Homework 7
1)
Calculate d4 on slide2 of lecture series 2 (show your work).
2)
Draw pulley systems with mechanical advantages of 1, 2, and 3 using a single system of pulleys
and 4, 5, 6, 7, 8, & 9 using a piggybacked system of pulleys.
3)
Repeat the upper tension problem on slide 4 of lecture series 2, with blocks 1, 2, & 3 having a
mass of 5, 6, & 9kg respectively.
4)
Repeat the lower tension problem on slide 4 of lecture series 2, with a 5kg mass and a horizontal
tension of 7N. Calculate the original angle A as well as the new angle with the above mass and
force.
5)
Repeat the upper tension problem on slide 6, of lecture series 2, with m
1
= 3kg and m
2
= 6kg.
6)
Repeat the lower tension problem on slide 6 of lecture series 2, with m
1
= 3kg and m
2
= 6kg.
7)
Repeat the tension problem on slide 5 of lecture series 2, using your own numbers for mass.
8)
Calculate the centripetal force on the car on slide 16 of lecture series 2, using a radius of 20m
and a velocity of 10m/s.
9)
Calculate the gravitational force between the moon and the earth on slide 17 of lecture series 2.
10)
What is the value of the gravitational constant G in terms of the variables period and radius of
orbit of a planet, and the mass of the sun. (Hint: Slide 21).
11)
Prove that the escape velocity =
√
(GM/
𝑟
).
12)
Repeat the momentum problem on slide 22, of lecture series 2, with the mass of the 18kg ball
unknown and a final velocity of 10m/s.
13)
Repeat the momentum problem on slide 23, of lecture series 2, with car A moving 3.0m/s and
car B moving
4.0m/s and at a 30
o
angle with respect to car A.
14)
Rank the four objects on slide 24 (excluding the two sticks and the pendulum), of lecture series
2, in terms of which will make it down the ramp the fastest.
15)
On slide 25, of lecture series 2, if m
1
= m
2
and m
2
has a tangential velocity of 3m/s calculate the
tangential velocity of m
2
if its radius is
¼
that of m
2
’s. What is the angular momentum of each if
r1 = 1m?
16)
A 5kg bucket is being spun in a circle on a 0.5m long string. It takes 0.5 seconds to make on
complete rotation. Calculate its 1) angular velocity, 2) centripetal acceleration, 3) centripetal
force, 4) angular momentum and 5) torque.
17)
Use Newton’s force equations to show that Galileo was right in that falling objects accelerate
the same, regardless of mass.
Chapter 6
Review Questions: 18-22.
Plug and Chug: 1-8
Exercises: 18, 19, 26, 27, 32
Problems: 2, 4, 6, 8, 10