Download i.i Observe and find a pattern In these three experiments, we will

Key
Kreutter: Work and Energy
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Lesson i: How Do We Ever Get Anything bone Around Here?
i.i
Observe and find a pattern
In these three experiments, we will study the ability for a group of objects to smash a piece of chalk.
a)
Consider a i-kg block with a flat bottom with a string attached to the top and Earth as your system.
There is also a piece of chalk sitting below the block. You pull up on the string so that the a-kg block
1 you release the block. It falls and
slowly rises 0.5 rn above the piece of chalk. After this lifting process
breaks the chalk
f Lift
I—
b)
Consider a i-kg dynamics cart that can roll on a low-friction horizontal dynamics track as your system.
There is also a piece of chalk that is taped to the fixed, vertical end of the track. You push the cart so that
it rolls faster and faster toward the chalk at the end of the dynamics track and the cart breaks the chalk
when it hits it.
Push
c)
chalk
I
rn H
wall
I
Now consider a slingshot that holds a piece of chalk as your system. You slowly pull back on the sling.
When you release the sling, the chalk shoots out at a high speed and hits the wall, causing the chalk to
break.
Complete this table.
Experiment
Draw an arrow indicating the direction of the
external forceyou exerted on each of the
0 s).
system objects that you studied (Py
Draw an arrow indicating the displacement of
the system object while you were exerting the
force (J).
)
Adapted from PUM
@2010,
El
wall
Rutgers, The State University of New Jersey
a)
b)
C)
Kreutter: Work and Energy
d)
Look for a pattern of what was done to the systems
that we studied to give them the chalk-smashing
pattern.
C
potential. Then, devise a new physical quantity to describe this
)
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/4
1.2
Observe and find a pattern
Now, suppose that a friend decides to save the chalk in the first two experiments by exerting, with her hands, an
opposing force on the block or on the cart after they are released. In each case, she pushes on the moving object
opposite to the direction of its velocity. Below, give the direction of the external force your friend exerts on the
moving object relative to its displacement as she stops it, thus causing the system to lose its potential to break the
chalk.
a)
After lifting the block, you release the block and it starts falling. Your friend then starts pushing upward
on the falling block, slowing it down, and the block does not break the chalk.
3
I
b)
:1
it rolls faster and faster, You then stop pushing. Just before the cart reaches the
chalk, your friend pushes it in a direction opposite to its direction of motion. This causes the cart to slow
down and stop so that it does not break the chalk.
You push the cart so that
ci
Complete this table.
that you studied
b)
a)
Experiment
Draw an arrow indicating the
direction of the external force your
friend exerted on the system object
(Yon
s).
J
Draw an arrow indicating the
displacement of the system object
while your friend was exerting the
force
c)
)
(J).
How could you modify the definition of the quantity you devised
in the previous activity to account for
the system’s loss of the chalk-breaking potential due to your friend’s intervention?
Adapted from PUM
©2010, Rutgers, The State University of New Jersey
Kreutter: Work and Energy
1.3
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Observe and find a pattern:
Consider Earth and a a-kg block as your system.
a)
You hold a string tied to a block so that it stays about 1 cm above a table. A piece of chalk is placed on the
table under the block. If you release the block and it falls on the chalk, the chalk will not break (it’s too close to
the chalk),
Next you slowly walk about 2 m beside the table, continually keeping the block a cm above the surface. After
walking the 2 m, the block hangs over a second, identical piece of chalk. Draw the force exerted by the string
on the block and the displacement of the block as you walked the 2 m.
A
b)
Discuss whether the vertical force the string exerted on the block while moving it horizontally above the
tabletop caused Earth and block to have a better chance of breaking the second piece of chalk than the first
piece
1
c)
Revise the quantity you devised in the last two activities to account for this result. Your revision will involve
the angle between the external force exerted on the system and the system object’s displacement. We call
this quantity work.
1.4
Observe and find a pattern (if you know trigonometry)
)
)
a)
Consider a a-kg dynamics cart a system. You pull it at angle 0 causing it to roll on a low-friction horizontal
dynamics track toward a piece of chalk that is taped to the fixed, vertical end of the track. You pull the
cart so that it rolls faster and faster toward the chalk at the end of the dynamics track and breaks the
chalk when it hits it. Draw the force exerted by you on the cart and the displacement of the cart while you
were pulling it.
b)
Discuss whether the angled force exerted on the cart while moving it horizontally gave it a better chance
of breaking the piece of chalk than the force exerted in activity 1.1 part (b).
Adapted from PUM
©2010, Rutgers, The State University of New Jersey
Kreutter: Work and Energy
C)
What trigbnometric function would help you determine the system’s increase in chalk-smashing ability?
Is this consistent with the increase, decrease,
pange in chalk-smashing potential for activities
1.1-1.3?
J)
L.
7
d)
•\
1
Revise the quantity you devised in the last thPee activities to account for this result. Your reviion will
involve the angle between the external force exerted on the system and the system object’s
displacement. We call this quantity work.
Work done by a constant force on an object is equal to the product of the force magnitude and displacement
magnitude with a positive sign (W = F
08 *d) if the force and displacement are in the same direction and the
product of the force and displacement with the negative sign (W = -FwOflB * d) if they are in the opposite
direction. If the force and displacement of the object are perpendicular to each other, the force does NO work!
/s
kgm
.
The units of work are Joules (J). One joule is equal to one NewtonMeter, or one 2
i.
Regular Problem
Jeff did 73 J of work on a sled, He pulled the sled for a distance of 30 m. Represent the sled as a box. Draw the
direction of the force Jeff exerts on the sled and the direction of the sled’s displacement. What is the average
force that he exerted on the system?
i.6 Regular Problem
Steve slowly lifts a 20 kg barbell a meter vertically. Represent the barbell as a box. Draw the direction of the force
Steve exerts on the barbell and the direction of the barbell’s displacement. How much work does he do on the
barbell? What assumptions did you make?
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1.7 Regular Problem
If Natasha slows a moving grocery cart by pulling on it exerting a force of 23 N over 2.3 m, what will be the work
she does on it? Represent the cart as a box. Draw the direction of the force Natasha exerts on the cart and the
direction of the cart’s displacement. What assumptions did you make?
(- a&)i\
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Adapted from PUM
©2o10, Rutgers, The State University of New Jersey
Kreutter: Work and Energy
-
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In problem 1.7 Natasha did negative work on the box. Notice that when the force exerted on the object and the
object’s displacement are in the opposite directions, the force does NEGATIVE work!
i.8 Regular Problem
Jessica, at a constant slow speed, moved a i kg book from a 2 m high shelf to the floor. Represent the book as a
box. Draw the direction the force Jessica exerts on the book and the direction of the book’s displacement. How
much work did she do on
1.9
Reason
1)
Dylan is trying to lift his bike into the back of his pick-up truck of height h. He attaches a light string to it and pulls
it vertically upward. If the bike is the system, what kind of work do Dylan and Earth do on the bike?
i. 4
Dylan does positive work on the bike. Earth does positive work on the bike.
-.
ii.
-
Dylan does positive work on the bike. Earth does negative work on the bike.
iii.
Dylan does negative work on the bike. Earth does positive work on the bike.
iv.
Dylan does negative work on the bike. Earth does negative work on the bike.
Homework
i..i
Relate
Describe a situation when you have done:
a)
+i
J of work on a system.
3
b)
-1
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J of work on a system.
1
c)
1.13
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o J of work on a system.
Regular Problem
While working out, a man lifts a io-kg object a vertical distance of o.8o m. He then carries it for 10 m where he
sets it down a vertical distance of o.8o m. How much work does he do on the object when he picks the object up,
when he carries it, and when he sets it back down? What is the total work that he does on it?
)
*
Adapted from PUM
@2010, Rutgers, The State University of New Jersey
Kreutter: Work and Energy
nt1ái
)
In another situation, you stretch a block-spring system and then release the block. The block slides toward the
wall and smashes a piece of chalk. Label whether the ability of the block-spring-wall system to crush the chalk
increases, decreases, or remains the same between each step.
s
Is this process consistent with the pattern we observed today between the net force exerted on an object and the
displacement of the object?
i.i
Regular Problem
Sara drops a a kg ball from the top of a cliff, it falls vertically with a constant acceleration (9.8 m/s
). What object
2
(if any) exerts a force that does work on the ball (system)? How much work has been done on the ball if it falls io
m? Sketch the situation. Draw the direction of the force exerted on the ball and the direction of the displacement.
)
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1
1i
i6 Regular Problem
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.
Minh is riding the elevator up to the top floor of a shopping mall. He moves with a constant velocity from te
ground level to the floor above ( m high). Estimate the work done on Minh by the elevator. To calculate the force
exerted on Minh, choose him as the system and draw a force diagram.
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Regular Problem
Shelly is now riding up the same elevator as Minh in the previous problem. She is going to the fifth floor so as the
elevator goes from the ground level to the first floor, it accelerates at a rate of i.o mis
. Estimate the work done
2
on Shelly by the elevator during this part of the trip if her mass is 2/3 the mass of Minh. To calculate the force
exerted by the elevator on Shelly, choose her as the system and draw a force diagram.
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Adapted from PUM
©2010, Rutgers, The State Un4ersi y of New Jersey
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Kreutter: Work and Energy
i.iB Regular Problem
As Shelly goes from the fourth floor to the fifth floor the elevator slows to a stop from 2.0 m/s. Estimate the work
done on Shelly by the elevator as it goes from the fourth to fifth floor. To calculate the force exerted by the
elevator on Shelly, choose her as the system and raw a force diagram.
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Evaluate
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Heather, Minh and Danny are arguing about the units of work. Minh says that the units of work are pounds
uc2cc)
inches, Heather thinks that the units of work are in Joules, and Danny thinks they are Newtons meters. Which of
them is right? Explain your answer. What are your assumptians?
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ii.
Regular Problem
Kate is waiting in the security line at the airport and has to keep picking up her suitcase, moving forward, and
setting it down again. Calculate the work done by Kate on her 15-kg suitcase when (a) slowly lifting it o.Bo m
upward, (b) when holding it and slowly moving forward 1.0 m, and (c) when lowering it o.8o m down again.
)
W
(
c
)(
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-
1 students will use trigonometry to express work done for a more
Work-Trigonometry Section: In this section
general range of situations.
Work
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—
—
—
—
—
—
—
5 cos(O) d
F
W= 0
agnitude of displacementa1ways positive
)
Adapted from PUM
©2010, Rutgers, The State University of New Jersey
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