our objects are situated along the y axis as follows: a 1.94 kg object is at +3.27 m, a 2.76 kg object is at +2.18 m, a 2.78 kg object is at the origin, and a 3.99 kg object is at -0.360 m. Where is the center of gravity of this system?
Add the four mass x position products and divide by the total mass.
[1.94*3.27 + 2.76*2.18 + 2.78*0 - 3.99*0.360]/11.47 = ___ m
To find the center of gravity of a system of objects, you need to calculate the weighted average position of each object. This can be done by considering both the mass and position of each object.
First, multiply the mass of each object by its position:
Object 1: 1.94 kg * 3.27 m = 6.34 kg⋅m
Object 2: 2.76 kg * 2.18 m = 6.01 kg⋅m
Object 3: 2.78 kg * 0 m = 0 kg⋅m (since it is at the origin)
Object 4: 3.99 kg * (-0.360) m = -1.43 kg⋅m
Next, sum up all the weighted positions:
6.34 kg⋅m + 6.01 kg⋅m + 0 kg⋅m + (-1.43 kg⋅m) = 11.92 kg⋅m
Finally, divide the total weighted position by the total mass of the system to get the center of gravity:
Center of gravity position = 11.92 kg⋅m / (1.94 kg + 2.76 kg + 2.78 kg + 3.99 kg) = 11.92 kg⋅m / 11.47 kg ≈ 1.040 m
Therefore, the center of gravity of this system is located at approximately +1.040 m along the y-axis.