Conservation Of Linear Momentum Formal Lab Report 2zt2d

Conservation of Linear Momentum Andrew Borgman Jake Miller Eric Millward

PHY 183 D October 8, 2012

I.

Abstract

In the Conservation of Linear Momentum lab, we studied the conservation of linear momentum and kinetic energy in both elastic and inelastic collisions. We measured the mass of the carts and the velocity of the carts, which gives us momentum, both before and after the collisions. To accomplish this, we used the photo gate program to measure of the velocity of the air carts before and after an inelastic or elastic collision, and calculated the linear momentum and kinetic energy to see if it was conserved. We found that the change in momentum of the system was very close to zero for both elastic and inelastic collision. We got the same results for the loss of kinetic energy, thus showing that kinetic energy was for the most part conserved in elastic, but not inelastic collisions. However, we had a 1-2% error in our calculations, probably due to an uneven track, or miscalculations in our measurements.

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II.

Introduction

Linear Momentum is a vector quantity obtained by multiplying the velocity and mass of an object, displayed by equation 1, with p equals momentum. In a closed system, not affected by external forces, the total linear momentum will not change, meaning that it is a conserved quantity. This is known as the law of conservation of momentum, which is implied by Newton’s laws of motion, proven by equations 2 and 3, when m equals mass and v equals velocity. P=mv

(1) (2) (3)

Using this knowledge of linear momentum, we hypothesized that the sum of momenta before the collision will be equal to that after the collision. We had the same theory for both part 1 (inelastic collision) and part 2 (elastic collision) of the lab. The purpose of the experiment was to study how linear momentum and kinetic energy is conserved in both elastic and inelastic collisions. To this concept, we measured velocity of the object in a nearly frictionless environment before and after a collision, and measured the deviation from the initial to the final values.

III.

Apparatus

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Air track and apparatus

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Computer

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Air carts with timing strip

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Photogate program

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Triple beam balance

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Red Cart

IV.

Air Track

Orange Cart

Procedure

First we measured the masses of the two carts on the triple beam balance, so that we can use them for calculations later on. We ran five trials with varying initial velocities, and using photogate we determined the velocity of the carts before and after the inelastic collision. Using the velocity and mass of the carts, we calculated the initial and final momentums of the carts, and then found the change in momentum of both cart 1 and 2. Next, we did the same process, except we changed from an inelastic collision to an elastic collision by turning the carts around. V.

Results and Discussion

Through our testing, we came to the conclusion the linear momentum will be completely conserved in both an elastic and inelastic collision, only if the conditions are perfect, and there are no external forces acting upon the objects. However, while kinetic energy is conserved during a perfectly elastic collision, it is NOT entirely conserved in an inelastic collision. PART 1: v1i (m/s) v1f (m/s) v2i (m/s) v2f (m/s) Pi (kgm/s) Pf (kgm/s)ΔP1 (kgm/s) ΔP2 (kgm/s) Δpsy s (kgm/s) Ki (J) Kf (J) loss in K (J) 0.1 0.07 0 0.07 0.0209 0.029316 -0.00627 0.014686 0.008416 0.001045 0.001026 -1.894E-05 0.26 0.1 0 0.1 0.05434 0.04188 -0.03344 0.02098 -0.01246 0.007064 0.002094 -0.0049702 0.36 0.14 0 0.14 0.07524 0.058632 -0.04598 0.029372 -0.016608 0.013543 0.004104 -0.009439 0.53 0.2 0 0.2 0.11077 0.08376 -0.06897 0.04196 -0.02701 0.029354 0.008376 -0.0209781

Data Table 1 (Inelastic Collision) Average (kgm/s) -0.0119155 Std. Dev. (kgm/s) 0.014872008

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The values of the change in momentum of cart 1 were negative values, whilst the values of ∆p for cart 2 were positive numbers, although both of the sets of numerical values were very close to each other (2). By looking at the data table, you can tell that the values of deviation are close to zero, suggesting that very little linear momentum was lost, thus linear momentum for the most part was conserved (3). However, kinetic energy was actually lost in the inelastic collision, which yielded different results than did the conservation of momentum. Kinetic energy was not conserved in the inelastic collision, because of the friction of the Velcro (4). This result is because it is only a partial inelastic collision that occurred. My answer for question 4 does make logical sense, because there are external forces acting upon the cart, such as friction between the Velcro pads (5). PART 2: v1i (m/s) v1f (m/s) v2i (m/s) v2f (m/s) Pi (kgm/s) Pf (kgm/s)ΔP1 (kgm/s) ΔP2 (kgm/s) Δpsy s (kgm/s) Ki (J) Kf (J) 0.27 0 0 0.19 0.05643 0.039862 -0.05643 0.039862 -0.016568 0.007618 0.003787 0.67 0 0 0.48 0.14003 0.100704 -0.14003 0.100704 -0.039326 0.04691 0.024169 0.45 0 0 0.32 0.09405 0.067136 -0.09405 0.067136 -0.026914 0.021161 0.010742 1.02 0 0 0.74 0.21318 0.155252 -0.21318 0.155252 -0.057928 0.108722 0.057443

loss in K (J) -0.0038312 -0.0227411 -0.0104195 -0.0512786

Data Table 2 (Elastic Collision) Average (kgm/s) -0.035184 Std. Dev. (kgm/s) 0.017789454

The values of the change in momentum of cart 1 were negative values, whilst the values of ∆p for cart 2 were positive numbers, although both of the sets of numerical values were very close to each other (7). The linear momentum was conserved in the elastic collision, you could tell by the very small standard deviation, and the ∆p1 is the negative initial momentum (8). Kinetic energy was mainly conserved in the elastic collision, because the initial kinetic energy value is close to the final kinetic energy value (9). My answer for question 9 does make logical sense because the reason for the conservation of kinetic energy is due to the clean bounce off the two surfaces,

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meaning there was relatively no friction (10). The conservation of linear momentum is more of a common occurrence in everyday life than you would expect. For example, hitting a baseball with a bat is an elastic collision, since the baseball and bat do not stick together (12). If a 747 jet were to strike a fly in flight, the fly would experience a larger change in linear momentum as a result of the collision, because it has a much smaller mass (13). Using this data, we are able to draw accurate conclusions on how linear momentum and kinetic energy are conserved in a closed system.

Conclusion In conclusion, we found that linear momentum is conserved in elastic and inelastic collisions when there are no external forces acting upon the objects. Although our hypothesis was partly correct, we proved that kinetic energy is not conserved in an inelastic collision. Our results were not perfect; there were various factors that affected our results, such as imperfect measuring tools, an uneven air cart track, and human errors in calculation. Even with these errors, the lab helped prove that without external forces, Newton’s law of conservation of momentum and energy are very correct.