I need help with physics lab report

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).