Q12P In Figure (a), particle聽A聽is f... [FREE SOLUTION]

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Chapter 13: Q12P (page 379)

In Figure (a), particleAis fixed in place at $x = - 0.20 m$ on thexaxis and particleB, with a mass of 1.0 kg, is fixed in place at the origin. ParticleC(not shown) can be moved along thexaxis, between particleBand $x = 鈭�$ .Figure (b)shows thexcomponent $F_{net, x}$ of the net gravitational force on particleBdue to particlesAandC, as a function of positionxof particleC. The plot actually extends to the right, approaching an asymptote of $鈭� 4 .17 脳 10^{10} N$ as $鈫� 鈭�$ . What are the masses of (a) particleAand (b) particleC?

Short Answer

Expert verified

a) The mass of particle A is $0.25 鈥刱驳$

b) The mass of particle B is $1 鈥刱驳$

Step by step solution

The given data

a) Mass of particle B, $m_{B} = 1 鈥刱驳$

b) Distance of particle A from origin, $x_{A} = 0.2 鈥刴(蹿谤辞尘蹿颈驳耻谤别)$

c) Distance of particle B from origin, $x_{B} = 0 鈥刴$

d) Distance of particle C from origin, $x_{C} = 0.4 m(fromfigure)$

e) Gravitational constant, $G = 6.67 脳 10^{鈭� 11} 鈥凬鈰� m^{2} {/kg}^{2}$

Understanding the concept of Newton’s Gravitational law

Force between two masses can be calculated by using Newton鈥檚 law of gravitation. According to Newton鈥檚 law of gravitation, the force of two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Formula:

Gravitational force, $F = \frac{G M m}{r^{2}}$ .......(i)

(a) Calculating the mass of particle A

Using equation (i),Force between mass A & B can be written as:

$\begin{matrix} F_{A B} = \frac{G m_{A} m_{B}}{{x_{A}}^{2}} \\ 4.17 脳 10^{鈭� 10} 鈥夆赌塏 = \frac{6.67 脳 10^{鈭� 11} 鈥夆赌塏鈰� m^{2} {/kg}^{2} 鈥夆赌� 脳鈥夆赌� m_{A} 鈥夆赌� 脳鈥夆赌� 1 鈥夆赌塳g}{{(0.2 鈥夆赌塵)}^{2}} 鈥夆赌� \\ m_{A} = 0.25 鈥刱驳 \end{matrix}$

Hence, mass of the particle A is $0.25 鈥刱驳$

(b) Calculating the mass of particle C

Using equation (i), Force between mass B & C can be written as:

$\begin{matrix} F_{B C} = \frac{G m_{B} m_{C}}{x^{2}} \\ 4.17 脳 10^{鈭� 10} 鈥夆赌塏 = \frac{6.67 脳 10^{鈭� 11} 鈥夆赌塏鈰� m^{2} {/kg}^{2} 脳 1 鈥夆赌夆€塳g鈥� 脳鈥夆赌� m_{C}}{{(0.4 鈥夆赌塵)}^{2}} \\ m_{C} = 1 鈥刱驳 \end{matrix}$