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

Modified Mastering Physics with Pearson eText -- Combo Access -- for Physics for Scientist and Engineers (18 week)

5th Edition

ISBN: 9780137504299

Author: Douglas C. Giancoli

Publisher: Pearson Education (US)

See similar textbooks

Concept explainers

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…

Question

Chapter 6, Problem 27P

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 26P

Chapter 6, Problem 28P

Students have asked these similar questions

Blue light has a wavelength of 485 nm. What is the frequency of a photon of blue light? Question 13 Question 13 What is the wavelength of radiofrequency broadcast of 104 MHz? Question 14 Question 14 1 Point 3. The output intensity from an x-ray exposure is 4 mGy at 90 cm. What will the intensity of the exposure be at 180 cm? Question 15 Question 15 1 Point What is the frequency of an 80 keV x-ray?

Under what condition is IA - BI = A + B? Vectors À and B are in the same direction. Vectors À and B are in opposite directions. The magnitude of vector Vectors À and 官 B is zero. are in perpendicular directions.

For the vectors shown in the figure, express vector 3 in terms of vectors M and N. M S =-M+ Ň == S=м- Ñ S = M +Ñ +N

Chapter 6 Solutions

Modified Mastering Physics with Pearson eText -- Combo Access -- for Physics for Scientist and Engineers (18 week)

Ch. 6.3 - Suppose you could double the mass of a planet but...Ch. 6.4 - Two satellites orbit the Earth in circular orbits...Ch. 6.4 - Could astronauts in a spacecraft far out in space...Ch. 6.5 - Suppose there were a planet in circular orbit...Ch. 6 - Does an apple exert a gravitational force on the...Ch. 6 - The Suns gravitational pull on the Earth is much...Ch. 6 - Will an object weigh more at the equator or at the...Ch. 6 - Why is more fuel required for a spacecraft to...Ch. 6 - The gravitational force on the Moon due to the...Ch. 6 - How did the scientists of Newton's era determine...

Ch. 6 - If it were possible to drill a hole all the way...Ch. 6 - A satellite in a geosynchronous orbit stays over...Ch. 6 - Which pulls harder gravitationally, the Earth on...Ch. 6 - Would it require less speed to launch a satellite...Ch. 6 - An antenna loosens and becomes detached from a...Ch. 6 - Describe how careful measurements of the variation...Ch. 6 - The Sun is below us at midnight, nearly in line...Ch. 6 - When will your apparent weight be the greatest, as...Ch. 6 - If the Earths mass were double what it actually...Ch. 6 - The source of the Mississippi River is closer to...Ch. 6 - People sometimes ask. What keeps a satellite up in...Ch. 6 - Explain how a runner experiences free fall or...Ch. 6 - If you were in a satellite orbiting the Earth, how...Ch. 6 - Is the centripetal acceleration of Mars in its...Ch. 6 - The mass of the planet Pluto was not known until...Ch. 6 - The Earth moves faster in its orbit around the Sun...Ch. 6 - Keplers laws tell us that a planet moves faster...Ch. 6 - Does your body directly sense a gravitational...Ch. 6 - Discuss the conceptual differences between g as...Ch. 6 - Prob. 1MCQ Ch. 6 - Prob. 2MCQ Ch. 6 - Prob. 3MCQ Ch. 6 - Prob. 4MCQ Ch. 6 - Prob. 5MCQ Ch. 6 - Prob. 7MCQ Ch. 6 - Prob. 9MCQ Ch. 6 - Prob. 11MCQ Ch. 6 - Prob. 12MCQ Ch. 6 - Prob. 1P Ch. 6 - Prob. 2P Ch. 6 - (I) Calculate the acceleration due to gravity on...Ch. 6 - Prob. 4P Ch. 6 - Prob. 5P Ch. 6 - Prob. 6P Ch. 6 - Prob. 7P Ch. 6 - Prob. 8P Ch. 6 - Prob. 9P Ch. 6 - Prob. 10P Ch. 6 - Prob. 11P Ch. 6 - Prob. 12P Ch. 6 - (II) Suppose the mass of the Earth were doubled,...Ch. 6 - (II) Determine the mass of the Sun using the known...Ch. 6 - (II) Estimate the acceleration due to gravity at...Ch. 6 - Prob. 16P Ch. 6 - Prob. 17P Ch. 6 - Prob. 18P Ch. 6 - Prob. 19P Ch. 6 - Prob. 20P Ch. 6 - Prob. 21P Ch. 6 - Prob. 22P Ch. 6 - (II) Two identical point masses, each of mass M,...Ch. 6 - Prob. 24P Ch. 6 - (III) (a) Use the binomial expansion...Ch. 6 - Prob. 26P Ch. 6 - Prob. 27P Ch. 6 - Prob. 28P Ch. 6 - Prob. 29P Ch. 6 - Prob. 30P Ch. 6 - Prob. 31P Ch. 6 - Prob. 32P Ch. 6 - Prob. 33P Ch. 6 - Prob. 34P Ch. 6 - Prob. 35P Ch. 6 - Prob. 36P Ch. 6 - Prob. 37P Ch. 6 - Prob. 38P Ch. 6 - Prob. 39P Ch. 6 - Prob. 40P Ch. 6 - Prob. 41P Ch. 6 - Prob. 42P Ch. 6 - Prob. 43P Ch. 6 - Prob. 44P Ch. 6 - (I) Neptune is an average distance of 4.5109 km...Ch. 6 - Prob. 46P Ch. 6 - (I) Use Keplers laws and the period of the Moon...Ch. 6 - (I) Determine the mass of the Earth from the known...Ch. 6 - (II) Table 63 gives the mean distance, period, and...Ch. 6 - (II) Determine the mean distance from Jupiter for...Ch. 6 - Prob. 51P Ch. 6 - Prob. 52P Ch. 6 - Prob. 53P Ch. 6 - (II) The asteroid belt between Mars and Jupiter...Ch. 6 - Prob. 55P Ch. 6 - (III) The orbital periods and mean orbital...Ch. 6 - (III) The comet Hale-Bopp has a period of 2400...Ch. 6 - Prob. 59P Ch. 6 - (II) (a) What is the gravitational field at the...Ch. 6 - Prob. 61P Ch. 6 - Prob. 62GP Ch. 6 - Prob. 63GP Ch. 6 - How far above the Earths surface will the...Ch. 6 - Prob. 65GP Ch. 6 - Show that the rate of change of your weight is...Ch. 6 - Prob. 67GP Ch. 6 - Prob. 68GP Ch. 6 - Prob. 69GP Ch. 6 - Prob. 70GP Ch. 6 - Prob. 71GP Ch. 6 - Prob. 72GP Ch. 6 - Prob. 74GP Ch. 6 - Newton had the data listed in Table 64, plus the...Ch. 6 - Prob. 76GP Ch. 6 - Prob. 77GP Ch. 6 - The gravitational force at different places on...Ch. 6 - Prob. 79GP Ch. 6 - A plumb bob (a mass m hanging on a string) is...Ch. 6 - A science-fiction tale describes an artificial...Ch. 6 - Prob. 82GP Ch. 6 - Suppose all the mass of the Earth were compacted...Ch. 6 - Prob. 84GP Ch. 6 - Between the orbits of Mars and Jupiter, several...Ch. 6 - Prob. 86GP

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

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

Concept explainers

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

Want to see the full answer?

Chapter 6 Solutions