You and your friend see kids playing on a seesaw. The two kids are balancing without their feet touching the ground. Your friend says that there is no way that a mother and daughter could do the same thing. You are not sure if that is true. Use what you know about the different types of variation to figure out how a mother and child could balance. Use the Lever Tool to verify the data, and then use what you know about variation to model the relationship between weight and distance from the fulcrum.

1. Use the Lever Tool to verify each weight and distance pair given in the video for your seesaw. Write the values in the table below. (Note: The pan on the lever weighs 100 units!) (1 point)
A: B:
Analyzing your data

2. Use the data from the table to make a graph. (3 points: 1 point each for labels, coordinates, and sketch)

3. Does it look as though there is a relationship between the weight and its distance from the fulcrum? What type of variation is there (if any)? Support your answer. (1 point)

4. Write an equation that models your data. Use variables of weight, W, and distance, D. (You will have to use one of your data points to find your constant of variation.) (3 points: 1 point for the general form of variation, 1 point for the constant of variation, and 1 point for the final equation)

5. The Lever Tool helps find values that will balance your seesaw, but it has limited range and precision. Use your graph to estimate a coordinate (W, D) that:

balances your seesaw
you could not simulate with the Lever Tool
To verify that your values are reasonable, substitute your coordinate into the equation you found in question 4. Is the coordinate you picked a good solution?
(3 points: 1 point for a value that cannot be shown on the Lever Tool, 1 point for the correct substitution, and 1 point for verification)

A new balance

Your turn: Choose a new fixed weight and fixed difference that are different from the one for the seesaw you selected. (Reminder: Seesaw A has a fixed weight of 600 units and a fixed distance of 150 units. Seesaw B has a fixed weight of 100 units and a fixed distance of 120 units.)

6. What new values did you pick? (1 point)

7. With your new constant values on one side of the seesaw, use the Lever Tool to find 5 new pairs of weights and distances that balance the seesaw. Record these values in the table below. (Reminder: The pan on the lever weighs 100 units!) (2 points)
Weight
Distance

8. Now use the table to sketch a graph. (3 points: 1 point each for labels, coordinates, and sketch)

9. Write an equation that represents your data and graph. Write your equation in terms of weight, W, and distance, D. (You will have to use one of your data points or your fixed point to find your constant of variation.) (3 points: 1 point for the general form of variation, 1 point for the constant of variation, and 1 point for the final equation)

Everybody on!
On a different playground, a woman and her two children are playing on a seesaw. This seesaw has seats that can move to different distances from the fulcrum. Riders can also add seats to the seesaw.
The woman weighs 145 pounds.
Her son weighs 95 pounds.
Her daughter weighs 70 pounds.
Each seat weighs 5 pounds.
10. The woman sits 48 inches to the left of the fulcrum. Her son balances the seesaw when he sits 72 inches to the right of the fulcrum.
Find the constant of variation for this seesaw. Show your work. (2 points)

11. The woman stays in the same location, but her son gets off the right side of the seesaw and her daughter gets on. The daughter adjusts the seat until she balances with her mother. How far from the fulcrum is the daughter when she balances with her mother? Show your work. (2 points)

We need to torque.
Torque is a force that produces a rotation. In a seesaw, the torque is the weight of an object times its distance from the fulcrum. Clockwise torques are negative, and counterclockwise torques are positive. To balance the seesaw, the sum of all torques must be 0.
12. The woman is on the left side of the seesaw, 60 inches from the fulcrum. The daughter and son both get on the right side. The son sits 60 inches from the fulcrum. Where should the daughter sit to balance the seesaw? Explain your reasoning and show your work. (6 points: 3 points for the location of the daughter and 3 points for the explanation)