Physics/Dr. Lankar
Name: ________________ section: ______________:
grade:
_______
KINETIC ENERGY VARIES AS THE SQUARE OF THE SPEED
MATERIAL:
DVD
Einstein's big idea from NOVA , soft clay, small funnel, fine
sand (craft store), tissues, large steel (or lead) balls,meter
sticks, cylinver 10ml
optional: cubes of different masses
PART1:
WATCH THE segment : Emilie du Chatelet. Discuss the experiment.
Emilie found that the kinetic energy is proportional to the speed __________. She disagreed with Newton and was right.
PART2: In Emilie's shoes
INTRODUCTION - FILL BLANKS
Like Emilie, You are going to drop metal spheres clay. Before falling, the spheres have _______________ energy.
this
energy is then transformed into ____________energy (energy of
motion ). Before hitting the clay, the speed of the spheres
is
maximum and can be computed by using the _______________ of energy
so m g h = 0.5 m V2 cross out the mass and solve for the speed V = __________. Keep this formula in mind.
if
you neglect air resistance, the speed does not depend on the _________ of the
spheres, only on the _____ and the acceleration due to gravity g.
(you already knew that. Regardless of their mass, objects fall at the same ______ if we neglect air resistance).
Then
the ball hit the clay and goes into it. The kinetic energy is
transformed into damage done to the clay. (the ball changes the ____ of
the clay).
Emilie du chatelet was able to show that, if you double
the speed of the ball, the kinetics energy is not multiplied by
________ but
by
____ ! and so is the damage done to the clay. SAmething on the
highway. If you bump into a car ahead of you, the kinetic energy
of
the car goes into damage (broken glass, folded metal .. ) . If
the speed is doubled, the damage will be multiplied by _____________.
When
you brake, the brake is doing work on the car. The brake applies a
force over a distance. (skid distance, it takes time for the car to
stop).
If you double the speed, the distance is not double but
multiplied by ________.
(work done by brake = force x _______= loss of kinetic energy of the _____ ).
In
this
experiment, You are going to show that if the speed is multiplied
by a factor f, the mark of the sphere in the clay is multiplied by f2
You
will be given 2 heights from which to drop the spheres. You will see what happen to the casts left on the clay.
PROCEDURE
PART1 : YOU NEED A LARGE SPHERE OF STEEL + CLAY + 2 METER STICKS + tissue + color craft sand + small funnel + cylinver 10ml
READ: 2 heights are considered: H1, H2 You will drop the sphere from
H1, then H2. We neglect friction .
STEP0: Find the mass of the sphere using a plate scale in grams. Mass = ___________g . Record in TABLE 1.
STEP1
prepare a pad of flat , soft clay and place on a paper on the ground. Get a heavy ball and Hold the
the sphere 0.9 meters (that is 90cm)
and drop it. Your partner will hold the meter stick.
Gently,
remove the sphere from the clay. Now you need to find the volume that fills the impression.
(you
can use water to find the volume in cm3 but I found it messy. Instead
you can gently carpet the bottom of the impression with a tissue
and
fill the cavity with the sand up to the surface of the pad. (see bellow
picture). Remove excess of sand. Lift the tissue with the sand
and pour the sand in a 10ml graduated cylinder using a funnel and record the height. That will be your volume. In that case, the volume is proportional to the height.
volume
of cylinder = base x height and since the base stays the same
then the volume is proportional to the height. We don't need to
know
the absolute value of the volume because we are computing ratio, comparing 2 volumes).
V = _________ ml
repeat the experiment 3 times and record the average value in table 1.
TABLE1
Mass = m = ______ g
drop height =h1= 0.9m (90 cm)
speed =s1= _________ ( √(2g x h1) | drop height = h2=1.6m (160cm)
speed =s2 =________ (√(2g x h2 ) ) |
| Volume V1 = | Volume V2 = |
The kinetic energy the sphere has (before hitting the clay) is being transformed damage done to the clay.
as
the speed s increases, the damage should _______________. The
damage is proportional to the ________ V of the mark.
So as the speed increases, the volume of the sphere should also ___________. Let's see if this is true.
STEP2: REpeat the procedure, dropping the balls from a height of 1.60m .
Fill TABLE 1
ANALYSIS PART I. (you can do this part at home)
1) Compute the speed s1, s2, of the sphere just before hitting the sphere.
Record
in TABLE 1. (use the formula )
2)
So s2/s1 = ______. (s2/s1)2 = ___________ Using the data recorded in table find V2/V1 =
__________. (ratio volume, damage done)
Is it consistent with Emilie statement ? (you should get V2/V1 = (s2/s1)2 )
What is Emilie statement ?
(the damage done (volume in clay) does not varies with the speed but with the _________________________ )
3)
So The kinetic energy is not proportional to the speed but to the speed
________. That means that the damage done to the clay is also
proportional to the speed _______. (kinetic energy = ability to do work or damage).
4) In this experiment, the manipulated variable (independent) was the __________. (what did you change)
The responding variable (dependent) was the ____________ in the clay. The controlled variable was the ________. (stays the same)
5) here we supposed that there was no air resistance. Is it a good approximation ?
why ?
6) we also suppose that all the kinetic energy of the sphere is transformed into the damage done to the clay.
Is
this right ? What other
kind of energy did we neglect ?
How can this affect your measurements.
7) We also suppoe that the spheres were falling in a straight line. Was is exact ?
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EXTRA CREDITS - PART II: SAME HEIGHT BUT DIFFERENT MASSES - EXTRA CREDIT PART
Now You are going to work with cube of different masses (manipulate or independent variable).
m1,
m2 and m3 (m3>m2>m1). They all have the same shape. (same area).
You will drop them from the same height (controlled variable).
So the speed is now the _________ for all the masses (if we neglect friction, they are in free-fall)/. You are going to compare
the volume of the shape in the clay. (therefore the damage done to it). Since kinetic energy is proportional to the mass
(not the mass squared) the volume should increase at the same rate as the masses. (m2/m1 = V2/V1)
If you double the mass, the damage is also multiplied by _____ not by _______
STEP1: Use metal cubes of the same volume but of different density. (like aluminum, copper , zinc ..)
Find the mass of each cube and record in TABLE 2.
STEP2: Drop teach of the cubes from the same height and record in the TABLE 2. (maybe 0.5m).
The shape in the clay should be perfect. corners are not ok/ See below a picture take by students in
my class. : (thank you Lara and Whynona). Record the depth of the shape.
TABLE 2
| object | Mass (g) | depth(cm) |
| aluminum (lighter) | m1 = _____ | D1 = ______ |
| zinc | m2 = ______ | D2 = _____ |
| copper (gold) | m3 = ________ | D3 = ______ |
because the width and the length of the shape in the clay are always the same, you will work with depth instead of volume.
Since we are studying ratios, it does not matter.
ANALYSIS PART II
1) Compare m2/m1 _____________ to D2/D1 = _______________
do you get the same ratio? Explain why it should be
2) Compare m3/m1 ______________ to D3/D1 = _______________--
Si
that the same ratio ?
Explain why it should be
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GOING FURTHER. Use change in kinetic energy = work done or 1/2 mV22 - 1/2mV12 = force x distance
convert km to m and hour to seconds. 1 km/h = 1000/3600 m/s
1)
A 875kg car speeds up from 22m/s to 44m/s while passing another car. What
were its initial and final energies, and how much work was done
on the car to increase its speed ? (the work in done by the engine, you are using fuel)
hint:
work done = increase energy. The work is the amount of energy
transfered from the oil (chemical energy) to the motion of the car
(kinetic energy).
2) A comet with a mass of 7.85 1011 kg strikes EArth at a speed of 25km/s
A) Find the kinetic energy of the comet in joules ?
hint: convert km to m
B) Compare the work is done by in stopping the comet (found in A) to the 4.2 1015J of energy that were released by the largest nuclear weapon ever built.
Such comet collision has been suggested as having caused the extinction of the dinosaurs.
3)
A) How much work is needed to accelerate a 5,700kg (almost 6 tons) trailer truck to 100km/h (from rest)?
hint: convert to m/s here is a short cut to convert.
B) What would be the truck's speed if half as much work were done on it?
hint: the work done is the change in kinetic energy. The new kinetic energy is what you found in A) divided by 2.
Then use work = 0.5 m V2 to solve for V.
C) What would be the truck 's speed if twice as much work were done on it ?
hint: multiply A) by 2 and solve for V
4)
A) Find the kinetic energy of a 5g snail moving at a speed 0.05km/h. Use scientific notation.
hint: convert g to kg and km/h to m/s
B) Find the kinetic energy of a 148g pitched baseball at 45m/s
hint: convert g to kg
C) Find the kinetic energy of 100kg orbiting satellite at 78km/s
hint: convert km/s to m/s
5) A riffle shoot a 4.20g bullet at a speed of 965m/s.
A) Find the kinetic energy of the bullet as it leaves the riffle
hint: convert g to kg, KE = 0.5 m V2
B) What work is done on the bullet as it leaves from rest?
hint:
work = energy transfered to bullet = change in kinetic energy of bullet
with Vinitial = 0 and Vfinal = 965m/s/ change in kinetic energy = 0.5mVfinal2 - 0.5mVinitial2
C) If the work is done over a distance of 0.75m (75cm), what is the average force on the bullet ?
hint: remember ? work (J)= force (N) x distance (m). The work has been computed in B)
D)
If the bullet comes to rest by penetrating 1.5cm into metal, what is
the magnitude and direction of the force the metal exerts ?
Assume the force is constant.
hint: convert cm to m. The energy is conserved. Use work found in B). use work = force x distance.
6) A steel ball has a mass of 4.0kg and rolls along a smooth , level surface at 62m/s.
A) Find its kinetic energy
hint: again, use the formula for KW
B)
At first, the ball was at rest on the surface. A constant force acted
it through a distance of 22m to give it the speed of 62m/s.
What was the magnitude of the force?
hint: again, change in kinetic energy = work done = force applied x distance / with Change in kinetic energy = 0.5mVfinal2 - 0.5mVinitial2 / Vfinal = 0
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