Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is W, is sitting at distance L to the left of the pivot, at what distance L1 should Marcel place Gilles, whose weight is w, to the right of the pivot to balance the seesaw? (figure 1) Part A) Express your answer in terms of L, W, and w. Part B) Now consider this problem as a more formal introduction to torque. The torque of each child about the pivot point is the product of the child's weight and the distance from the pivot to the child's center of mass (center of gravity.) The sign of the torque is taken to be positive by convention if it would cause a counterclockwise rotation of the seesaw. The distance is measured perpendicular to the line of force and is called the moment arm. (figure 1) Find the torque τ about the pivot due to the weight w of Gilles on the seesaw. Part C) Marcel wants the seesaw to balance, which means that there can be no angular acceleration about the pivot. For the angular acceleration to be zero, the sum of the torques about the pivot must equal zero: (figure 1) ∑τ=0 Determine ∑τ, the sum of the torques on the seesaw. Consider only the torques exerted by the children. Part D) Gilles has an identical twin, Jean, also of weight w. The two twins now sit on the same side of the seesaw, with Gilles at distance L2 from the pivot and Jean at distance L3 . (Figure 2) Where should Marcel position Jacques to balance the seesaw?
Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is W, is sitting at distance L to the left of the pivot, at what distance L1 should Marcel place Gilles, whose weight is w, to the right of the pivot to balance the seesaw? (figure 1) Part A) Express your answer in terms of L, W, and w. Part B) Now consider this problem as a more formal introduction to torque. The torque of each child about the pivot point is the product of the child's weight and the distance from the pivot to the child's center of mass (center of gravity.) The sign of the torque is taken to be positive by convention if it would cause a counterclockwise rotation of the seesaw. The distance is measured perpendicular to the line of force and is called the moment arm. (figure 1) Find the torque τ about the pivot due to the weight w of Gilles on the seesaw. Part C) Marcel wants the seesaw to balance, which means that there can be no angular acceleration about the pivot. For the angular acceleration to be zero, the sum of the torques about the pivot must equal zero: (figure 1) ∑τ=0 Determine ∑τ, the sum of the torques on the seesaw. Consider only the torques exerted by the children. Part D) Gilles has an identical twin, Jean, also of weight w. The two twins now sit on the same side of the seesaw, with Gilles at distance L2 from the pivot and Jean at distance L3 . (Figure 2) Where should Marcel position Jacques to balance the seesaw?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is W, is sitting at distance L to the left of the pivot, at what distance L1 should Marcel place Gilles, whose weight is w, to the right of the pivot to balance the seesaw?
(figure 1)
Part A)
Express your answer in terms of L, W, and w.
Part B)
Now consider this problem as a more formal introduction to torque. The torque of each child about the pivot point is the product of the child's weight and the distance from the pivot to the child's center of mass (center of gravity.) The sign of the torque is taken to be positive by convention if it would cause a counterclockwise rotation of the seesaw. The distance is measured perpendicular to the line of force and is called the moment arm.
(figure 1)
Find the torque τ about the pivot due to the weight w of Gilles on the seesaw.
Part C)
Marcel wants the seesaw to balance, which means that there can be no angular acceleration about the pivot. For the angular acceleration to be zero, the sum of the torques about the pivot must equal zero: (figure 1)
∑τ=0
Determine ∑τ, the sum of the torques on the seesaw. Consider only the torques exerted by the children.
Part D)
Gilles has an identical twin, Jean, also of weight w. The two twins now sit on the same side of the seesaw, with Gilles at distance L2 from the pivot and Jean at distance L3
. (Figure 2)
Where should Marcel position Jacques to balance the seesaw?
Transcribed Image Text:L.
L1
Transcribed Image Text:L3
L
L2
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