iClicker Quiz
G
You throw a ball with a launch velocity of v0 =(30m/s, 40 m/s)
toward a wall . Your distance from the wall is 90 m.
How long does it take for the ball to hit the wall?
A)
B)
C)
D)
E)
1.0 sec
1.8 sec
2.25 sec
3.0 sec
4.5 sec
G
v0
1
A ball is rolled horizontally off a table with an initial speed of
0.24 m/s. A stopwatch measures the ball’s trajectory time
from table to the floor to be 0.60 s.
(a) What is the height of the table? ( Use g = 9.8 m/s2 and
neglect air resistance.)
(b) What is the horizontal distance between the edge of the
table and the impact position on the floor?
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Chapter 4. Laws of Motion
Force
Net force
Newton’s 1st Law
Newton’s 2nd, 3rd laws
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Chapter 4: The Laws of Motion
Motivation
So far, we learned about
Units, 1d motion, 2d motion, vectors, …
Æ How to describe motions
Then, what causes the motion ???
What causes an apple to fall?
What causes a ball to undergo projectile motion?
Answer Æ
Chapter 4: The Laws of Motion
Today,
Forces, Newton’s 1st, 2nd, and 3rd laws
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2
Forces
The measure of interaction between two objects (pull or push).
Vector – force has magnitude (unit: N, Newton) and direction
Force on one object from the other object
Example
F
Force
on
n apple
ppl f
from
m your h
hand
nd
apple
Your hand
Gravitational Force on apple from earth
Earth
5
G
Fnet
Net Force
If forces from many objects are applied on a single object
Net force : Vector sum of forces on an object
F
Force
on
n apple
ppl from
f m your hand
h nd
apple
Your hand
G
G
G
Fnet on apple = Fhand + Fgravity
Gravitational Force on apple from earth
Earth
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3
iClicker Quiz
Two forces of magnitude
g
5 N are acting
g on an object.
j
What is the magnitude of the net forces?
A) 10 N
B) 0 N
C) Not enough information
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iClicker Quiz
3N and 4 N forces are acting on
an object as shown.
Which is closest to the magnitude of the net force?
(a)
(b)
(c)
(d)
(e)
Zero
3.0 N
40N
4.0
5.0 N
7.0 N
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4
Example
+y
2N
4N
90 deg
120 deg
Three forces are acting on an object.
+x
3N
Find the net force and its magnitude.
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Newton’s First Law of Motion (The Law of Inertia)
If net force on an object is zero.
the object at rest remains at rest,
the object moving continues to move with the same velocity
(same speed and same direction).
G
G
If Fnet = 0, v does not change.
An additional force is NOT required to keep a cart moving
with a constant velocity on a frictionless track!
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5
iClicker Quiz
G
F1
Not moving
G
F2
A block is not moving on a frictionless horizontal surface.
Two forces F1 and F2 are acting on the block as shown above.
Which force has a greater magnitude?
(a) F1
(b) F2
(c) They have the same magnitude
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iClicker Quiz
G
F1
v = 2.5 m/s
G
F2
A block is moving to the right at a constant velocity 2.5 m/s
on a frictionless horizontal surface.
Two forces F1 and F2 are acting on the block as shown above.
While the block is moving at a constant velocity,
Which force has a greater magnitude?
(a) F1
(b) F2
(c) They have the same magnitude
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6
Newton’s Second Law of Motion
G
G
If Fnet ≠ 0, v changes, in other words, accelerates.
• Non-zero net force causes object to accelerate.
• An object of mass m has an acceleration a, equal to the net force F,
divided by the mass of the object, m.
G
Fnet
The acceleration is given by
G
G Fnet
a=
m
G
G F
a = net
m
m
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G
G
G Fnet
G
a=
⇒ Fnet = ma
m
m
[1N ] = [1kg ] × ⎡⎢1 2 ⎥⎤
⎣ s ⎦
kg m
s2
SI unit of force is a Newton:
1N ≡ 1
Non-SI unit for force: pound (lb)
1 N = 0.225 lb
Newton’s 2nd law in 2
2-D
D for each component
Fnet , x = ma x ; Fnet , y = ma y
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7
iClicker quiz
If the net force acting on an object is in the
positive x-direction, the _____ of the object is
always
y in the p
positive x-direction.
(a) displacement
(b) velocity
(c) acceleration
(d) All of the above
(e) None of the above
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iClicker
In this projectile motion,
While the ball is going up, the direction
of the net force is
(a)
(b)
(c)
(d)
(e)
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8
iClicker Quiz
m
m
5N
10 N
4 m/s2
a=?
(a) 1 m/s2
(b) 2 m/s2
(c) 4 m/s2
(d) 8 m/s2
(e) 16 m/s2
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Example
| F1 | = 5 N
v is changing
| F2 | = ? N
A block of mass 4 kg starts from rest and accelerates at a
constant rate 5.0 m/s^2 on a frictionless horizontal surface.
Two forces F1 and F2 are acting on the block as shown above.
While the block is accelerating,
If F1 has a magnitude of 5 N, then the magnitude of F2 is ______ .
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9
iClciker Q.
An object is moving to +x direction at 5 m/s at time t=0.
What is the direction of the net force at t=0?
A)
B)
C)
D)
E)
+x
-x
Zero magnitude, no direction
+y or –y direction
Not enough information
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Example
A car of 1000 kg is moving to +x direction at 8 m/s at time t=0.
Later, at time t=2 sec, the car is moving to +x direction at 3 m/s.
What is the direction of the net force on the car between t=0 and
t=2 sec?
Find the net force.
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10
Action-reaction pair: Equal magnitude and opposite direction
Action and Reaction forces are acting on different objects, NOT on
a single object.
Æ Don’t add them to find the net force!!!
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Action-reaction versus net force
• The 3rd law pair of forces are always applied to different
objects!
Net force in Newton’s 1st and 2nd laws is the sum of forces on the
same object.
Ex mpl of
Examples
f action
ti n & reaction
ti n
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11
iClicker Quiz
Find reaction force for the gravity on the cantaloupe
(a) Force on the cantaloupe from the table
(b) Gravity force on the earth from the cantaloupe
(c) Force on the table from the cantaloupe
(d) Force on the earth from the table
(e) Gravity force on the table from the earth
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