Transcript Chapter 4 2D Kinematics

Chapter 6
Application of Newton’s Laws
Dr. Jie Zou PHY 1151
Department of Physics
1
Outline

Frictional Forces






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
2
Frictional Forces

The origin of friction: Even
“smooth” surfaces have
irregularities when viewed at the
microscopic level. This type of
roughness contributes to friction.

Two types of friction:


Kinetic friction
Static friction
Dr. Jie Zou PHY 1151
Department of Physics
3
Kinetic Friction

Kinetic friction fk: The friction encountered when
surfaces slide against one another with a finite
relative speed.



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
4
Kinetic Friction: Example 1

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.

(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
5
Kinetic Friction: Example 2

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
6
Static Friction

Static friction fs: Static friction tends to keep
two surfaces from moving relative to one
another.




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
no1151
friction.
Dr. Jiewere
Zou PHY
Department of Physics
7
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
8
Strings and Tension: Example

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

(Ideal) Springs and Hooke’s Law



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.


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
10
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
11
Connected Objects

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
12
Circular Motion

Centripetal acceleration, acp:



Newton’s 2nd Law applied to circular
motion:


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.

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:


Direction: Directed toward the center of the
circle
Magnitude: fcp = macp = mv2/r
Dr. Jie Zou PHY 1151
Department of Physics
13
Circular Motion: Example

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


See online homework assignment at
www.masteringphysics.com
Hand-written homework assignment:

Chapter 6, Page 178, Problems: #10
Dr. Jie Zou PHY 1151
Department of Physics
15