
Concept explainers
(a)
The speed and magnitude of the acceleration of a person standing on the equator.
(a)

Answer to Problem 67P
A person standing on the equator has a speed
Explanation of Solution
Given:
Time taken by the Earth to rotate once on its axis,
Radius of the Earth,
Formula used:
The speed
The person on the equator experiences a centripetal acceleration
The total acceleration at the equator is given by,
Calculation:
A person standing on the equator, revolves in a circular path of radius
Calculate speed
All particles fixed on the Earth experience a centripetal force directed towards the center of its circular path. Hence it would experience a centripetal acceleration towards the center of its circular path.
Calculate the centripetal acceleration
Express the acceleration as a percentage of
The total acceleration experienced by the person is given by equation (3).
Conclusion:
Thus, a person standing on the equator has a speed
(b)
The direction of the acceleration vector of the person on the equator.
(b)

Answer to Problem 67P
The acceleration vector of the person is directed towards the center of the Earth.
Explanation of Solution
Introduction:
A person on the surface of the Earth experiences two forces-(i) Gravitational force
An object in order to move in a circular path requires
Figure 1
However, the weight, as felt by the person on the surface of the earth, is equal to the Normal force he experiences.
Hence, the acceleration
Conclusion:
Thus, the acceleration vector of the person on the Equator is directed towards the center of the Earth.
(c)
The speed and magnitude of the acceleration of a person standing at
(c)

Answer to Problem 67P
The speed of the person at
Explanation of Solution
Given:
The latitude where the person was standing,
Radius of the earth at equator,
The speed of the person at equator,
The centripetal acceleration at the equator,
Formula used:
The person at
The speed of person at
His speed at equator is given by
From equations (4) and (5),
The centripetal acceleration at the equator is given by the expression,
The centripetal acceleration at
From equations (4) and (5),
The person also experiences acceleration
The magnitude of the resultant acceleration is determined by using parallelogram law of vectors.
Calculation:
The motion of the person at
Figure 2
From Figure 2, it can be seen that
Use equation (11) in equation (6).
Substitute the value of the variables in the above equation.
Use equation (11) in equation (9) and substitute the values of the variables to calculate the value of
The vector
Substitute the values of variables in equation (10) and calculate the magnitude of the resultant acceleration
Conclusion:
Thus, the speed of the person at
(d)
The angle between the direction of the acceleration at
(d)

Answer to Problem 67P
The angle between the direction of the acceleration at
Explanation of Solution
Given:
The magnitude of centripetal acceleration at
The value of acceleration of free fall,
The latitude where the person was standing,
Formula used:
The direction of the acceleration at the equator is along the horizontal direction parallel to the direction of the centripetal acceleration at
Hence the angle
The vector diagram representing the accelerations is shown below:
Figure 3
This is given by
Calculation:
Substitute the values of the variables in equation (12).
Conclusion:
Thus, the angle between the direction of the acceleration at
Want to see more full solutions like this?
Chapter 3 Solutions
Physics for Scientists and Engineers
- Don't use ai to answer I will report you answerarrow_forwardA shopper standing 2.00 m from a convex security mirror sees his image with a magnification of 0.200. (Explicitly show on paper how you follow the steps in the Problem-Solving Strategy for mirrors found on page 1020. Your instructor may ask you to turn in this work.) (a) Where is his image (in m)? (Use the correct sign.) -0.4 m in front of the mirror ▾ (b) What is the focal length (in m) of the mirror? -0.5 m (c) What is its radius of curvature (in m)? -1.0 marrow_forwardAn amoeba is 0.309 cm away from the 0.304 cm focal length objective lens of a microscope.arrow_forward
- Two resistors of resistances R1 and R2, with R2>R1, are connected to a voltage source with voltage V0. When the resistors are connected in series, the current is Is. When the resistors are connected in parallel, the current Ip from the source is equal to 10Is. Let r be the ratio R1/R2. Find r. I know you have to find the equations for V for both situations and relate them, I'm just struggling to do so. Please explain all steps, thank you.arrow_forwardBheem and Ram, jump off either side of a bridge while holding opposite ends of a rope and swing back and forth under the bridge to save a child while avoiding a fire. Looking at the swing of just Bheem, we can approximate him as a simple pendulum with a period of motion of 5.59 s. How long is the pendulum ? When Bheem swings, he goes a full distance, from side to side, of 10.2 m. What is his maximum velocity? What is his maximum acceleration?arrow_forwardThe position of a 0.300 kg object attached to a spring is described by x=0.271 m ⋅ cos(0.512π⋅rad/s ⋅t) (Assume t is in seconds.) Find the amplitude of the motion. Find the spring constant. Find the position of the object at t = 0.324 s. Find the object's velocity at t = 0.324 s.arrow_forward
- Min Min is hanging from her spring-arms off the edge of the level. Due to the spring like nature of her arms she is bouncing up and down in simple harmonic motion with a maximum displacement from equilibrium of 0.118 m. The spring constant of Min-Min’s arms is 9560. N/m and she has a mass of 87.5 kg. What is the period at which she oscillates? Find her maximum speed. Find her speed when she is located 5.00 cm from her equilibrium position.arrow_forward(a) What magnification in multiples is produced by a 0.150 cm focal length microscope objective that is 0.160 cm from the object being viewed? 15.9 (b) What is the overall magnification in multiples if an eyepiece that produces a magnification of 7.90x is used? 126 × ×arrow_forwardGravitational Potential Energyarrow_forward
- E = кедо Xo A continuous line of charge lies along the x axis, extending from x = +x to positive infinity. The line carries positive charge with a uniform linear charge density 10. (a) What is the magnitude of the electric field at the origin? (Use the following as necessary: 10, Xo, and ke.) (b) What is the direction of the electric field at the origin? O O O O O O G -y +z ○ -z +x -x +yarrow_forwardInclude free body diagramarrow_forward2 Spring 2025 -03 PITT Calculate the acceleration of a skier heading down a 10.0° slope, assuming the coefficient of cold coast at a constant velocity. You can neglect air resistance in both parts. friction for waxed wood on wet snow fly 0.1 (b) Find the angle of the slope down which this skier Given: 9 = ? 8=10° 4=0.1arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningAn Introduction to Physical SciencePhysicsISBN:9781305079137Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar TorresPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning





