EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
1st Edition
ISBN: 9780100546714
Author: Katz
Publisher: YUZU
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Chapter 7, Problem 28PQ
To determine

Find the net gravitational force on the sphere at the origin.

Expert Solution & Answer
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Answer to Problem 28PQ

The net gravitational force on the sphere at the origin is (1.04×1010i^+2.67×1010j^)N_.

Explanation of Solution

Force on mass m1 due to mass m2 is along the x axis and is directed along the negative x direction.

Write the equation to find the gravitational force on mass m1 due to m2.

    F21=Gm1m2r122(i^)                                                                                                  (I)

Here, F21 is the force on mass m1 due to m2, G is gravitational constant, m1 is the mass of first sphere, m2 is the mass of second sphere, r12 is the distance between first and second sphere

Gravitational force on mass m1 due to m3 is along the y axis and is directed in the positive y direction.

Write the equation to find the gravitational force on mass m1 due to m3.

    F31=Gm1m3r132(j^)                                                                                                 (II)

Here, F31 is the force on mass m1 due to m3, G is gravitational constant, m3 is the mass of third sphere, r13 is the distance between first and third sphere

Write the equation to find the net force on m1 due to m2 and m3.

    Fnet=F21+F31                                                                                                      (III)

Here, Fnet is the net force

Conclusion

Substitute 6.67×1011Nm2/kg2 for G, 12.5kg for m1, 4.50kg for m2 and 6.00m for r12 in equation (I) to get F21

    F21=(6.67×1011Nm2/kg2)(12.5kg)(4.50kg)(6.00m2)(i^)=(1.04×1010N)(i^)

Substitute 6.67×1011Nm2/kg2 for G, 12.5kg for m1, 8.00kg for m2 and 5.00m for r13 in equation (II) to get F31

      F31=(6.67×1011Nm2/kg2)(12.5kg)(8.00kg)(5.00m2)(j^)=(2.67×1010N)(j^)

Substitute (1.04×1010N)(i^) for F21 and (2.67×1010N)(j^) for F31 in equation (III) to get Fnet

    Fnet=((1.04×1010N)i^+(2.67×1010N)j^)N

Therefore, the net gravitational force on the sphere at the origin is (1.04×1010i^+2.67×1010j^)N_.

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Chapter 7 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

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