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Q. 72

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 356

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Short Answer

shows a particle of mass m at distance from the center of a very thin cylinder of mass and length . The particle is outside the cylinder, so .

a. Calculate the gravitational potential energy of these two masses.

b. Use what you know about the relationship between force and potential energy to find the magnitude of the gravitational force on when it is at position

a. The gravitational potential energy of these two masses

b. The gravitational force on is

See the step by step solution

Step by Step Solution

Step 1: Given Expression

The expression for gravitational P.E. is,

Here, is universal universal gravitational constant, are masses, and is distance of separation between the masses.

Step 2: potential energy (a)

(a) Assume that the rod is split into thin sections each of width with mass of as shown within the figure. because the width of the rod is tiny, all of the mass is assumed to be at a distance faraway from the mass .

Step 3: Gravitation (a)

The fractional of mass of every section and total mass is.

The expression for gravitational P.E. of the masses and is

Substitute within the above equation.

Calculate the overall P.E. by integrating the above equation.

Therefore, the gravitational mechanical energy of the masses is

Step 4: Gravitational Force (b)

(b) Calculate the force on the mass at distance .

Therefore, the force on the mass is

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