Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A person carries a plank of wood 1.9 m long with one hand pushing down on it at one end with a force F1 and the other hand holding it up at 56 cm from the end of the plank with force F2. If the plank has a mass of 15 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces F1 and F2? (The distance of 56 cm is measured from the location of F1.)F1 = F2 =

Sagot :

We will have the following:

[tex]\sum\tau=0[/tex]

Thus, assuming the axis of rotation is at F1, we will have that:

[tex]\tau_2-\tau_3\Rightarrow\tau_2=\tau_3[/tex]

Then:

[tex]\begin{gathered} r_2F_2=r_3F_3\Rightarrow F_2=\frac{r_3F_3}{r_2} \\ \\ \Rightarrow F_2=\frac{(0.95m)(15kg\ast9.8m/s^2)}{0.56m}\Rightarrow F_2=249.375N \end{gathered}[/tex]

So, the magnitude of F2 is 249.375 N.

Now, since the system is in equilibrium we will have that:

[tex]\begin{gathered} \sum F=0=-F_1+F_2-F_3=0 \\ \\ \Rightarrow F_1=F_2-F_3\Rightarrow F_1=(249.375N)-(15kg\ast9.8m/s^2) \\ \\ \Rightarrow F_1=102.375N \end{gathered}[/tex]

So, the magnitude of F1 is 102.375 N.

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.