Two girls are sitting on the same side of a see-saw. One girl is 28 kg and sitting 2.4 m away from the middle. The other girl is 35 kg and 2.6 m away from the middle. Their dad can balance them out if he sits 2.0 m away from the middle on the other side. What is their dad's mass?
M= 79.1 kg because..
35*2.6 + 28*2.4= m*2
Helpful?
To find the dad's mass, we can use the principle of moments, which states that the anti-clockwise moment is equal to the clockwise moment for an object to be in equilibrium.
The moment of an object is calculated by multiplying its mass by the distance from the pivot point.
For the girls, their moments would be:
- Girl 1: 28 kg * 2.4 m = 67.2 kg·m
- Girl 2: 35 kg * 2.6 m = 91 kg·m
To balance the see-saw, the dad's moment should be equal to the sum of the girls' moments. Let's call the dad's mass "M" and his distance from the middle "x":
M * x = 67.2 kg·m + 91 kg·m
We know the distance from the middle of the see-saw is 2.0 m. Substituting the values, we have:
M * 2.0 m = 67.2 kg·m + 91 kg·m
2M = 67.2 kg + 91 kg
2M = 158.2 kg
Divide both sides by 2:
M = 79.1 kg
Therefore, the dad's mass is 79.1 kg.
To determine the dad's mass, we can use the principle of moments, where the sum of the moments on one side of an object is equal to the sum of the moments on the other side.
First, let's calculate the moments caused by the two girls. The moment of an object is calculated by multiplying its weight by its distance from the middle.
Girl 1: Moment = 28 kg * 2.4 m = 67.2 kg·m
Girl 2: Moment = 35 kg * 2.6 m = 91 kg·m
Next, let's solve for the dad's mass. Since the see-saw is balanced, the sum of the moments caused by the two girls must be equal to the moment caused by the dad.
Girl Moments = Dad Moment
67.2 kg·m + 91 kg·m = Dad Mass * 2.0 m
Now, we can solve the equation for the dad's mass:
158.2 kg·m = Dad Mass * 2.0 m
Dad Mass = 158.2 kg·m / 2.0 m
Dad Mass = 79.1 kg
Therefore, the dad's mass is 79.1 kg.