Download Kreutter: Work and Energy Intro to Work: How Do We Ever Get

Kreutter: Work and Energy
Intro to Work: How Do We Ever Get Anything Done Around Here?
1.1 Observe and find a pattern
In these three experiments, we will consider “chalk-smashing ability” of a system.
a)
Consider a block 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 1-kg block slowly rises 0.5 m above the
piece of chalk. After this lifting process, you release the block. It falls and breaks the chalk.
1 kg
Lift
1 kg
chalk
b) Consider a 1-kg dynamics cart as your system. There is also a piece of chalk that is taped to a wall nearby.
You push the cart so that it rolls faster and faster toward the chalk . The cart breaks the chalk when it hits
it.
wall
Push
c)
wall
Now consider a rubber band that holds a piece of chalk as your system. You slowly pull back on the
rubber band. When you release it, 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 force you exerted on each of the
system objects that you studied (𝐹⃗Y on S).
a)
b)
c)
Draw an arrow indicating the displacement of
the system object while you were exerting the
force (𝑑⃗).
d) Look for a pattern in your above representations. What did you do to the systems to increase their chalksmashing ability?
Adapted from PUM
©2010, Rutgers, The State University of New Jersey
Kreutter: Work and Energy
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. Draw in the direction of this force in the pictures below.
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.
b) You push the cart so that 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.
Complete this table.
Experiment
Draw an arrow indicating the
direction of the external force your
friend exerted on the system object
that you studied (𝐹⃗Y on S).
a)
b)
Draw an arrow indicating the
displacement of the system object
while your friend was exerting the
force (𝑑⃗).
c)
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 ability due to your friend’s intervention?
1.3 Observe and find a pattern :
Consider Earth and a 1-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. Why does the
chalk not break?
Adapted from PUM
©2010, Rutgers, The State University of New Jersey
Kreutter: Work and Energy
Next you slowly walk about 2 m beside the table, continually keeping the block 1 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.
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.
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.
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 = FW on B *d) if the force and displacement are in the same direction and the
product of the force and displacement with the negative sign (W = -FW on B * 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!
The units of work are Joules (J). One joule is equal to one Newton·Meter, or one kg·m 2/s2.
1.4 Regular Problem
Jeff did 573 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?
1.5 Regular Problem
Steve slowly lifts a 20 kg barbell 1 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?
Adapted from PUM
©2010, Rutgers, The State University of New Jersey
Kreutter: Work and Energy
1.6 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?
In problem 1.6 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!
1.7 Regular Problem
Jessica, at a constant slow speed, moved a 1 kg book from a 2 m high shelf to the floor. Represent the book as a
box. Draw the direction of the force Jessica exerts on the book and the direction of the book’s displacement. How
much work did she do on the book?
1.8 Reason
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. 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.
1.9 Relate
Describe a situation when you have done:
a)
+1 J of work on a system.
Adapted from PUM
©2010, Rutgers, The State University of New Jersey
Kreutter: Work and Energy
b) -1 J of work on a system.
c)
0 J of work on a system.
1.10 Regular Problem
While working out, a man lifts a 10-kg object a vertical distance of 0.80 m. He then carries it for 10 m where he
sets it down a vertical distance of 0.80 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