n Statics there are two conditions for equilibrium: First - Forces must sum to z
ID: 3163815 • Letter: N
Question
n Statics there are two conditions for equilibrium:
First - Forces must sum to zero
Fx = 0, Fy = 0
Second - Torques must sum to zero
= 0
You are going to set up these three equations for this system.
Use the following as variables:
Fh = Horizontal pivot force
Fv = Vertical pivot force
FT = Tension in the cable
m1 = mass of pole
m2 = mass of bell
= angle cable makes with pole
l = length of pole
x = distance of bell from wall
g = acceleration of gravity
1) Input your equation for the sum of forces in the y direction (vertical).
2) Input your equation for the sum of forces in the x direction (horizontal).
3) Input your equation for the sum of torques.
Look at the information tab to obtain the following variables:
m1, m2, and l
4) Plug in the numbers for m1, m2, l, g, and .
Solve your = 0 equation for F in terms of x.
This should come out as a linear relationship.
Input your equation for F in terms of x below.
5) Compare the coefficents of your equation for FT with the coefficents of your Tension vs Distance linear trendline equation.
How far is each term off, as a percent error?
6) Solve your Fx equation for Fh in terms of FT.
Plug in values for variables and plug in the equation FT in term of x used in Question 8 (for FT)
Solve this to obtain a linear equation for Fh in terms of x.
Input your equation for Fh in terms of x.
7) Compare the coefficients of your equation for Fh with the coefficents of your Horizontal Pivot Force vs Distance linear trendline equation.
How far is each term off, as a percent error?
8) Solve your Fy equation for Fv in terms of FT.
Plug in values for variables and plug in the equation FT in terms of x used in Question 8 (for FT).
Solve this to obtain a linear equation for Fv in terms of x.
Input your equation for Fv in terms of x.
9) Compare the coefficient of your equation for Fv with the coefficients of your Vertical Pivot Force vs Distance linear trendline equation.
How far is each term off as a percent error?
gravity tension pivot forces 0.20 distance of bell from wall (m) 0.70 distance of attachment point above hinge (m) tension 628 N horizontal pivot force 581 N vertical pivot force 839 NExplanation / Answer
A)
in the y direction
Fh + FT * sin() - (m1 + m2) * g = sum of forces in y direction
B) in the x direction
Fx - FT * cos() = sum of forces in x direction
C) for the sum of torques
FT * sin() * l - m1 * g * l/2 - m2 * g * x = sum of torque
D)
for the value of m1 and m2
FT * sin() * l - m1 * g * l/2 - m2 * g * x = 0
for FT
FT = (m1 * g * l/2 + m2 * g * x)/( sin() * l )
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