Physic 151 Kinetic energy lab report full

7/22/2019 Physic 151 Kinetic energy lab report full

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Physics 151

Lab 11

Momentum and Energy

4/20/12



Purpose:

To examine the conservation/ loss of momentum and energy in inelastic and elastic

collisions.

Theory:

This lab observes one dimensional collision of two objects; two types of collisions are

possible:

Elastic collision – Characterized by the objects involved deflecting off of each other, momentum

and kinetic energy is conserved.

Inelastic collision – Characterized by the objects involved adhering with one another, kinetic

energy is not conserved; momentum is conserved.

The apparatus used in the lab has the properties of a conservative system, that is, there are

no net external forces - such as friction- acting on the objects. In a conservative system,

momentum is conserved throughout a collision, regardless of whether it is elastic or inelastic;

theoretically, the momentum of the whole system before the collision is equal to the momentum

after the collision.

This is represented by equation is the symbol for momentum, which is

defined as the product of an object’s mass (m) and its velocity (v). Momentum for an object is

given by Note that velocity is a vector, mass is scalar; therefore momentum is

actually a vector product. This means that an object can have negative momentum, such as when

an object retraces its path as the result of a collision. When calculating the total mass of a system,

all masses must be accounted for. For example:



In a collision, momentum is exchanged between two or more bodies. The law of

conservation of momentum states that the sum of each body's momentum before a collision

equals the sum of each body's momentum after a collision, and/or after a collision, the

momentum lost by one object equals the momentum gained by another.

An elastic collision conserves kinetic energy as well as momentum. With two object’s

colliding, such as observed in the lab, the total kinetic energy is given by

With an inelastic collision – two objects observed - the two bodies will combine and

move at the same velocity as one unit.

Procedure:

SI units are used in this lab, mass is in kilograms, velocity is m/s, momentum is in kg(m/s), the

flags lengths are converted to meters.

http://www.s-cool.co.uk/category/subjects/a-level/physics/momentum-and-impulse



The gliders that used by the group were identical; at the least, the flags on the gliders must be

uniform in size. This is because the flag length will be used to find the velocity of the glider.

For each trial, the percent difference between momentum values will be calculated to find the

momentum lost from the collision. For momentum, this is given by:||

This

must remain under ten percent to consider the lab a success. To avoid doing hand calculations,

which will slow down the efficiency of the lab, it is recommended to set up an excel table to

calculate the data as it is collected.

Trials Mass 1 (kg) Mass 2 (kg) Time bef. (1) Time aft. (1) Time bef. (2)

Time aft. (2) Int. Velocity (1) Initial Vec. (1) Final Vec. (1)

The photograph to the left show

an apparatus that is very similar

the one used by the group. All

collisions in the experiment mu

occur between the two photo

gates. The track itself should be

level. The masses of each glide

must be found in kilograms;

initially the gliders will not

significantly differ in mass. Mak

sure the air track is level and

working correctly before

proceeding with the experimen

https://reader009.{domain}/reader009/htm



Final Vec. (2) Initial momentum (p) Final momentum (p) % Difference

After having the excel table set up, and the mass of the gliders determined; the trials can begin.

Part 1 deals with elastic collisions, the ends of the gliders must be set up to bounce off of

each other. Glider 2 will be placed in a stationary position in between the two photo gates. Glider

1 is given an initial push towards glider 2. Glider 1 will pass through the first photo gate, collide

and bounce off of glider 2, causing it to re-trip the photo gate that it has passed. The photo gates

are set to read the total time tripped by the gliders, and keep a memory of its first trip time. The

collision will cause glider 2 to move from its stationary position and tripped the second photo

gate. After the collision, both gliders will be headed outward to each end of the air track, they

must be stopped after they trip/re-trip the photo gates. The before and after momentum values

must be calculated for this trial, since glider 1 starts out in a stationary position, it’s initial

velocity is zero. Glider 1 has no initial momentum, so the initial momentum of the system will be

equal to, . Remember that the initial velocity of the

glider will be given by

. After the collision, glider one is

stopped, so its final velocity is zero. The final velocity of glider two will be its speed as it passes

through the second photo gate:

. Since glider 1 stops, the final

momentum will be found by . Calculate the percent difference of

the momentums; repeat the procedure until 3 trials are completed with acceptable results.

Part 1.2 observes elastic collisions, this time the gliders approach the photo gates from

one end of the air track. Glider 2 is placed is front of glider 1 so it is closer to the photo gates

than glider 1. Glider 2 is given a push towards the photo gates and shortly after, glider 1 is given



a push so that it collides with glider 2 while they are in between the photo gates. It is important

that glider 1 passes through the first photo gate before glider 2 collides with it. The two gliders

will bounce off of each other but continue down the air track. Both gliders will trip the second

photo gate; they should be stopped when they reach the end of the track. Glider 2 is the leading

glider; it is the first to trip both the first and second photo gate. The photo gates will display their

total recorded trip time, as well as their initial reading. The initial velocity of the glider 2 is

calculated through:

The same concept applies for

the final velocity, at the second photo gate,

. The

photo gates display the total time that the gates where tripped, so to find the velocity of glider 1,

the difference of the total reading and the initial reading is

used.

The same applies the final velocity,

Now the momenta values can be found,

( ) After completing

these calculations, the next step is to find the percent difference. Then complete at least two more

trials for this part, place the data on the excel table.

Part 1.3 repeats part 1, with one modification. 100 grams - 50 on each side - will be

added to glider (2). Glider 2 will again be placed in a stationary position between the two photo

gates. The procedure from part 1 is followed to with the mass changed for glider 2.



Part 1.4 is a reproduction of part 1.2, again there is a modification. The leading glider will

have 100 grams added to it. The procedure of part 1.2 can be followed with the change in the

mass of glider 2.

Part 2.1 deals with inelastic collisions, so the gliders must have the appropriate ends

towards each other that would make them stick. The masses of the two gliders should be equal

for this part of the lab, remove any riding masses. Glider 2 will be placed at rest in between the

two photo gates, it should remain stationary. The initial momentum is calculated as it was in part

1, that is, The same goes for the initial velocity

measurement,

Except, now the two gliders will combine and

pass through the second photo gate as one unit, so they will share a common final velocity. The

combined gliders will have two flags that will trip the photo gate twice. If a flag cannot be

removed from a glider, then simply use the initial reading of the second photo gate to find the

unit’s final velocity.

The final momentum is

calculated with the use of the shared final velocity,

The next step is to calculate the

percent difference of the momenta values. Part 2 also asks for the kinetic energy values before

and after the collision; recall that

Since glider 2 is not initially

moving, it has no kinetic energy; the initial kinetic energy of the system becomes,

After the collision there should be a much different kinetic

energy value, it is not expected that kinetic energy will be conserved, being that this is an

inelastic collision. Final kinetic energy of the system,

( )

By obtaining the difference



between final and initial kinetic energy, one may be able to tell whether or not kinetic energy is

observed. It may be desirable to use the percent difference formula to illustrate the discrepancy

in the values. ||

At least two more trials need to be

conducted; the formulas are used as needed.

Part 2.2 is the last part of the lab, it deals with inelastic collisions. The gliders should

already be set to stick to each other. The procedure in this part is similar to part 1.2; the gliders

approach the photo gates from one end of the air track. Just like 1.2, glider 2 is placed is front of

glider 1. Glider 2 is given a push, shortly after; glider 1 is given a push, and the two gliders

collide whilst they are in between the photo gates. The two gliders will stick to each other and

trip the second photo gate as they continue to travel down the air track. The equation for the

initial velocity for glider two is the same as that in part 1.2

As well as in part 1.2, the initial velocity of

glider 1 is found with the difference of the total reading and the initial reading of the first photo

gate.

The final velocity will be

shared;

The method for finding the initial

momentum follows part 1.2

The final

momentum is found just like it is in part 2.1

The gliders are one unit when

they pass through the second photo gate:



Like the other trials, the percent difference of momenta must be calculated, and for this part, the

discrepancy for the initial and final kinetic energy values as well. This time the each glider has

its own initial velocity, the total initial kinetic energy is

Then the final

kinetic energy, after the crash, is:

( )

Determine if there is at all a

conservation of kinetic energy, use the percent difference formula. ||

After completion of all parts, print out the Excel tm table.

Measurements and Calculations:

The group’s recorded values can be found on the print out of the Microsoft Exceltm

table.

Parts 1, 1.2, 1.3, and 1.4:

Is momentum conserved? Explain any discrepancies.

The trials in parts 1 – 1.4 had a percent difference of momentum transfer that remained

under 5 %. Therefore, it is safe to conclude that momentum was conserved for this portion of the

lab. Ideally, the momentum transferred from glider to glider would be exact, but in reality this is

an exceedingly rare occurrence. There is a high probability that an inefficient transfer of

momentum is responsible for the percent difference values. The ends of the glider may have

absorbed for momentum than it projected. There is also the case of friction, which was negligible

but not absolutely diminished. Friction would count as an external force; this would change the

system to be non-conservative.



Part 2.1:

Is momentum conserved for inelastic collisions? Explain any discrepancies.

With percent differences that stayed under 9 %, one can conclude that momentum was

conserved for these trials. Again there is there possibility of friction; however it is more

likely that the stationary glider absorbs momentum itself. The velocity of the moving glider

slows down due to the collision while the stationary speeds up due to the collision. The two

velocities meet at an equilibrium point and the masses are combined. This new momentum

is equal to the initial momentum; ideally the momentum values are exact.

Is kinetic energy conserved for inelastic collisions? Explain any discrepancies.

Kinetic energy values for Part 2 were calculated using the values on the table.

Part 2.1

Trial 1 0.0163794312 0.0083602603 64. 8 %

Trial 2 0.0305687222 0.0161377568 61.8 %

Trial 3 0.0170548323 0.0101117310 51.5 %

A high percent difference was expected for the inelastic collision portion of the lab.

Inelastic collisions are characterized by the known change of kinetic energy.

Part 2.2:

Record your data, calculate the momenta before and after the collision, and kinetic

energy before and after the collision. Explain any discrepancies.



Momentum was conserved for these last trials as well; percent difference did not stray above

2 %. Air resistance is a very small factor but it may have played a more significant role in

these last trials. As the front glider moves, it disrupts the air it travels through, the glider

behind is likely to be effected by this draft of the front glider. Essentially, the draft would

affect the glider’s velocity; this effect would not be perceivable to the naked eye, but it could

explain such a low percent error.

Kinetic energy values:

Part 2.2

Trial 1 0.0268857407 0.10878624 120.733 %

Trial 2 0.0457650738 0.1830491145 119.96 %

Trial 3 0.0200776868 .080314004 120 %

Again it was expected that there be a high percent difference in the kinetic energy values.

All factors that were present in the previous trials were also acting on the gliders in these last

trials.

Conclusion:

The transference of momentum is something used in everyday life. For example, a UFC

fighter who wants to drive his partner to the ground, would build up his velocity towards

him, that combined with his mass will build momentum. The momentum alone may be

enough to achieve his objective, then there is proper technique. There is a relationship

between momentum and energy. Kinetic Energy is a scalar (no specified direction) while

momentum is a vector (has a definite direction). Their applications are different kinetic energy is a



quantity that can increase or decrease by changing the momentum of an object. An object will build

kinetic energy as it builds momentum. In an inelastic collision, the loss of kinetic energy is

sometimes noticeable, such as a car crashing into a wall and stopping. Elastic collisions that

conserve momentum are often needed for activities. Basketball for example, relies on constant

elastic collisions with the ball and the floor. This is a simple task referred to as dribbling; what’s

going on is that the ball has a kinetic energy and a momentum downward. The ball has an elasticity

that causes it to bounce off of the floor and return with almost the same kinetic energy and

momentum. There is a slight loss due to conversion of energy to sound, but the elastic event suffices

for the purpose of the sport.

Physic 151 Kinetic energy lab report full

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