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

mg Physics 1501: Lecture 8, Pg 8

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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

mg Physics 1501: Lecture 8, Pg 10

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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

mg Physics 1501: Lecture 8, Pg 14

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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

mg Physics 1501: Lecture 8, Pg 15

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

mg Physics 1501: Lecture 8, Pg 16

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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

mg Physics 1501: Lecture 8, Pg 17

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