I need help with physics lab report
Ahmed_jr
NORTHERN ILLINOIS UNIVERSITY
PHYSICS DEPARTMENT
Physics 253 – Basic Mechanics Fall 2016
Lab #10
Bring to Lab your USB Flash Drive with the Excel Template file from Lab WebPage
Lab Writeup Part #1 Due: Mon/Tue/Wed/Thu, Nov. 7/8/9/10, 2016
Part #2 Due: Mon/Tue/Wed/Thu, Nov. 14/15/16/17, 2016
Read Giancoli: Chapters 7,8,9 (Lecture Notes #9,10,11)
Collisions
Apparatus
An ideal track would be without friction, but friction can be minimized with well
lubricated and aligned wheels on a cart. The track must also be level to negate any
effects of gravity. There are two carts: a heavy cart of mass m 1 and length
1 and a
light cart of mass m 2
and length 2
. The carts use repulsive magnets to cause elastic
collisions, and the carts use velcro to cause inelastic collisions.
A t-shaped metal bracket, or fin, is attached to each cart which will block a
photogate beam. Two photogates are positioned over the track and can measure the time
t that a cart passes through the beam. The times can be read from the Logger Pro software when the photogates are attached to the computer. The photogates record the
elapsed time between the time the rectangular fin blocks the beam until it is no longer
blocked, but they do not record the direction of motion. The experimenter must
determine the direction of motion.
Theory
Velocity is the time rate of change of position of an object. If the time it takes to
travel a known distance is measured, then the velocity is
distance
v elapsed time
(1)
The sign of the velocity depends on the direction of the object. If it is moving in the
positive direction, the velocity is positive, and if it is moving in the negative direction, the
velocity is negative. An object at rest has a velocity of 0.
Momentum, p , is the product of mass, m , and velocity, v . Since velocity is a vector and has direction, so does momentum. For two or more interacting objects, the
total momentum is just the sum of the individual momenta. For two masses (m 1 ,m 2
)
and velocities (v 1 ,v 2
) moving only in one dimension, the total momentum, P , is
P p p m v m v 1 2 1 1 2 2
(2)
If there are no forces acting on a set of objects other than internal interactions
between them, the system is called an isolated system. In any isolated system the total
momentum of a set of objects is constant. We say that the total momentum in an isolated
system is conserved. During a collision the time is so short that any external forces
present do not have much affect on the momentum of the system. This allows us to
describe all collisions in this lab as occurring in an isolated system and allows us to use
conservation of momentum. If the initial total momentum is iP and the final total
momentum is fP , conservation of momentum is i fP P .
Objects in motion also possess kinetic energy. Kinetic energy, K , is a scalar quantity that is never negative. It also depends on the mass and velocity according to
K mv 2 1
2 (3)
Like the total momentum, the total kinetic energy of a system is just the sum of the
individual kinetic energies. For a system of two objects the total kinetic energy is
K m v m v 2 2 1 1 2 2
1 1
2 2 (4)
In certain collisions between objects that only involve a conservative force, such as an
ideal spring (magnetic spring), the initial total kinetic energy, iK , equals the final total
kinetic energy, fK . This type of collision is called an elastic collision.
Other collisions are called inelastic and involve some loss of energy during the
collision. The final total kinetic energy is always less than the initial total kinetic energy
of the system. A completely inelastic collision occurs when the two objects collide and
stick together. This means that the two objects leave the collision with identical
velocities: f f f v v v 1 2
. We can write Eq. (2) for a completely inelastic collision as
i i f f fm v m v m v m v m m v 1 1 2 2 1 1 2 2 1 2 (5)
Data Collection
Bring the Excel Spreadsheet Template for this lab on your USB flash drive
All green colored cells of the Template must be filled out and you must calculate the
velocities in Step (2) before you leave the lab.
(1) Each cart should have a metal t-shaped bracket, or fin, mounted on them. One cart (the heavy cart) should have an additional magnetically attached mass under the
rectangular fin. Measure and record (in the appropriate green colored cells of your
Excel Spreadsheet Template) the total mass ( L m (light cart) and
H m (heavy cart))
of the two carts and their uncertainties. Also measure the length of the rectangular
fin of each cart ( L d and
H d ). Adjust the distance between the sensors, D , of the
photogates to be half a meter or less (but not less than the total length of the two
carts). Record these distances as well as their uncertainties in your Excel
Spreadsheet, and also give them the symbolic names expressed in the Template.
(2) Velocity of each cart: Open the Logger Pro software and make certain that the photogate sensors are interfaced. Make a trial run by pushing the light cart so that it
passes through both photogates, but be sure to catch the cart before it hits the end of
the track. Record the times from the computer—you should get only 4 time data
points (make certain you understand why) for 1 pass through both photogates. If you
get more than 4 time data points, make certain your photogates are properly aligned
(they should be perpendicular to the track). Once you get 4 time data points, with
your 3 distances, L d , D , and Hd , calculate the two velocities:
(1) the velocity at the 1st photogate (calculate this in the Excel green cell D11).
(2) the velocity at the 2nd photogate (calculate this in the Excel green cell F13)
Do the same for the heavy cart. You will need these results in the Analysis Section.
(3) Elastic collisions: Place two carts on the track so that their magnets are facing each other. We want the carts to collide with each other, but making no physical
contact. This is called an elastic collision. Place the light cart between the
photogates. Measure and record in your logbook its distance from both photogates.
Push the heavy cart so that it goes through the 1st photogate (you should not be
pushing as it goes through the photogate), then collides with the light cart (the heavy
cart should have completely passed through the 1st photogate before the collision),
and then either both carts go through the 2nd photogate or the heavy cart goes back
through the 1st photogate and the light cart goes through the 2nd photogate (either
result is fine). You will have to do several trial runs to accomplish this. You should
get 6 time data points allowing you to find the initial velocity of the heavy cart, and
the final velocities of the heavy and light carts.
(4) Repeat Step (3) with the light cart pushed to collide with the heavy cart.
(5) Inelastic collisions: Now we want the carts to make physical contact during the collision and stick together. Place the light cart between the photogates (measure and
record its distance from both photogates) and push the heavy cart hard enough so that
they collide and stick together due to the velcro. From the timing data, you should be
able to determine the initial velocity of the heavy cart and the final velocity of the
combined heavy and light cart.
Analysis
(1) Find the initial and final velocity of the heavy and light carts through each photogate in Step (2). Determine the acceleration (and its uncertainty) of the carts (they slow
down because of friction).
(2) Using your results from Part (1) and measurements in Step (2), determine the kinetic frictional force (and its uncertainty) for each cart. What is the coefficient of kinetic
friction for each cart? (remember to 1st draw your free body diagram and then write
Newton’s 2nd law along the x and y -directions and use the kinematical equations of motion)
(3) For the elastic and inelastic collisions (and ignoring friction), find the kinetic energies (and their uncertainties) of each cart before the collision and after the
collision. Is the total kinetic energy of the carts before the collision equal to the total
kinetic energy of the carts after the collision? Do they agree to within your
uncertainties? Is conservation of energy being violated? How much energy is
missing? What type of energy is this missing energy?
(4) For the elastic collisions, now take friction into account in your conservation of energy relations [use the coefficient of kinetic friction determined in Part (2)]. Does
this improve the conservation of energy result?
(5) For the inelastic collision, and including the effect due to friction, estimate the thermal energy generated (and its uncertainty) in the deformation of the carts. Try to
get an estimate of the temperature rise (and its uncertainty) of the carts at the point
of collision (use Eq. 19-2 [page 499] in Giancoli—I have posted this on the Physics
253 Lab WebPage). Is this temperature increase easy to measure?
(6) Summarize your results for Part (4) & (5) (i.e.: what’s your conclusion to all of this?)
(7) For the elastic and inelastic collisions, find the total momentum (and its uncertainty) of the carts before and after each collision. Is the total momentum of the carts before
the collision equal to the total momentum of the carts after the collision? Do they
agree to within your uncertainties? Is conservation of momentum being violated? If
conservation of momentum is being violated, what is causing it? What types of
external forces are involved? Assume the collisions occur in 100 milliseconds—do
your results improve when you take into account the external forces? Summarize
your results in a paragraph.
Due in 24 hours:
(a) Upload your Excel Spreadsheet to Blackboard assignment Collisions #0. This assignment will not be graded, it is just a way for the TA to have your measured
quantities before lab starts next week. That way the TA will be prepared to
answer any questions you have regarding your lab. The spreadsheet does not
have to have any calculations completed—the TA is only interested in getting
your measured quantities.
Due next week: Part #1:
(a) Complete Analysis (1)—this is accomplished by filling out Part (2) in the Template Excel spreadsheet.
(b) Complete Analysis (2) and Analysis (3)—accomplished by filling out Parts (3), (4), and (5) in the Template Excel spreadsheet. Put in your carefully answered
questions wherever asked for in the Excel spreadsheet.
(c) Upload your Excel Spreadsheet to Blackboard assignment Collisions #1
No further writeup is required (no Word document is required).
Due in two weeks: Part #2:
(a) Complete the rest of the Analysis section: Analysis (4) to Analysis (7).
(d) Upload your entire Excel Spreadsheet (Part(1) to Part (5) & Analysis (1) to Analysis (7)) to Blackboard assignment Collisions #2. Answer all questions in
the Analysis sections.
No further writeup is required (no Word document is required).