Chapter 6
Application of Newton’s Laws
Dr. Jie Zou PHY 1151
Department of Physics
1
Outline
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Frictional Forces
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Kinetic friction
Static friction
Strings and Tension
Connected objects
Springs and Hooke’s Law for Spring
Forces
Circular Motion
Dr. Jie Zou PHY 1151
Department of Physics
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Frictional Forces
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The origin of friction: Even
“smooth” surfaces have
irregularities when viewed at the
microscopic level. This type of
roughness contributes to friction.
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Two types of friction:
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Kinetic friction
Static friction
Dr. Jie Zou PHY 1151
Department of Physics
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Kinetic Friction
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Kinetic friction fk: The friction encountered when
surfaces slide against one another with a finite
relative speed.
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Direction of the force of kinetic friction: Kinetic
friction fk acts to oppose the sliding motion at the point
of contact between the surfaces.
Magnitude of the force of kinetic friction: In general,
the force of kinetic friction is found to be proportional to
the magnitude of the normal force, N, or fk = kN.
The constant of proportionality, k, is referred to as the
coefficient of kinetic friction.
Dr. Jie Zou PHY 1151
Department of Physics
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Kinetic Friction: Example 1
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Someone at the other end of
the table asks you to pass
the salt. You slide the 50.0-g
salt shaker in their direction,
giving it an initial speed of
1.15 m/s.
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(a) If the shaker comes to a
rest with constant acceleration
in 0.840 m, what is the
coefficient of kinetic friction
between the shaker and the
table?
Dr. Jie Zou PHY 1151
Department of Physics
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Kinetic Friction: Example 2
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A trained sea lion slides
from rest with constant
acceleration down a 3.0-mlong ramp into a pool of
water. If the ramp is inclined
at an angle of 23 above the
horizontal and the
coefficient of kinetic friction
between the sea lion and
the ramp is 0.26, how long
does it take for the sea lion
to make a splash in the
pool?
Dr. Jie Zou PHY 1151
Department of Physics
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Static Friction
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Static friction fs: Static friction tends to keep
two surfaces from moving relative to one
another.
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There is an upper limit to the force that can be
exerted by static friction, fs,max.
fs,max = sN. The constant of proportionality is called
s, the coefficient of static friction.
Magnitude: The force of static friction, fs, can have
any value between zero and fs,max.
Direction: The direction of fs is parallel to the surface
of contact, and opposite to the direction the object
would move if there
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friction.
Dr. Jiewere
Zou PHY
Department of Physics
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Static Friction: Example
A flatbed truck slowly tilts its
bed upward to dispose of a
95.0-kg crate. For small angles
of tilt the crate stays put, but
when the tilt angle exceeds
23.3 the crate begins to slide.
 (a) What is the coefficient of
static friction between the
bed of the truck and the
crate?
 (b) Find the magnitude of
the static friction acting on
the crate.
Dr. Jie Zou PHY 1151

Department of Physics
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Strings and Tension: Example
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To hang a 6.20 kg
pot of flowers, a
gardener uses two
wires-one attached
horizontally to a
wall, the other
sloping at an angle
of  = 40.0 and
attached to the
ceiling. Find the
tension in each wire. Dr. Jie Zou
PHY 1151
Department of Physics
9
Springs and Hooke’s Law
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(Ideal) Springs and Hooke’s Law
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Magnitude of the spring force: The spring force
is proportional to the amount, x, by which it is
stretched or compressed.
Direction of the spring force: Opposite to the
displacement from the equilibrium length of the
spring.
Hooke’s Law: F = - k x.
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k: Force constant of the spring, units: N/m.
x: displacement from the equilibrium length of the
spring
Dr. Jie Zou PHY 1151
Department of Physics
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Springs and Hooke’s Law:
Example

A 1.50-kg object hangs motionless from
a spring with a force constant k = 250
N/m. How far is the spring stretched
from its equilibrium length?
Dr. Jie Zou PHY 1151
Department of Physics
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Connected Objects
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A block of mass m1 slides
on a frictionless tabletop.
It is connected to a string
that passes over a pulley
and suspends a mass m2.
Find (a) the acceleration
of the masses and (b) the
tension in the string.
Dr. Jie Zou PHY 1151
Department of Physics
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Circular Motion
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Centripetal acceleration, acp:
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Newton’s 2nd Law applied to circular
motion:
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To make an object move
in a circle with constant
speed, a force must act on
it that is directed toward
the center of the circle.
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Direction: Directed toward the center of the
circle
Magnitude: acp = v2/r, where v = speed and r
= radius
The centripetal force is proportional to the
centripetal acceleration.
fcp = macp
Centripetal force, fcp:
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Direction: Directed toward the center of the
circle
Magnitude: fcp = macp = mv2/r
Dr. Jie Zou PHY 1151
Department of Physics
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Circular Motion: Example
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A 1200-kg car rounds a corner of radius r = 45
m. If the coefficient of static friction between
the tires and the road is s = 0.82, what is the
greatest speed the car can have in the corner
without skidding?
Dr. Jie Zou PHY 1151
Department of Physics
14
Homework
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See online homework assignment at
www.masteringphysics.com
Hand-written homework assignment:
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Chapter 6, Page 178, Problems: #10
Dr. Jie Zou PHY 1151
Department of Physics
15