Answer:
Step-by-step explanation:
To calculate the new center of gravity (CG) location after changing the values, we can use the principle of moments. The center of gravity is the point where the weight of an object can be considered to act. It can be calculated by taking moments about a reference point.
Let's assume the reference point is the left end of the teeter-totter (or the pivot point). The original scenario has a 20 kg box at a distance of 0.6 meters from the pivot and a 10 kg box at a distance of 0.4 meters from the pivot.
To find the CG location, we multiply the mass of each object by its distance from the pivot, then sum up these moments and divide by the total mass. Mathematically:
CG = (m1 * d1 + m2 * d2) / (m1 + m2)
where m1 and m2 are the masses of the boxes, and d1 and d2 are their respective distances from the pivot.
Original scenario:
m1 = 20 kg
d1 = 0.6 meters
m2 = 10 kg
d2 = 0.4 meters
Calculating the CG location for the original scenario:
CG = (20 kg * 0.6 meters + 10 kg * 0.4 meters) / (20 kg + 10 kg)
= (12 + 4) / 30
= 16 / 30
= 0.5333 meters
Therefore, in the original scenario, the center of gravity is located at approximately 0.5333 meters from the pivot point.
Now, if we change the scenario by replacing the 20 kg box with a 30 kg box and changing the distance to 0.4 meters, we can recalculate the CG location:
New scenario:
m1 = 30 kg
d1 = 0.4 meters
m2 = 10 kg
d2 = 0.4 meters
Calculating the new CG location:
CG = (30 kg * 0.4 meters + 10 kg * 0.4 meters) / (30 kg + 10 kg)
= (12 + 4) / 40
= 16 / 40
= 0.4 meters
Therefore, in the new scenario, the center of gravity is located at 0.4 meters from the pivot point.