lesson_6_problem_set3.completed
docx
keyboard_arrow_up
School
University Of Arizona *
*We aren’t endorsed by this school
Course
111
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
4
Uploaded by nicolejj20
PHY 111
Lesson 6 Problem Set 3
Name __Nicole Jauregui_______________
UCM and Gravity
Section _25902_____
Directions:
Several of the following problems are missing some of the given variable
information. Your instructor will provide the values through email in the “From Your Instructor”
section of the weekly lesson or in a course announcement. Use the values provided by your
instructor to answer all of the questions.
Show all your work
. Make sure to use appropriate
labels and units, and highlight your final answers if they are numerical.
1.
A student connects an object with mass m to a rope with a length r and then rotates the rope
around her head parallel to the ground. The object takes 0.5 seconds to complete one rotation.
a)
What is the object’s speed of rotation? (4 pts)
r= 0.50m
V= ∆d/∆t
d= circumference 2pi(r)
∆d= 2pi*0.50m
∆d= 3.14m
V= 3.14m/0.5s
V= 6.28 m/s
b)
What is the object’s centripetal acceleration? (4 pts)
ac=v^2/r
ac= (6.28m/s)^2/ 0.50m
ac= (39.408m^2/s^2)/0.50m
ac= 78.8 m/s^2
c)
What tension force is required to maintain this motion? (4 pts)
M=0.75kg
ΣF=m*ac
Σ
F=0.75kg*78.8m/s^2
Σ
F=59.1 N
2.
A student places an object with a mass of m on a disk at a position r from the center of the disk.
The student starts rotating the disk. When the disk reaches a speed of 0.8 m/s, the object starts
to slide off the disk. What is the coefficient of static friction between the object and the disk? (4
pts)
M=200g=0.2kg
r= 0.2m
Σ
F=mv^2/r
Σ
F=0.2kg(0.8m/s)^2/0.2m
Σ
F=0.512N
μ= 0.512N/(0.2kg*9.8m/s/s)
μ= 0.512N/1.96N
μ= 0.261
3.
A car with mass m travels over a hill with a radius of curvature of r at a speed of 15 m/s. What is
the normal force on the car when the car is at the top of the hill? (6 pts)
M=1500kg r=20m
N= m(g)+(m*v^2/r)
N= 1500kg(9.8m/s^2)+1500kg(15m/s)^2/20m
N=14700N+11250N
N=25950N
4.
A student with a mass of m rides a roller coaster with a loop with a radius of curvature of r. What
is the minimum speed the rollercoaster can maintain and still make it all the way around the
loop? (6 pts)
m*g=m*v^2/r
v=sqrt(g*r)
v=sqrt(9.8m/s/s*5.0m)
v=sqrt(49m^2/s^2)
v=7m/s
5.
A particular satellite with a mass of m is put into orbit around Ganymede (the largest moon of
Jupiter) at a distance 300 km from the surface. What is the gravitational force of attraction
between the satellite and the moon? (Ganymede has a mass of 1.48x10
23
kg and a radius of 2631
km.) (4 pts)
r= 300km+2631km
conversion:
r= (300km +2631km)*1000m/km
r= 2931000m
F=g*m1*m2/r^2
F=(6.67x10^-11N*m^2/kg^2)(450kg)(1.48x10^23kg)/(2931000m)^2
F=(3.0015x10^-8N*m^2/kg^2)(1.48x10^23kg)/(8.59x10^12m^2)
F=4.45122x10^15N*m/8.59x10^12m
F=518,248N is the force between the satellite and moon
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
b) What is the satellite’s centripetal acceleration? (4 pts)
v=1833 m/s
ac=v^2/r
ac=(1833m/s)^2/2931000)
ac=1.145 m/s^2
c)
What is the satellite’s period of rotation? (4 pts)
T=2pi(r)/v
T=(2*3.14*2,931,000)/1833m/s
T=(18,398,220m)/1833m/s
T=10,038 s