Stuff you asked about:
I really don't like elevator ques3ons. Aside from being unrealis3c, they are hard to visualize. If it's accelera3ng upward, then the force would be upward, but when in an accelera3ng elevator, you feel heavier. Some clarifica3on would be nice. I understand the elevator scenarios, however, when there is a spring in the elevator instead of a string, does the force from the spring act the same way the tension force does? I'm preCy sure that clock hit a student when it fell off the wall in the last lecture. Although the same force was exerted between the two, I bet he felt it a liCle more than the clock did. Can we go over the elevator/spring checkpoint? Also, since we are talking about gravita3onal forces. I thought I'd let ya know that I'm reading a book about an3-­‐gravity. It's impossible to put down. I kinda blew through this because I was having dinner with my girlfriend. She began to get really upset that I was doing hw while with her, and became even more annoyed when I asked her to do it for me. The prelecture says that g=9.81 m/s^2 only works near the surface of Earth. According to the Universal Law of Gravita3on, and assuming that the Earth's radius at sea level is constant, g=9.79 on Mt. Everest and 9.85 in the Mariana Trench. So accelera3on due to gravity varies by only 0.6% between the highest and lowest points on Earth. Physics 211
Lecture 5
Today’s Concepts: a) Free Body Diagrams b) Force due to strings c) Force due to springs d) Force due to gravity Classical Mechanics
Free Body Diagrams
1)Choose system (object or group)
2)Draw forces acting on object
-Gravity
-Things touching (contact)
T
m
mg
Free Body Diagrams
Q: Understand the concepts but what always confuses me is
that doesn't each of these forces have an equal and opposite
forces? Why is there ever a net force?
A: The “other” force does not act on the same object !
Free Body Diagrams
Free Body Diagrams
Tension Force
Direction: Parallel to rope, always pulling.
Magnitude: As much or little as needed for Fnet=ma
T
m
mg
Checkpoint
BOX IN THE ELEVATOR
A box of mass m is hung with a string from the ceiling of an elevator that is accelera3ng upward. Which of the following best describes the tension T in the string: A) T < mg B) T = mg C) T > mg
a
“Please explain the elevator question thoroughly, if the elevator accelerates
upward does that mean that the force also acts upward? and is so then why
is the tension on the string greater?”
Watch out for subtle mistakes…
Many people got the right answer with
explanations like this one:
“Since the elevator is accelerating upwards
the total downward acceleration on the box
is increased and this increase is taken into
account by the tension on the string”
T
m
Don’t view problem from accelerating
reference frame or you may get confused
mg
Just Remember: Net force causes acceleration
a
Normal Force
Normal force is the force perpendicular to the surface that
prevents the objects from passing through each other.
1)  Direction: Perpendicular to surface and out
2)  Magnitude: As much or little required keep objects separate.
“Please explain how normal force is not an example of Newton's third law
but why we are still allowed to set F=mg equal to the normal force.”
Checkpoint
A block sits at rest on a horizontal fric3onless surface. Which of the following sketches most closely resembles the correct free body diagram for all forces ac3ng on the block? Each arrow represents a force. A
B
C
D
“The force of gravity is acting upon the box…However if gravity were the
only force acting upon it the box would accelerate into the floor. There is
another force perpendicular to the surface the box rests on, which is both
equal and opposite of the gravitational force, keeping the box stationary..”
Clicker Question
A block accelerates down a fric3onless inclined plane. Which of the following sketches most closely resembles the correct free body diagram for all forces ac3ng on the block? Each arrow represents a force. A
B C -­‐ Gravity is down. -­‐ Normal is perpendicular to surface. D Spring Force
Direction: Parallel to spring: Push or pull
Magnitude:F=-kx
I feel uncomfortable while solving the spring problems. Can you please do
some problems in which we have to take the direction of the force of the
spring into play?
Springs Example
A 5 kg mass is suspended from a
spring with spring constant 25 N/m.
How far is the spring stretched from
its equilibrium position?
∑F
= ma
kΔx − Mg = 0
Mg
5*9.8
Δx =
=
k
25
A) 0.5 m
B) 2 m
C) 5 m
Checkpoint
A box of mass m is hung by a spring from the ceiling of an elevator. L
When the elevator is at rest the length of the spring is L = 1 m. If the elevator accelerates upward the length of the spring will be: A) L = 1 m
“The box is accelerating upward,
so the spring force must be
B) L < 1 m
greater than the gravity force.
Thus, L is larger than normal
C) L > 1 m
length.”
a
m
Accelerating reference frames can confuse…
The upwards acceleration will
increase the force pulling down on
the box, making the string longer
due to the increased force.
a
L
m
These arguments may feel good, but
all you really need to remember is this:
Net force causes acceleration
Aside: How a Spring Scale works
F
F
There is a spring in there
F
F
Δx
The dial just shows how much it has been stretched, Δx.
Tension Clicker Question
A block weighing 4 lbs is hung from a rope aCached to a scale. The scale is then aCached to a wall and reads 4 lbs. What will the scale read when it is instead aCached to another block weighing 4 lbs? ?
m
A) 0 lbs. B) 4 lbs.
m
m
C) 8 lbs. Clicker Question
You are traveling on an elevator up the Sears tower. As you near the top floor and are slowing down, your accelera3on A) is upward a
B) is downward C) is zero V
mg
N
Clicker Question
You are traveling on an elevator up the Sears tower, and you are standing on a bathroom scale that measures N. As you near the top floor and are slowing down, the Normal a
force is. A) More than your usual weight B) Less than your usual weight C) Your usual weight mg
N
Clicker Question
A cart with mass m2 is connected to a mass m1 using a string that passes over a fric3onless pulley, as shown below. The cart is held mo3onless. m2
The tension in the string is A) m1g
B) m2g
C) 0
m1
Clicker Question
A cart with mass m2 is connected to a mass m1 using a string that passes over a fric3onless pulley, as shown below. Ini3ally, the cart is held mo3onless, but is then released and starts to accelerate. a
m2
Aeer the cart is released, the tension in the string is A) = m1g
B) > m1g
C) < m1g
a
m1
Universal Gravitation
v
v2
am =
REm
REm
Both are cases of free-fall
FEb
ae=g
am RE2
= 2
ae REm
RE
Can you please explain what happens when a little
boy is in the elevator, and the elevator cord is
cut. What happens? Also what happens when he
drops two balls while falling inside the elevator?
If you took a video of the boy in the falling elevator,
it would just like the video of an astronaut on the
space station.
Universal Gravitation
Near surface of earth r = Rearth
Mearth m
F =G 2
Rearth
= 6.67 × 10−11 ⎡⎣m3 / kg s2 ⎤⎦
5.97 × 1024 [kg ]
6
2
⎡
⎤⎦ m
=
9.8
m
/
s
m
⎣
2
(6.4 × 10 [m])
You should have taught us what
"G" (Gravitational Constant) is equal