / (1.50 kg + 2.04 kg)
Calculating the y-coordinate of the center of mass:
y_cm = (1.50 kg * 0 + 2.04 kg * 4.00 m) / (1.50 kg + 2.04 kg)
Now, let's calculate the values:
x_cm = (-3.825 kg·m + 8.16 kg·m) / 3.54 kg
y_cm = (0 kg·m + 8.16 kg·m) / 3.54 kg
x_cm = 4.085 m
y_cm = 2.313 m
Therefore, the center of mass of the system is (4.085 m, 2.313 m).