Does distance affect torque in hanging sign problem?

[paulimerci]

Yes. Find an expression for $R_y$ containing $x$. Then substitute $x=1.00$ m and see if you get the answer that you already got in part (b).

Correction to your work: The right chain should be $x+0.3~$m.

Okay, if there are changes in distances does the values of $T_c$, $T_L$, and $T_R$ remains the same? If there is no change, then in the torque equation can I substitute for the values i calculated earlier for $T_c$, $T_L$, $T_R$?

 

[paulimerci]

Okay, if there are changes in distances does the values of $T_c$, $T_L$, and $T_R$ remains the same? If there is no change, then in the torque equation can I substitute for the values i calculated earlier for $T_c$, $T_L$, $T_R$?

$$\sum\tau= T_c \cdot d_c-Mg \cdot d_B-T_L \cdot x-T_R \cdot (x+0.30)$$
$$1.2 \cdot T_c = 27.2+ 13 \cdot x + 13 \cdot(x+0.3)$$
$$T_c = \frac {31.1 +26 \cdot x} {1.2}$$
Substitute $T_c$ in the equation of $R_y$ we get,
$$ R_y = Mg +T_L+T_R-T_c$$
$$ R_y = 34+13+13- \frac{31.1+26\cdot x} {1.2}$$
$$ R_y = 60 - \frac{31.1+26\cdot x} {1.2}$$
have I done it right?

 

[kuruman]

Very good. Now you can answer parts (c) and (d) based on the equation you derived for $R_y.$

 

[paulimerci]

Very good. Now you can answer parts (c) and (d) based on the equation you derived for $R_y.$

Thanks for your guidance.
Part C,
Therefore, from the equation of $R_y$ we can justify that as the distance of the sign is moved farther away from the wall, the magnitude of the force on the hinge decreases.

 

[kuruman]

Thanks for your guidance.
Part C,
Therefore, from the equation of $R_y$ we can justify that as the distance of the sign is moved farther away from the wall, the magnitude of the force on the hinge decreases.

Correct. Now for the plot. Use a spreadsheet if you know how.

 

[paulimerci]

Correct. Now for the plot. Use a spreadsheet if you know how.

 

[kuruman]

I think you're done. Congratulations! I hope you learned something from this experience.

 

[paulimerci]

View attachment 317979

Looks like I plotted for $T_c$ vs $x$. S

I think you're done. Congratulations! I hope you learned something from this experience.

Definitely! It was a humongous problem and I didn't believe I can do it and I thank you so much for guiding me throughout! Thanks to @haruspex for his guidance too!