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Physics 218
Lecture 6: Dynamics
Alexei Safonov
Basics: Reminders
• Acceleration always implies a non-zero net force
and vice versa
• Numerically, F=ma
– Mass m is essentially a measure of how much a
particular body “resists” a force applied
• Light objects give in easily (large a for a given F), heavy
objects resist a lot (smaller a for the same F)
• Forces are applied by objects onto other objects,
each experiences the same force
– Action = Reaction
• Today we will do more exercising in using these
concepts
Clicker Question
• A force F is applied to a small block, that pushes a
larger block. The two blocks accelerate to the right.
Compare the NET FORCE on the block with mass M,
to the net force on the block with mass 5M.
• A) FM < F5M
• B) FM = F5M
• C) FM > F5M
a
F
M
5M
Clicker Question
• A force F is applied to a small block, that pushes a
larger block. The two blocks accelerate to the right.
Compare the NET FORCE on the block with mass M,
to the net force on the block with mass 5M.


 F  ma
• A) FM < F5M
• B) FM = F5M
• C) FM > F5M
Net Force
Same acceleration, so larger
mass has larger net force.
a
F
M
5M
You tie a brick to the end of a rope and whirl
the brick around you in a horizontal circle.
Which best describes the path of the brick
after you suddenly let go of the rope.
A. The brick drops directly straight down
to the ground.
B. The brick continues in its circular
path.
C. The brick spirals outward.
D. The brick flies off in a straight line.
Reminder: Newton’s Third Law
“Whenever one object exerts a
force on a second object, the
second exerts an equal and
opposite force”
OR
“To every action there is an equal
and opposite reaction”
Pre-Lecture Question 2
A
B
C
D
E
Pre-Lecture Question 2
CheckPoint
• You are driving a car with constant speed around a horizontal circular
track. The net force acting on your car
•
•
•
•
•
A) Points radially inward toward the center of the circular track
B) Points radially outward, away from the center of the circular track
C) Points forward in the same direction your car is moving
D) Points backward, opposite to the direction your car is moving
E) Is zero.
CheckPoint Responses
•
You are driving a car with constant speed around a horizontal circular track. The net
force acting on your car
•
•
•
•
•
A) Points radically inward toward the center of the circular track
B) Points radically outward, away from the center of the circular track
C) Points forward in the same direction your car is moving
D) Points backward, opposite to the direction your car is moving
E) Is zero.
A) Force is in the same direction as
acceleration (in this case, centripetal).
B) the acceleration is outwards, therefore the
force is outwards
C) The car is moving forward so the net force must
be forward.
E) Because the car is moving at a constant speed,
so there is no a. We get the net force is zero.
Aside: Centripetal acceleration
and force
• 1) Objects moving in a circle always have a
component of acceleration, called centripetal,
which is toward the center of the circle.*
• 2) Centripetal acceleration must be caused by a
force:
– Friction, gravity – whatever force keeps it moving in a
circle.
– This force is often called the “centripetal force”
• 3) There is no “new” kind of force here.
• 4) There is no such thing as centrifugal force.
* They can have also have tangential acceleration if their speed is not constant
Free Body Diagrams
Same tricks as in Chapters 1-3:
1. Draw a diagram: Draw each force on an
object separately! Force diagram!
2. Break each force into the X and Ycomponents, THEN sum!!!
– Show your TA that you know the difference
between a force, and a component of force
– GREAT way to pick up partial credit
Pulling a box
A box with mass m is pulled along a frictionless
horizontal surface with a force FP at angle Q as given
in the figure. Assume it does not leave the surface.
a)What is the acceleration of the box?
FP
b)What is the normal force?
Q
Rope Problems
If a rope is massless and doesn’t
stretch, this means:
• The acceleration of any part of a rope
is the same as any other part
• The magnitude of the acceleration of
the two things it attaches are equal
• The tension (Force) exerted by each
end is the same
2 boxes connected with a string
Two boxes with masses m1 and m2 are placed on a
frictionless horizontal surface and pulled with a
Force FP. Assume the string between doesn’t
stretch and is massless.
a)What is the acceleration of the boxes?
b)What is the tension of the strings between the
boxes?
M2
M1
Clicker Question
• A cart with mass m2 is connected to a mass m1
using a string that passes over a frictionless
pulley, as shown below. The cart
a is held
motionless.
m2
g
The tension in the string is
A) m1g
B) m2g
C) 0
Let’s talk more about tensions and strings
m1
Closer Look at Elevators
A box of mass m is hung with a string
from the ceiling of an elevator that is
accelerating upward. Which of the
following best describes the tension T
in the string:
A) T < mg
B) T = mg
C) T > mg
Lets walk over this step by step
a
Clicker Question
• You are traveling on an
elevator up the Sears
tower. As you near the top
floor and are slowing down,
your acceleration
• A) is upward
• B) is downward
• C) is zero
Clicker Question
• You are traveling on an
elevator up the Sears
tower, and you are standing
on a bathroom scale.
• As you near the top floor
and are slowing down, the
scale reads
• A) More than your usual
weight
• B) Less than your usual
weight
• C) Your usual weight
A crate is suspended from the end
of a vertical rope. The tension in
the rope is greater when:
A. The crate is at rest.
B. The crate is moving up at a constant
speed.
C. The crate is moving down at a
constant speed.
D. The tension for A, B and C are the
same.
Spring Scale
• What is the reading in the spring scale?
Next time
• Will talk about friction, tension, circular
motion, and more on applying Newton
Laws