Homework 4 solutions
Notes: Please keep in mind that most of the problems in MasteringPhysics with numerical answers are randomized for each student. The solutions below correspond to the version of the problem that is in the paper copy of the textbook. There may be some differences between the textbook version and the online version.
1. Reading questions
a. This is true. Choose a point on the circle. Draw a velocity arrow for the object just before it reaches that point, and another velocity arrow for the object just after it passes that point. The velocity change arrow that changes that first arrow into the second points directly towards the center of the circle. Since the velocity change arrow is in the direction of the acceleration of the object then the acceleration of the object is towards the center of the circle as well.
b. This is true to a reasonably high degree. Newton’s 2nd law is only valid when used from a
non-accelerated reference frame. However, since Earth rotates once every 24 hours, it means the surface of Earth and everything on it is moving in uniform circular motion and therefore has non-zero acceleration. But, the magnitude of this acceleration is very small, so while Newton’s 2nd law
isn’t perfectly applicable, it is applicable to high degree.
2. Tutorial (the problem parts plus the hints in MasteringPhysics walk you through how to do it)
3. Problem 4.05
Assuming Earth’s orbit to be circular, Earth’s acceleration is:
� ! =
�!
�
To determine Earth’s speed use the idea that Earth completes one orbit (one circumference of a circle) in one year.
�=2 ��
�
Putting these two equations together, inserting appropriate values (and the necessary unit conversions):
�
! =
2�� �
!
� =
4�!� �! =
4�! 1.5×10!!�
1�� 3.154×10
!�
1 ��
! =6.0×10! !
� �!
4. Tutorial (the problem parts plus the hints in MasteringPhysics walk you through how to do it)
