Explanation From Figure 1, shows the surface of the rotating earth for an object at rest, the vector force F → grav and F → N adds up to give the net force F → net where F → grav is the force of gravity which is directed towards the center of the earth and F N → is the normal force. The radius of the object in circular motion is given by r = r E cos θ , and speed of the circular motion is given by v = 2 π r T Write the general expression for normal force. F → N = − m g eff → (I) Rearrange equation (I) to get g eff → . g eff → = − F → N m (II) Write the expression for gravitational force from Figure 1. F → grav = − G m E m r E 2 j ^ (III) Write the expression for net force on the body on the surface of the rotating earth from figure 1. F → net = m v 2 r sin θ i ^ − m v 2 r cos θ j ^ (IV) Write the newton’s second law of motion using free body diagram from figure 1. F net → = F grav → + F N → (V) Use equation (II) and (III) in equation (IV), and Rearrange equation (IV), to get F N → . F N → = m v 2 r sin θ i ^ + ( G m E m r E 2 − m v 2 r cos θ ) j ^ Use v = 2 π r T , and r = r E cos θ from Figure 1 in equation (V).to get F N → F N → = m [ 4 π 2 r E cos θ T 2 sin θ i ^ + ( G m E r E 2 − 4 π 2 r E cos θ T 2 ) j ^ ] (VI) Write the expression for angle where F N → makes with the normal in figure 1. ϕ = tan − 1 ( F Nx F Ny ) (VII) Here, F Nx is the magnitude of x component of F N , F Ny is the magnitude of y component of F N , and ϕ is the angle F N → makes with the normal

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force betwe…

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Chapter 6, Problem 21P

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The effective value of g both in magnitude and direction wise at a latitude of 45°.

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Chapter 6, Problem 20P

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Chapter 6 Solutions

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The effective value of g both in magnitude and direction wise at a latitude of 45°.

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