Question
Asked Nov 25, 2019
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You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M = 7 kg, length L = 7 m) 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 = 11 cm from the end of the board when seated as shown.

You have selected a child of mass m = 29 kg (shown on the right), and an adult of mass n =3 times the mass of the child (shown on the left) to test out your prototype. d=1.59m

Determine the magnitude of the force exerted on the pivot point by the see-saw in N. 

.
offset
Xoffset
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. offset Xoffset

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Expert Answer

Step 1

Given data:

Mass of the board, M = 7 kg.

Length of the board, L =  7 m

Xoffset = 11 cm = 0.11 m

Mass of the child, m1 = 29 kg

Mass of the adult, m2 = 3 x 29 = 87 kg

X1
X2
0.11 m
0.11 m
d
Mg
mig
m2g
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X1 X2 0.11 m 0.11 m d Mg mig m2g

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Step 2

From fig.

X1 = L / 2 -  Xoffset – d  = 7 /2 – 0.11 – d = 3.39 - d

X2 = L /2 + d - Xoffset = 7 /2 + 0.11 – d = 3.61 - d

Step 3

Taking moment about the pivot:

...
т,gx, - т,gx, —Mgd %3D 0
Ма %3 т,gx, — т,gx,
Ма - т, х (3.61 —- d)-т, x (3.39 — d)
7xd387x3.61-87хd-29х3.39 + 29 хd
=-58d215.76
65d 215.76
d 3.31 m
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т,gx, - т,gx, —Mgd %3D 0 Ма %3 т,gx, — т,gx, Ма - т, х (3.61 —- d)-т, x (3.39 — d) 7xd387x3.61-87хd-29х3.39 + 29 хd =-58d215.76 65d 215.76 d 3.31 m

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