Question

Two children weighing 40 lbs and 50 lbs each are balancing their teacher weighing 120 lbs on a seesaw. The teacher is sitting 5 feet from the fulcrum, and the child weighing 50 lbs is seated 8 feet from the fulcrum. Find the distance (in feet) from the fulcrum where the child weighing 40 lbs should taker her place.

Answer 1

The child weighing 40 lbs should sit 5 feet from the fulcrum to balance the seesaw. This is determined by equating the torques on both sides of the seesaw and solving for the unknown distance.

Step-by-step explanation:

The question asks how to balance two children and their teacher on a seesaw based on their distances from the fulcrum and their weights. This problem requires an understanding of torques and the concept of equilibrium in physics, but within the context of mathematics, we are applying algebraic methods to solve for an unknown distance.

The torque (τ) produced by a force is given by the equation τ = r × F, where r is the distance to the fulcrum and F is the weight or force due to gravity. To balance the seesaw, the total torque on one side must equal the total torque on the other side. Considering the teacher as one side and the two children as the other side, we are given:

• Teacher's weight (F1) = 120 lbs
• Teacher's distance from fulcrum (r1) = 5 ft
• First child's weight (F2) = 50 lbs
• First child's distance from fulcrum (r2) = 8 ft

To find the second child's distance from the fulcrum (r3), we would set up the equation: F1 × r1 = (F2 × r2) + (F3 × r3), where F3 is the weight of the second child (40 lbs), and solve for r3.

120 lbs × 5 ft = (50 lbs × 8 ft) + (40 lbs × r3)

600 lbs-ft = 400 lbs-ft + (40 lbs × r3)

We then isolate r3:

600 lbs-ft - 400 lbs-ft = 40 lbs × r3

200 lbs-ft = 40 lbs × r3

r3 = 200 lbs-ft / 40 lbs

r3 = 5 ft

Therefore, the child weighing 40 lbs should sit 5 feet from the fulcrum to balance the seesaw.

Answer 2

5 feet

Step-by-step explanation:

First lets imagine that the values are in meters and kg, to make it easier for me.

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The force created by the teacher is 120 × 5 = 600N.

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The force created by the 50 kg student is 50 × 8 = 400N

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The force that needs to be created by the 40 kg student is 600N - 400N = 200N.

To create that force that student needs to sit 200 ÷ 40 = 5m.

So the 40 lbs student is sitting 5 feet from the fulcrum.