Question
Asked Nov 7, 2019

Problem 1:  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 xoffsetfrom 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. 

 
   

Part (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.
Expression   :
τ = __________________________________________

Select from the variables below to write your expression. Note that all variables may not be required.
αβθdghjkLmMnPtxoffset

Part (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.
Expression   :
τ = __________________________________________

Select from the variables below to write your expression. Note that all variables may not be required.
αβθdghjkLmMnPtxoffset

Part (c) Derive an expression for the torque applied by the board in terms of given quantities and variables available in the palette.
Expression   :
τ = __________________________________________

Select from the variables below to write your expression. Note that all variables may not be required.
αβθdghjkLmMnPtxoffset

Part (d) Determine the distance d in terms of ng, and the masses and lengths in the problem.
Expression   :
d = __________________________________________

Select from the variables below to write your expression. Note that all variables may not be required.
αβθdghjkLmMnPtxoffset

Part (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 variables available in the palette.
Expression   :
Fnet = __________________________________________

Select from the variables below to write your expression. Note that all variables may not be required.
αβθdghjkLmMnPtxoffset


HI
Хsset
Xoffset
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HI Хsset Xoffset

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check_circleExpert Solution
Step 1

(a)The torque is defined as the product of force and the perpendicular distance. Consider the figure in the question.

Hence the torque by the adult rider is.

L
ache'=nmxg
et
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L ache'=nmxg et

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Step 2

(b)Child will apply a clockwise torque and clockwise torque is taken as negative.

Hence the torque is.

+d-Xer
mg
Tchid
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+d-Xer mg Tchid

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Step 3

(c)The torque applied...

Doard -Mgd
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Doard -Mgd

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