Microsoft PowerPoint - Lecture_11_20211101_Chap5Application of
Newton’s Laws Involving Friction*
Uniform circular motion – Kinematic*
Drag and Terminal Velocity*
Fig. a Fig. b
7. A ball with mass m is hold at rest at position A by two strings
and T1 is the tension of the string, as shown in Fig. a. Fig. b
shows a conical pendulum () with a ball , mass m, moving in a
circle and T2 is the tension of the string. What is the ratio of
T1/T2 ?
(A) 1 (B) (C) (D) (E)
(F) (G) (H) (I)
T2
1: sin 0 x T T : cos 0 y mg T
cos T mg 1 sin
tan T T mg
2 cosT mg
radius R. Since she is in circular motion,
there has to be a centripetal force. At the top
of the hill, what is Fc of the skier equal to?
PRS 5-3
A. 1 B. 2 C. 3 D. 4 E. 5
1 2 3 4 5
6% 4% 0%
radius R. Since she is in circular motion,
there has to be a centripetal force. At the top
of the hill, what is Fc of the skier equal to?
2PRS 5-3
m
Draw the free body diagram for cases, when the bob of the pendulum
reaches that highest position, and the lowest position.
m
m
2 2(1 .5 ) 4 .5 0 .5
m sr
va r
0 2sin 9.8 sin 20 3.36 m
t s a g
2 2 25.62 m
1 0tan 36.7t
1 2
High speed
1 2
DF bv ( Drag force )
dt
Math for Solving a Simple Differential Equation
( ) (1 ) (0) b bt t m mmgv t e v e
b
( )
( ) (0)
( )(0)
v tv
v mg b
Terminal velocity.
(0) 0,For v / /(1 ) (1 );bt m tmg mgv e e b b
m b
( ) (1 ) (0) b bt t m mmgv t e v e
b
A rock is thrown vertically upward with initial speed v0. Assume a
drag force proportional to , where is the velocity of the rock.
Which of the following is correct?
(A) The acceleration of the rock is always equal to g (B) The
acceleration of the rock is equal to g only at the top of the
flight. (C) The acceleration of the rock is always less than g (D)
The speed of the rock upon return to its starting point is v0 (E)
The rock can attain a terminal speed greater than v0 before
it
returns to its starting point.
v v
A rock is thrown vertically upward with initial speed v0. Assume a
drag force proportional to , where is the velocity of the rock.
Which of the following is correct?
(A) The acceleration of the rock is always equal to g (B) The
acceleration of the rock is equal to g only at the top of the
flight. (C) The acceleration of the rock is always less than g (D)
The speed of the rock upon return to its starting point is v0 (E)
The rock can attain a terminal speed greater than v0 before
it
returns to its starting point.
v v
maF vbmgF
0F
A bullet of mass m is shot downward from a plane at high latitude,
if the initial speed of the bullet is 10 mg/b, calculate and draw
the velocity of the bullet as a function of time.
maF vbmgF
g = 9.8 m/s2, m = 1Kg, b = 0.1
( ) ( (0) )(1 ) 9 (1 ) b bt t m mmg mg mg mgv t v e e
b b b b
2 DF bv
2 dvmg bv m dt
A B C ( ) a b ca v v v
( ) c a bc v v v
(d) impossible to determine
PRS 5-10
A B C
(d) impossible to determine
PRS 5-10
Chapter 6 Gravitation and Newton’s Synthesis
Chapter 6 Gravitation and Newton’s Synthesis
Newton’s realization was that the force must come from the
Earth.
If the force of gravity is being exerted on objects on Earth, what
is the origin of that force?
He further realized that this force must be what keeps the Moon in
its orbit.
6-1 Newton’s Law of Universal Gravitation*
Newton’s Law of Universal Gravitation
1 2 21 122
Cavendish experiment
21 21
2r
1r
12r
x
y
Find the direction and magnitude of the gravitational force
experienced by m1, assume that m1=m2=100kg
m1
m2
(2,4)
(-2,1)
y
x
Find the direction and magnitude of the gravitational force
experienced by m1, assume that m1=m2=100kg
11 21
F
m1
m2
(2,4)
N
If there are many particles, the total force is the vector sum of
the individual forces: (Superposition principle)
1 12 13 14 1 1 2
n
