(a) Explanation Given info: For the system, mass one is 1.0 kg , mass two is 2.0 kg , mass three is 3.0 kg , mass four is 4.0 kg , length of the rectangle is 0.20 m and breadth is 0.1 m . The universal gravitational constant is 6.67 × 10 − 11 N ⋅ m 2 / kg 2 . Figure ( 1 ) The formula for gravitational potential energy is, U e = − G m a m b r ab (1) Here, U e is the gravitational potential energy m a is mass a m b is mass b r ab is the distance between mass a and mass b G is the universal gravitational constant For gravitational potential energy between mass one and mass two substitute U 1 for U e , m 1 for m a , m 2 for m b , r 12 for r ab in equation(1). U 1 = − G m 1 m 2 r 12 Substitute 1.0 kg for m 1 , 2.0 kg for m 2 , 0.20 m for r 12 , 6.67 × 10 − 11 N ⋅ m 2 / kg 2 for G in above expression. U 1 = − ( 6.67 × 10 − 11 N ⋅ m 2 / kg 2 ) ( 1.0 kg ) ( 2.0 kg ) ( 0.20 m ) U 1 = − 6.67 × 10 − 10 J For gravitational potential energy between mass two and mass three substitute U 1 for U e , m 2 for m a , m 3 for m b , r 23 for r ab in equation (1). U 2 = − G m 2 m 3 r 23 Substitute 2.0 kg for m 2 , 3.0 kg for m 3 , 0.10 m for r 23 , 6.67 × 10 − 11 N ⋅ m 2 / kg 2 for G in above expression. U 2 = − ( 6.67 × 10 − 11 N ⋅ m 2 / kg 2 ) ( 2.0 kg ) ( 3.0 kg ) ( 0.10 m ) U 2 = 40.02 × 10 − 10 J . For gravitational potential energy between mass three and mass four substitute U 3 for U e , m 3 for m a , m 4 for m b , r 34 for r ab in equation (1). U 3 = − G m 3 m 4 r 34 Substitute 3.0 kg for m 3 , 4.0 kg for m 4 , 0.20 m for r 34 , 6.67 × 10 − 11 N ⋅ m 2 / kg 2 for G in above expression. U 3 = − ( 6.67 × 10 − 11 N ⋅ m 2 / kg 2 ) ( 3.0 kg ) ( 4.0 kg ) ( 0.20 m ) U 3 = − 40.02 × 10 − 10 J . For gravitational potential energy between mass one and mass two substitute U 5 for U e , m 4 for m a , m 1 for m b , r 41 for r ab in equation(1). U 4 = − G m 4 m 1 r 41 Substitute 1.0 kg for m 1 , 4.0 kg for m 4 , 0.20 m for r 41 , 6.67 × 10 − 11 N ⋅ m 2 / kg 2 for G in above expression. U 4 = − ( 6.67 × 10 − 11 N ⋅ m 2 / kg 2 ) ( 1 (b) To determine The change in the gravitational potential energy of the system with two times increase in masses of the system. (c) To determine The value of total potential energy of the system, with change in sides of rectangle to half.

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Chapter 12, Problem 39PCE

(a)

To determine

The total gravitational potential energy of the system.

(b)

To determine

The change in the gravitational potential energy of the system with two times increase in masses of the system.

(c)

To determine

The value of total potential energy of the system, with change in sides of rectangle to half.

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Chapter 12, Problem 38PCE

Chapter 12, Problem 40PCE

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The total gravitational potential energy of the system.

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The total gravitational potential energy of the system.

The change in the gravitational potential energy of the system with two times increase in masses of the system.

The value of total potential energy of the system, with change in sides of rectangle to half.

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Chapter 12 Solutions