Physics 1501 – Lecture 8 Physics 1501: Lecture 8
Announcements Homework #3 : due next Monday
Topics Review of Newton s Laws. Friction Some applications of Newton s laws.
Physics 1501: Lecture 8, Pg 1
Review Newton s Laws 1, 2, 3
Isaac Newton (1643 - 1727) published Principia Mathematica in 1687. In this work, he proposed three laws of motion:
Law 1: An object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame. Law 2: For any object, FNET = Σ F = ma Law 3: Forces occur in pairs: FA ,B = - FB ,A (For every action there is an equal and opposite reaction.)
Physics 1501: Lecture 8, Pg 2
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Physics 1501 – Lecture 8
Exercise: Inclined plane
A block of mass m slides down a frictionless ramp that makes angle θ with respect to horizontal. What is its acceleration a ? m
a
θ
Physics 1501: Lecture 8, Pg 3
Inclined plane...
Define convenient axes parallel and perpendicular to plane: Acceleration a is in x direction only. j m
a
θ
i
Physics 1501: Lecture 8, Pg 4
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Physics 1501 – Lecture 8
Inclined plane...
Consider x and y components separately: i: mg sin θ = ma a = g sin θ
j: N - mg cos θ = 0.
N = mg cos θ ma
j
mg sin θ
N θ
mg cos θ
i
mg Physics 1501: Lecture 8, Pg 5
Angles of an Inclined plane
ma = mg sin θ
N θ + φ = 90°
θ
θ
mg
φ
θ
Physics 1501: Lecture 8, Pg 6
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Physics 1501 – Lecture 8 Example Gravity, Normal Forces etc. Conside a women on a swing:
Active Figure
When is the tension on the rope largest. Is it : A) greater than B) the same as C) less than the force due to gravity acting on the woman Physics 1501: Lecture 8, Pg 7
New Topic: Friction
What does it do? It opposes motion!
How do we characterize this in terms we have learned? Friction results in a force in a direction opposite to the direction of motion! j
N FAPPLIED fFRICTION
ma
i
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Physics 1501 – Lecture 8
Friction...
Friction is caused by the microscopic interactions between the two surfaces:
Physics 1501: Lecture 8, Pg 9
Friction...
Force of friction acts to oppose motion: Parallel to surface. Perpendicular to Normal force.
j
N F ma fF
i
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Physics 1501 – Lecture 8
Model for Sliding Friction
The direction of the frictional force vector is perpendicular to the normal force vector N.
The magnitude of the frictional force vector |fK| is proportional to the magnitude of the normal force |N |. |fK| = µK | N | ( = µK | mg | in the previous example) The heavier something is, the greater the friction will be...makes sense!
The constant µK is called the coefficient of kinetic friction .
Physics 1501: Lecture 8, Pg 11
Model...
Dynamics: i: j: so
F - µKN = m a N = mg F - µKmg = m a
j
N F ma µK mg
i
mg Physics 1501: Lecture 8, Pg 12
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Physics 1501 – Lecture 8 Lecture 8, ACT 1 Friction and Motion A box of mass m1 = 1 kg is being pulled by a horizontal string having tension T = 40 N. It slides with friction (µk= .5) on top of a second box having mass m2 = 2 kg, which in turn slides on an ice rink (frictionless). What is the acceleration of the second box ? (a) a = 0 m/s2 (b) a = 2.5 m/s2 (c) a = 10 m/s2
T
m1
a=?
m2
slides
with friction (µk=0.5 )
slides without friction Physics 1501: Lecture 8, Pg 13
Static Friction...
So far we have considered friction acting when something moves. We also know that it acts in un-moving static systems:
In these cases, the force provided by friction will depend on the forces applied on the system.
N F
j i
fS
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Physics 1501 – Lecture 8
Static Friction...
Just like in the sliding case except a = 0. i: F - fS = 0 j: N = mg
While the block is static: fS = F (unlike kinetic friction)
N
j
F
i fS
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Static Friction...
The maximum possible force that the friction between two objects can provide is fMAX = µSN, where µs is the coefficient of static friction . So fS ≤ µS N. As one increases F, fS gets bigger until fS = µSN and the object breaks loose and starts to move.
N F
j i
fS
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Physics 1501 – Lecture 8
Static Friction...
µS is discovered by increasing F until the block starts to slide: i: FMAX - µSN = 0 j: N = mg µS = FMAX / mg j
N FMAX
µSmg
i
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Additional comments on Friction:
Since f = µN , the force of friction does not depend on the area of the surfaces in contact. By definition, it must be true that µS > µK for any system (think about it...). Graph of Frictional force fF = µSN vs Applied force: fF = µKN
Active Figure
fF fF = FA FA Physics 1501: Lecture 8, Pg 18
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Physics 1501 – Lecture 8 Lecture 8, ACT 2 Two-body dynamics
A block of mass m, when placed on a rough inclined plane (µ > 0) and given a brief push, keeps moving down the plane with constant speed. If a similar block (same µ) of mass 2m were placed on the same incline and given a brief push, it would:
(a) stop (b) accelerate (c) move with constant speed m
Physics 1501: Lecture 8, Pg 19
Example with pulley
A mass M is held in place by a force F. Find the tension in each segment of the rope and the magnitude of F. Assume the pulleys massless and frictionless. Assume the rope massless. We use the 5 step method. Draw a picture: what are we looking for ? What physics idea are applicable ? Draw a diagram and list known and unknown variables. Newton s 2nd law : F=ma
T4 T1
T3
T2
F