Applying Newton’s Laws
Topics:
• Equilibrium
• Using Newton’s second law
• Mass, weight, and apparent weight
• Static and kinetic friction • Applying Newton’s third law
pp y g
Sample
p q
question:
Before his parachute opens, why does this skydiver fall at a
constant speed? And why does he suddenly slow down when his
parachute opens?
Slide 5-1
Equilibrium
An object is in equilibrium when
the net force acting on it is zero.
In component form, this is
The net force on each
man in the tower is
zero.
Slide 5-8
Slide 5-9
Example
A 100 kg block with a weight of 980 N hangs on a rope
rope. Find
the tension in the rope if
a) the block is stationary.
b) it’s moving upward at a steady speed of 5 m/s
m/s.
Slide 5-10
Example
A wooden box
box, with a mass of 22 kg
kg, is pulled at a constant
speed with a rope that makes an angle of 25° with the wooden
floor. What is the tension in the rope?
Slide 5-11
Checking Understanding
A rod is suspended by a string as shown
shown. The lower end of
the rod slides on a frictionless surface. Which figure correctly
shows the equilibrium position of the rod?
Slide 5-12
Answer
A rod is suspended by a string as shown
shown. The lower end of
the rod slides on a frictionless surface. Which figure correctly
shows the equilibrium position of the rod?
Slide 5-13
Example
A ball weighing 50 N is pulled back by a rope to an angle of 20°
20 .
What is the tension in the pulling rope?
Slide 5-14
Using Newton’s Second Law
Slide 5-15
Example
A sled with a mass of 20 kg slides along frictionless ice at 4
4.5
5
m/s. It then crosses a rough patch of snow which exerts a
friction force of 12 N. How far does it slide on the snow before
coming
i tto rest?
t?
Slide 5-16
Example
Macie pulls a 40 kg rolling trunk by a strap angled at 30°
30 from
the horizontal. She pulls with a force of 40 N, and there is a 30
N rolling friction force acting on trunk. What is the trunk’s
acceleration?
l ti ?
Slide 5-17
Example
Find the x- and y-components of w in each of these three
coordinate systems.
y
Slide 5-18
Example
A 75 kg skier starts down a 50
50-m-high,
m high 10°
10 slope on
frictionless skis. What is his speed at the bottom?
Slide 5-19
Example
Burglars are trying to haul a 1000 kg safe up a frictionless ramp
to their getaway truck. The ramp is tilted at angle θ. What is the
tension in the rope if the safe is at rest? If the safe is moving up
the ramp at a steady 1 m/s? If the safe is accelerating up the
ramp at 1 m/s2? Do these answers have the expected behavior
in the limit θ → 0° and θ → 90°?
Slide 5-20
Example
The same burglars push the 1000 kg safe up a 20°
20 frictionless
slope with a horizontal force of 4000 N. What is the safe’s
acceleration?
Slide 5-21
Mass and Weight
–w
w = may = m(–g)
m( g)
w = mg
Slide 5-22
Apparent Weight
Slide 5-23
Example
A 50 kg student gets in a 1000 kg elevator at rest
rest. As the elevator
begins to move, she has an apparent weight of 600 N for the first
3 s. How far has the elevator moved, and in which direction, at
th end
the
d off 3 s?
?
Slide 5-24
Static Friction
fs max = µsn
Slide 5-25
Kinetic Friction
fk = µkn
Slide 5-26
Working with Friction Forces
Slide 5-27
Example
A car traveling at 20 m/s stops in a distance of 50 m
m. Assume
that the deceleration is constant. The coefficients of friction
between a passenger and the seat are μs = 0.5 and μk = 0.3.
Will a 70 kkg passenger slide
lid off
ff th
the seatt if nott wearing
i a seatt
belt?
Slide 5-28
Applying Newton’s Third Law: Interacting Objects
Acceleration Constraints
Slide 5-29
Slide 5-30
Example
Block A has a mass of 1 kg; block B’s
B s mass is 4 kg
kg. They are
pushed with a force of magnitude 10 N.
a) What is the acceleration of the blocks?
b) With what force does A push on B? B push on A?
Slide 5-31
Checking Understanding
Which pair of forces is an action/reaction pair?
A.
B.
C.
D.
The string tension and the friction force acting on A.
The normal force on A due to B and the weight of A.
The normal force on A due to B and the weight
g of B.
The friction force acting on A and the friction force acting on B.
Slide 5-32
Answer
Which pair of forces is an action/reaction pair?
D. The friction force acting on A and the friction force acting on B.
Slide 5-33
Example
What is the acceleration of block B?
Slide 5-34
Ropes and Pulleys
Slide 5-35
Example
Block A
A, with mass 4
4.0
0 kg
kg, sits on a frictionless table
table. Block B
B, with
mass 2.0 kg, hangs from a rope connected through a pulley to
block A. What is the acceleration of block A?
Slide 5-36