91影视

1. From figure and data, radius= Rand pressure= p
2. Radius of hemisphere,$R=30cm$
3. Inside pressure,$p_i=0.10atm$
4. Outside pressure, $p_0=1.00atm$

We use the concept of pressure to find the force by integrating the formula of it concerning pressure and covered area. Also, we find the value of the force by using the values.

Formula:

Pressure on the body by force F on an area A,

$p=\frac{F}{A}$ (i)

Let鈥檚 assume that the team of horses is pulling the sphere towards the right. To pull the sphere apart, it must exert a force equal to the horizontal component of the total force. This can be found by the integration of force and component of each force.

Consider the force vector at angle$胃$. Since pressure, $鈭�p=F/A$from equation (i), we can write the leftward component of force as $\left(鈭�p\right)\cos 胃\left(dA\right)$

Here, dA is the area at which the force is applied. We can consider the symmetry; so let dA be that of the ring of constant $胃$on the surface.

Radius of the ring is $r=R\sin 胃$, R is the radius of the sphere; if the angular width of the ring is $d胃$then its width is $Rd胃$and its area is $dA=2蟺R^2\sin 胃d胃$.

Thus, the net horizontal component of force of air is

$$\begin{gathered} F_k=2蟺R^2鈭�p{鈭�}_0^{\frac{\mathrm{蟺}}{2}}\mathrm{蝉颈苍胃肠辞蝉胃}d\mathrm{胃} \\ ={\left|{\mathrm{蟺搁}}^2鈭�{\mathrm{psin}}^2\mathrm{胃}\right|}_0^{\frac{\mathrm{蟺}}{2}} \\ =蟺R^2鈭�p.............................\left(1\right) \end{gathered}$$

Hence, the derived expression for force is $蟺R^2鈭�p$

$$\begin{gathered} 鈭�p=p_o-p_i \\ =\left(1-0.10\right)atm \\ =0.90atm \\ =9.09脳{10}^{4}Pa\left(鈭�1atm=1.01脳{10}^{5}Pa\right) \end{gathered}$$

Hence, the magnitude of force using equation ( 1) can be given as:

$$\begin{gathered} F_h=\mathrm{蟺}{\left(0.30\right)}^2\left(9.09脳{10}^4\right) \\ =2.6脳{10}^{4}N \end{gathered}$$

Hence, the magnitude of force is$2.6脳{10}^{4}N$

One team of horses could be used if one half of the sphere was attached to a sturdy wall.

Hence, the force of the wall on the sphere balances the force of the horses.