physics 207: lecture 8, pg 1 lecture 8 l goals: (finish chap. 6 and begin ch. 7) solve 1d & 2d...
DESCRIPTION
Physics 207: Lecture 8, Pg 3 Mass l We have an idea of what mass is from everyday life. l In physics: Mass (in Phys 207) is a quantity that specifies how much inertia an object has (i.e. a scalar that relates force to acceleration) (Newton’s Second Law) l Mass is an inherent property of an object. l Mass and weight are different quantities; weight is usually the magnitude of a gravitational (non-contact) force. “Pound” (lb) is a definition of weight (i.e., a force), not a mass!TRANSCRIPT
Physics 207: Lecture 8, Pg 1
Lecture 8 Goals: (Finish Chap. 6 and begin Ch. 7)Goals: (Finish Chap. 6 and begin Ch. 7)
Solve 1D & 2D motion with friction
Utilize Newton’s 2nd Law
Differentiate between Newton’s 1st, 2nd and 3rd Laws
Begin to use Newton’s 3rd Law in problem solving
Assignment: HW4, (Chap. 6 & 7, due 10/5)
Finish reading Chapter 7
1st Exam Wed., Oct. 7th from 7:15-8:45 PM Chapters 1-7
in room 2103 Chamberlin Hall
Physics 207: Lecture 8, Pg 2
Net force gives rise to acceleration!In physics:
A force is an action which causes an object to accelerate (translational & rotational)
This is Newton’s Second Law
zz
yy
xx
maF
maF
maF
amFF
0net
and mass plays a role
Physics 207: Lecture 8, Pg 3
Mass We have an idea of what mass is from everyday life. In physics:
Mass (in Phys 207) is a quantity that specifies how much inertia an object has
(i.e. a scalar that relates force to acceleration)(Newton’s Second Law)
Mass is an inherent property of an object. Mass and weight are different quantities; weight is
usually the magnitude of a gravitational (non-contact) force.
“Pound” (lb) is a definition of weight (i.e., a force), not a mass!
Physics 207: Lecture 8, Pg 4
Inertia and Mass The tendency of an object to resist any attempt to
change its velocity is called Inertia Mass is that property of an object that specifies how
much resistance an object exhibits to changes in its velocity (acceleration)If mass is constant then
If force constant
Mass is an inherent property of an object Mass is independent of the object’s surroundings Mass is independent of the method used to measure it Mass is a scalar quantity The SI unit of mass is kg
netFa
ma 1||
|a|
m
Physics 207: Lecture 8, Pg 5
ExerciseNewton’s 2nd Law
A. increasingB. decreasingC. constant in timeD. Not enough information to decide
An object is moving to the right, and experiencing a net force that is directed to the right. The magnitude of the force is decreasing with time (read this text carefully).
The speed of the object is
Physics 207: Lecture 8, Pg 6
Exercise Newton’s 2nd Law
A. AB. BC. CD. DE. G
A 10 kg mass undergoes motion along a line with velocities as given in the figure below. In regards to the stated letters for each region, in which is the magnitude of the force on the mass at its greatest?
Physics 207: Lecture 8, Pg 7
Now: Back to forces that oppose motion
Physics 207: Lecture 8, Pg 8
Static and Kinetic Friction Friction is a model force that exists between objects & it is
conditional At Static Equilibrium: A block, mass m, with a horizontal force F
applied, Direction:
1. Force vector to the normal force vector N N 2. 2. Opposite to the direction of acceleration if were 0.
Magnitude: f is proportional to the applied forces such that
fs ≤ s N
s called the “coefficient of static friction”
Physics 207: Lecture 8, Pg 9
Friction: Static frictionStatic equilibrium: A block with a horizontal force F applied,
As F increases so does fs
Fm
1
FBD
fs
N
mg
Fx = 0 = -F + fs fs = F
Fy = 0 = - N + mg N = mg
Physics 207: Lecture 8, Pg 10
Static friction, at maximum (just before slipping)
Equilibrium: A block, mass m, with a horizontal force F applied, Direction: A force vector to the normal force vector N N and the
vector is opposite to the direction of acceleration if were 0. Magnitude: fS is proportional to the magnitude of N
fs = s N F
m fs
N
mg
Physics 207: Lecture 8, Pg 11
Kinetic or Sliding friction (fk < fs)Dynamic equilibrium, moving but acceleration is still zero
As F increases fk remains nearly constant (but now there acceleration is acceleration)
Fm
1
FBD
fk
N
mg
Fx = 0 = -F + fk fk = F
Fy = 0 = - N + mg N = mg v
fk = k N
Physics 207: Lecture 8, Pg 12
Sliding Friction: Modeling
Direction: A force vector to the normal force vector N N and the vector is opposite to the velocity.
Magnitude: ffk is proportional to the magnitude of N N
ffk = k N N ( = Kmg g in the previous example)
The constant k is called the “coefficient of kinetic friction” Logic dictates that S > K for any system
Physics 207: Lecture 8, Pg 15
Coefficients of Friction
Material on Material s = static friction k = kinetic friction
steel / steel 0.6 0.4
add grease to steel 0.1 0.05
metal / ice 0.022 0.02
brake lining / iron 0.4 0.3
tire / dry pavement 0.9 0.8
tire / wet pavement 0.8 0.7
Physics 207: Lecture 8, Pg 18
An experiment (with a ≠ 0)Two blocks are connected on the table as shown. Thetable has unknown static and kinetic friction coefficients.Design an experiment to find K.
Non-equilibrium: Set m2 and adjust m1 to find regime where a ≠ 0
Requires two FBDs
T
Mass 2
Fx = m2a = -T + fk = -T + k N
Fy = 0 = N – m2g
m1
m2
m2g
N
m1g
T
fk
Mass 1
Fy = m1a = T – m1g
T = m1g + m1a = k m2g – m2a k = (m1(g+a)+m2a)/m2g
Physics 207: Lecture 8, Pg 21
Forces at different angles
Case 1 Case 2
F
mg
N
Case1: Downward angled force with frictionCase 2: Upwards angled force with frictionCases 3,4: Up against the wallQuestions: Does it slide?
What happens to the normal force?What happens to the frictional force?
mg
Cases 3, 4
mg
N NF
F
ff
ff
ff
Physics 207: Lecture 8, Pg 22
Inclined plane with “Normal” and Frictional Forces
1. Static Equilibrium Case2. Dynamic Equilibrium (see 1)
3. Dynamic case with non-zero acceleration
Block weight is mg
NormalForce
Friction Force
“Normal” means perpendicular
mg cos
f
x
y
mg sin
F = 0
Fx= 0 = mg sin – f
Fy= 0 = –mg cos + N
with mg sin = f ≤ S N
if mg sin > S N, must slide
Critical angle s = tan c
Physics 207: Lecture 8, Pg 23
Inclined plane with “Normal” and Frictional Forces
1. Static Equilibrium Case
2. Dynamic Equilibrium Friction opposite velocity
(down the incline)
mg
NormalForce
Friction Force
“Normal” means perpendicular
mg cos
fK
x
y
mg sin
F = 0
Fx= 0 = mg sin – fk
Fy= 0 = –mg cos + N
fk = k N = k mg cos
Fx= 0 = mg sin – k mg cos
k = tan (only one angle)
v
Physics 207: Lecture 8, Pg 24
Inclined plane with “Normal” and Frictional Forces3. Dynamic case with non-zero acceleration
Result depends on direction of velocity
Weight of block is mg
NormalForce
Friction ForceSliding Down
vmg sin fk
Sliding Up
Fx= max = mg sin ± fk
Fy= 0 = –mg cos + N
fk = k N = k mg cos
Fx= max = mg sin ± k mg cos
ax = g sin ± k g cos
Physics 207: Lecture 8, Pg 26
Velocity and acceleration plots:
Notice that the acceleration is always down the slide and that, even at the turnaround point, the block is always motion although there is an infinitesimal point at which the velocity of the block passes through zero.
At this moment, depending on the static friction the block may become stuck.
Physics 207: Lecture 8, Pg 27
Recap
Assignment: HW4, (Chapter 6 & 7 due 10/5)
Finish Chapter 7