E
or Analysis
PHYS 1401 SPRING XXXXXXXXXXSection 2103
PHYS 1401 Spring 2020
Collisions
Overview
Collisions
(Section 8.3 and 8.4) Collisions can be classified according to energy relationships and final velocities. In an elastic collision between two objects, kinetic energy is conserved, and the initial and final relative velocities have the same magnitude. In an inelastic two-object collision, the final kinetic energy is less than the initial kinetic energy; if the two objects have the same final velocity (for instance, if they stick together), the collision is completely inelastic.
(8.6)
(8.11)
(8.12)
Virtual Set Up & Equipment
Dynamics track & end stops
Two carts with additional mass
Two photogates & Smart Time
Picket fences
Download Collisions, Momentum and KE Excel Spread Sheet
Preliminary question
1. In one or two paragraphs, describe the difference between elastic, inelastic and completely inelastic collisions with respect to Conservation of Linear Momentum and Conservation of Energy.
Experimental Set Up
Virtual Procedure Procedures
If you were to conduct this lab in class:
1. Make sure that your track is completely level, to the best of your ability.
2. Assign each cart a number, “1” or “2” to each cart and measure the mass of each cart and the picket fence that sits atop the cart. .
3. Activate the Smart Timer. Settings are to measure initial and final velocities of both carts. The photogates are positioned such that there is room for several gliders between the two gates.
4. Place each cart outside the photogates with the magnetic bumpers facing each other and “gently” push the carts toward each other. Make sure that the collision takes place entirely between the two photogates and that the carts to not jump off the track during the collision.
6. The accompanying Excel spread sheet analyzes data based upon 2 carts, each of mass 267 grams. Data is recorded for
v1i (cm/s)
v2i (cm/s)
v1f (cm/s)
v2f (cm/s)
Based upon the data for v1i (cm/s) & v2i (cm/s), calculate the theoretical values of v1f (cm/s) and v2f (cm/s) and compare with those on the spreadsheet.
Calculate Initial and final momenta are calculated for both carts, and the initial and final kinetic energies for both carts. Note that you are using cm, s, g and expressing energy in ergs.
7. Based upon the data provided in the spread sheet, comment on the magnitude of the gain/loss of momentum and kinetic energies for the carts and where in the collision process these losses/gains occur.
8. Play around with the data and provide and insert a chart into this report best representing your comments in (7).
· Be careful! Velocity is a vector, and the timer will only tell you the speed. You will need to choose a positive and negative direction and record your velocities accordingly.
Analysis
1. Choose two of the five trials which provide the most consistent data and calculate the total initial and final momentum (pi and pf) percent difference between them.
pi
pf
% difference
2. For each of your ten trials, calculate the initial and final kinetic energy in J for each cart. Put your answers in the form of a table:
K1i
K2i
K1f
K2f
In this formula for percent difference, pavg is the average of pi and pf.
3. For each of your ten trials, examine the data of the initial and final kinetic energy in J for each cart. Put your answers in the form of a table:
K1i
K2i
K1f
K2f
4. Calculate the total initial and final kinetic energy (Ki and Kf) for each trial run, as well as the percent difference between them.
Ki
Kf
% difference
5. Was momentum conserved in each collision (within 10%)? Explain your reasoning. If not, why do you think it wasn’t?
6. Was kinetic energy conserved in each collision (within 10%)? Explain your reasoning. If it wasn’t, did your system gain or lose kinetic energy?
7. Determine which type of collision you think these represent: elastic, inelastic or completely inelastic? If it doesn’t fit precisely into any category, which does it most closely represent?
8. Summarize your conclusions, noting any unexpected results.
υA, f =
mA − mB
mA + mB
υA, i
u
A, f
=
m
A
-m
B
m
A
+m
B
u
A, i
υB, f =
2mA
mA + mB
υA, i
u
B, f
=
2m
A
m
A
+m
B
u
A, i
Track
Conservation of Linear Momentum in Elastic Collisions
Photogates
Gate 1
Gate 2
Cart 2
Cart 1
10 cm
opaque
and
10 cm
opaque
and
mA(υA, i, x )+ mB(υB, i, x ) = (mA + mB ) (υf, x )
m
A
(u
A, i, x
)+m
B
(u
B, i, x
)=(m
A
+m
B
) (u
f, x
)