You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M, length L) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset from the end of the board when seated as shown. You have selected a child of mass m (shown on the right), and an adult of mass n times the mass of the child (shown on the left) to test out your prototype. (a) Derive an expression for the torque applied by the adult rider (on the left) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive. (b) Derive an expression for the torque applied by the child rider (on the right) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive. (c) Derive an expression for the torque applied by the board in terms of given quantities and variables available in the palette. (d) Determine the distance d in terms of n, g, and the masses and lengths in the problem. (e) Determine the magnitude of the force exerted on the pivot point by the see-saw while in use in terms of given quantities and Xoffset Xoffset ©theexpertta.com variables available in the palette.
You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M, length L) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset from the end of the board when seated as shown. You have selected a child of mass m (shown on the right), and an adult of mass n times the mass of the child (shown on the left) to test out your prototype. (a) Derive an expression for the torque applied by the adult rider (on the left) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive. (b) Derive an expression for the torque applied by the child rider (on the right) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive. (c) Derive an expression for the torque applied by the board in terms of given quantities and variables available in the palette. (d) Determine the distance d in terms of n, g, and the masses and lengths in the problem. (e) Determine the magnitude of the force exerted on the pivot point by the see-saw while in use in terms of given quantities and Xoffset Xoffset ©theexpertta.com variables available in the palette.
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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Transcribed Image Text:You have been hired to design a family-friendly see-saw. Your design
will feature a uniform board (mass M, length L) that can be moved so that the pivot is a
distance d from the center of the board. This will allow riders to achieve static equilibrium
even if they are of different mass, as most people are. You have decided that each rider will
be positioned so that his/her center of mass will be a distance xoffset from the end of the
board when seated as shown.
You have selected a child of mass m (shown on the right), and an adult of mass n times the
mass of the child (shown on the left) to test out your prototype.
(a) Derive an expression for the torque applied by the adult rider (on the left) in terms of given
quantities and variables available in the palette. Assume counterclockwise is positive.
(b) Derive an expression for the torque applied by the child rider (on the right) in terms of
given quantities and variables available in the palette. Assume counterclockwise is positive.
(c) Derive an expression for the torque applied by the board in terms of given quantities and variables available in the palette.
(d) Determine the distance d in terms of n, g, and the masses and lengths in the problem.
(e) Determine the magnitude of the force exerted on the pivot point by the see-saw while in use in terms of given quantities and
Xoffset
Xoffset
©theexpertta.com
variables available in the palette.
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