Download Kreutter: Dynamics 9 Lesson 9: Applying Newton`s Second Law

Kreutter: Dynamics 9
Lesson 9: Applying Newton’s Second Law
Problem-Solving Strategy for Dynamics Problems
Sketch and Translate:
• Read the problem. Be sure you understand what the problem is saying. Visualize the problem.
• Sketch the situation described in the problem; include all known information.
• Choose a system object and make a list of objects that interact with the system.
• Indicate the direction of acceleration, if you know it.
Simplify and Diagram:
• Consider the system as a particle.
• Decide if you can ignore any interactions of the environment with the system object.
• Draw a force diagram for the system. Label the forces with two subscripts. Make sure the diagram is
consistent with the acceleration of the system object (if known). Include perpendicular x- and y-coordinate
axes.
• Draw a motion diagram and make sure the force and the motion diagrams match.
Represent Mathematically:
• Apply Newton’s Second Law in component form (this means horizontal and vertical forces are separate) to
the situation you represented in the force diagram.
• Add kinematics equations if necessary.
Solve and Evaluate:
• Solve the equations for an unknown quantity and evaluate the results to see if they are reasonable (the
magnitude and the sign of the answer, its units, and how the result changes if one of the quantities becomes
zero – do these all make sense? Make sure you go back to the force and motion diagrams to make sure your
answer is consistent with both.
Here is an example that applies the strategy shown above: A 5-kg object
(Earth exerts a 50 N force on it) is lifted by a cable that exerts a 70 N force on
it. Calculate the acceleration of the object.
FC on O
Translate: The object is our system; Earth and the cable interact with the
object. The acceleration is up.
(-)
FE on O
Simplify and Diagram: In this case there are two forces exerted on the object
– one exerted by the cable and one exerted by Earth. We choose the positive
axis to be up.
Represent Mathematically: Newton’s second law in component form:
aO y 
FC on O y  FE on O y
mO
Solve and Evaluate: The component of the force exerted by the cable is positive as the force points in the
positive direction. The component of the force exerted by Earth is negative. Thus:
A=
(70𝑁) + (−50𝑁)
5𝑘𝑔
= 4 m/s2
Adapted from PUM: Dynamics
©2010, Rutgers, The State University of New Jersey
Kreutter: Dynamics 9
The positive sign of acceleration means that it is pointed upward – the elevator is accelerating in the upward
direction (not necessarily moving in the upward direction).
9.1
Description
of the
object of
interest is
underlined
1) A 2.2 kg
bucket of
clams sits at
rest on a
desk.
A
Sketch the
situation.
Circle the
object of
interest.
Draw the
direction of
the
acceleration,
if known.
B
Translate
the givens
into
physical
quantities.
C
Draw a force
diagram for the
object of interest.
D
Can you
evaluate
any of
the
forces in
the force
diagram?
E
Write Newton’s Second Law in
component form. This means keep
vertical and horizontal forces
separate.
Fill in anything you know and solve
for anything you do not know.
Which
are
negative
and
which
are
positive?
Given in
description:
a = 0 (sits )
m = 2.2kg
Ftable on bucket
FEarth on bucket
Adapted from PUM: Dynamics
©2010, Rutgers, The State University of New Jersey
ay 
0
Bucket
2) A 5kg
bucket of
clams hangs
motionless
from a
spring that
stretches
40 cm.
FE on B y = mg=-22 N
FEarth on Bucket y  FTable on Bucket y
m
(22N)  FTable on Bucket
2.2kg
Kreutter: Dynamics 9
3) A man
pulls a 40kg
refrigerator
up an
elevator
shaft with a
rope at a
constant
speed.
Come up
with your
own for an
object in
equilibrium
with 3 or
more other
objects
interacting
with it.
9.2 In a grocery store, you push a 14.5 kg shopping cart. It is initially rolling at a constant speed of 2 m/s. You
push on it in the direction opposite to its motion exerting a force of 12 N.
a) Draw a force diagram and a motion diagram for the cart when you start pushing in the direction
opposite to its motion.
b) Write Newton’s second law in component form for the process.
c)
Assuming you push the cart exerting constant force for a while, how far will it travel in 3 seconds?
(Ignore friction for all parts of this problem.) Use the problem-solving strategy steps illustrated above.
Adapted from PUM: Dynamics
©2010, Rutgers, The State University of New Jersey
Kreutter: Dynamics 9
9.3 An astronaut, while pushing a beam into place on the International Space Station, exerted a 150-N force
2
on the beam. The beam accelerates at 0.15 m/s . Determine the mass of the beam.
9.4 An elevator is pulled upward so it moves with increasing upward speed—the force exerted by the cable
on the elevator is constant and greater than the downward gravitational force exerted by Earth. When the
elevator is moving up medium fast, the force exerted by the cable on the elevator changes abruptly to just
balance the downward gravitational force of Earth—the sum of the forces that the cable and Earth exert on
the elevator is now zero. Now what happens to the elevator? Explain. Represent your answer with position
and velocity-versus-time graphs. What assumptions did you make?
Adapted from PUM: Dynamics
©2010, Rutgers, The State University of New Jersey
Kreutter: Dynamics 9
9.5 Fill in the table below. The system object is underlined.
Description
of the
object of
interest is
underlined
A
Sketch the
situation.
Circle the
object of
interest.
Draw a
motion
diagram and
the direction
of the
acceleration,
if known
B
Translate
the givens
into
physical
quantities.
1) A 72 kg
crate on a
freight
elevator
accelerates
upwards at
a rate of 0.2
m/s2 while
moving
down.
2) A 172 kg
crate on a
freight
elevator
accelerates
downwards
at a rate of
0.4 m/s2
while
moving up.
3) A physics
teacher of
mass m is
holding onto
a rope
attached to
a hot air
balloon and
is
accelerating
upwards at
a m/s2.
Adapted from PUM: Dynamics
©2010, Rutgers, The State University of New Jersey
C
Draw a
force
diagram
for the
object of
interest.
D
Can you
evaluate any of
the force
components in
the force
diagram?
Which are
negative and
which are
positive? What
if you changed
the direction of
the axes?
E
Write Newton’s Second Law in
component form.
What can you determine using
the information in the problem?