Physics lab report 5 PDF

Preview

Summary

momentum lab report ...

Description

Lab #5: Momentum Misheel Dolguun, Anna Hofbauer Introduction Momentum is described as the product of mass and velocity: , because velocity is a vector, momentum is also a vector. The total momentum of an object is conserved if there are no external forces acting on the object. In the collision of two objects, momentum is conserved before, during, and after the collision. Collisions can be classified as elastic, inelastic, or totally inelastic collisions. In elastic collisions, the total kinetic energy is conserved in the collision. The total kinetic energy is not conserved in inelastic collisions. Kinetic energy is also not conserved in totally inelastic collisions, but the two colliding objects stick together and move as a single object following the collision. The kinetic energy of a cart depends on its mass and velocity: KE=½ mv2. The total kinetic energy of a system can be found by adding the kinetic energies of the individual carts. The impulse generated by colliding objects is related to the internal forces acting on one of the objects during a collision. Impulse is a measure of both the strength and duration of a force during a collision. Impulse is defined as the product of the duration of time of the collision and the average force exerted during the collision: . The impulse is also equal to change in momentum: . However, force is not normally constant during the time of the collision so the area under the area under the real force curve must be utilized to find the total impulse over an entire collision: . Experiment #1 - Types of Collisions Procedure Trial 1 - Totally Inelastic Collision: In this portion of the experiment, two carts with velcro strips facing one another, were placed on opposite ends of a track. A motion detector was placed on each side of the track, behind the carts. Each sensor measured one cart. A 250 g mass was placed on top of each cart. Before beginning the collision, the sensors were both zeroed while both carts were stationary. Recording on the PASCO software was started, and one cart was pushed toward the other on the other side of the track, to cause a collision. The cart being pushed, attached to the velcro of the other cart when they collided shortly before separating, and the other cart being propelled across the track. Note, that there were some delays and possible loss in force due to the wheels on cart 1 being sticky. Trial 2 - Elastic Collision: The procedure was repeated with the both of the magnetic sides of the carts facing each other. The cart being pushed propelled the other cart without touching it due to the repulsion of the magnetized sides facing each other getting closer. Trial 3 - Inelastic collision : The procedure was repeated with opposite sides of the carts facing each other, one cart with the velcro side, and the other with the magnetic side, facing the track. After one cart was pushed, it collided with the other cart, physically propelling it. There was no attachment of the carts, but they did touch during the collision. Data Analysis Trial 1: Totally Inelastic Collision

cart

(kg・m/s)

Event Collision: 2 velcro carts

(kg・m/s)

KEf (J)

0.14 kg・m/s

0.02 J

=(.253+.25)kg(0.53)m/ s= 0.27 kg・m/s

KE=½ mv2 = ½ (.503 kg)(0.53 m/s)2 = 0.07 J

0kg・m/s

0J

0.14 kg・m/s

0.02 J

Moving: velcro cart

Stationary: velcro cart

KEi (J)

(kg・m/s)

= (.503 kg)(.53 m/s)+(.503 kg)(0 m/s) = 0.27 kg・ m/s

KEi (J) KEi= KEi1+KEi2 = 0.07 +0 = 0.07 J

(kg・m/s) 0.28 kg・m/s

KEf (J) 0.04 J

This was an inelastic collision because kinetic energy was not conserved; the individual carts had the same momenta and kinetic energy after the collision. The momenta of the collision is almost the same before and after the collision. Kinetic energy was lost in the collision; the kinetic energy after the collision is lower than the initial kinetic energy, 0.03 J of energy was lost as it was converted to some other form of energy. Kinetic energy was not conserved in this interaction. Trial 2: Elastic Collision

cart

(kg・m/s)

KEi (J)

(kg・m/s)

KEf (J)

Moving: magnetic cart

0.23kg・m/s

0.05 J

0.21 kg・m/s

0.04 J

Stationary: magnetic cart

0 kg・m/s

0J

11.1 kg・m/s

122 J

Event Collision: 2 magnetic carts

(kg・m/s) 0.23 kg・m/s

KEi (J) 0.05 J

(kg・m/s) 11.3 kg・m/s

KEf (J) 122.04 J

This was an elastic collision because total kinetic energy is conserved as a result of the repulsion of the magnets on the carts. Momentum increases after the collision and the final kinetic energy after the collision is much higher than the initial kinetic energy before the collision. Trial 3: Inelastic Collision

cart

(kg・m/s)

KEi (J)

(kg・m/s)

KEf (J)

Moving: magnetic cart

0.16 kg・m/s

0.03 J

0.03 kg・m/s

0.001 J

Stationary: velcro

0 kg・m/s

0J

11.1 kg・m/s

122 J

Event Collision: 1 magnetic cart, 1 velcro cart

(kg・m/s) 0.16 kg・m/s

KEi (J) 0.03 J

(kg・m/s) 11.1 kg・m/s

KEf (J) 122 J

This was an inelastic collision where the kinetic energy is conserved. For the cart that is pushed, the momenta and kinetic energy decreased after the collision, but the total momentum and kinetic energy of the system increased greatly after the collision. The second trial with the magnetic carts was the most elastic, both the momenta and kinetic energy of the system increased after the collision. The least elastic collision was the first trial, with the velcro carts, the momenta of the system remains roughly the same and kinetic energy is lost after the collision. In the third trial with the magnetic and velcro carts, energy is conserved but the collision is inelastic. The kinetic energy is lost to the environment, possibly as heat or sound energy. Experiment #2 - Zero Momentum Systems

Procedure Trial 1: In this portion of the experiment both carts were placed in the middle of the track, with the spring plunger of the first cart loaded to the second notch, touching the second cart. It was difficult to make sure the carts were touching and centered on the track because the track was not level, the second cart kept rolling toward the end of the track when being placed. A 250 g mass was placed in each cart. Two motion detectors were placed on both ends of the track, and zeroed with the carts stationary. Recording was started on the PASCO system, and the plunger release button was pushed quickly to avoid interference with the cart’s motion. The carts accelerated in opposite directions. Trial 2: The procedure from the first trial was repeated with both of the weights placed on the first cart and none on the second. The first cart accelerated much less due to the weights. Trial 3: The procedure was repeated with one weight on the second cart and none on the first. The acceleration of the second cart was lessened with the addition of the weights. Data Analysis Trial 1: Mass, Final Velocity, and Final Momentum of Both Carts Cart

Mass (kg)

Vf (m/s)

Cart 1

(0.253 + 0.250)kg = 0.503 kg

0.26 m/s

0.13 kg・m/s

Cart 2

0.503 kg

31.79 m/s

16.0 kg・m/s

Event Collision

(kg・m/s)

(kg・m/s)

(kg・m/s)

pi = mvi(cart1) + mvi(cart2) (0.503 kg) (0 m/s) + (0.503 kg)(0.09 m/s) = 0.045 (kg・m/s)

pf = mvf(cart1) + mvf(cart2) (0.503 kg) (0.26 m/s) + (0.503 kg) (31.79 m/s) = 16.13 (kg・m/s)

Momentum of Cart 1 and 2

Trial 2: Cart

Mass (g)

Vf (m/s)

Cart 1

(0.253 + 0.500)kg = 0.753 kg

0.12 m/s

0.09 kg・m/s

Cart 2

0.253 kg

0.66

0.17 kg・m/s

Event Collision

(kg・m/s)

(kg・m/s)

(kg・m/s)

pi = mvi(cart1) + mvi(cart2) (0.753 kg) (0 m/s) + (0.253 kg)(0 m/s) = 0 kg・m/s

pf = mvf(cart1) + mvf(cart2) (0.753 kg) (0.12 m/s) + (0.253 kg)(0.66 m/s) = 0.257 kg・m/s

Trial 3: Cart

Mass (g)

Vf (m/s)

Cart 1

.253 kg

0.56 m/s

0.14

Cart 2

.503 kg

31.71

16.0

Event Collision

(kg・m/s) pi = mvi(cart1) + mvi(cart2) (0.253 kg) (0 m/s) + (0.503 kg)(0.06 m/s) = 0.0302 kg・m/s

(kg・m/s)

(kg・m/s) pf = mvf(cart1) + mvf(cart2) (0.253 kg) (0.56 m/s) + (0.503 kg)(31.71 m/s) = 16.1 kg・m/s

Experiment #3 - Impulse During Collisions Procedure A force sensor was attached to one end of the track by mounting it to a support rod. A motion detector was placed on the opposite end of the track to measure the velocity of a cart. One end of a string was attached to the force sensor hook, and the other end to a cart. The elastic

string was checked for stretching and the force sensor, for force. Both sensors were zeroed. Recording was started on the PASCO software, then the cart was pushed down the track. Obtaining a reasonable amount of force data was difficult due to the cart running over and getting caught on the string on its return from the push. Data Analysis Force as a Function of Time During Cart Movement

The shape of the force vs. time graph is a negative parabola.The tension in the elastic band as it stretches will exert a force on the cart and change its momentum. Determining the momentum vs. time graph and analyzing when the momentum changes reveals that the cord was exerting a force on the cart from 2.125 s to 3.6 s. The region highlighted is where the elastic cord was exerting a force on the cart. The integral of this function is equal to -0.188 N(s). Using the impulse equation, , the impulse is equal to -0.188 kg(m/s). Momentum as a Function of Time During Cart Movement

The shape of the momentum graph resembles a negative parabola that extends past the x axis and then descends linearly. At equal times before and after the collision the momentum was -0.07 kg(m/s) and 0.07 kg(m/s) respectively. The change in the momentum from the graph is -0.14 kg(m/s). Ideally this value would be equal to the calculated impulse but there is a 0.044 difference. Conclusion Experiment 1 demonstrated the conservation of momentum and the effects of various types of collisions on conservation of momentum and energy. In the first trial, the both velcroed sides of the two carts attached after colliding. This was determined to be a totally inelastic collision because kinetic energy was not conserved, the momentum of the system remained the same and kinetic energy was lost. The initially stationary cart had no initial velocity and both the carts had the same final velocity due to the attachment of the velco after the collision. In the second trial, the magnetized sides of the two carts repelled one another when the moving cart approached the stationary cart. This was determined to be an elastic collision because total kinetic energy was conserved in the interaction. The momenta and kinetic energy of the system increased greatly after the collision. In the third trial, there was no attachment or repulsion

because the velcro side and magnetic side of the two carts have no special interaction besides the physical collision component. This was determined to be an inelastic collision, because the momenta and kinetic energy of the system increased after the collision, but energy was still conserved. These results indicate that in elastic collisions momentum and kinetic energy are conserved, and in ideal inelastic collisions momentum and kinetic energy are not conserved. There are also inelastic collisions that will not be totally inelastic which exhibit no conservation of energy or momentum for the object that force is initially applied to, but will exhibit conservation of both for the total system. Experiment 2 compared the final and initial momentum of the entire system which consisted of two carts. In all of the trials the initial momentum was 0 or negligible because the initial velocity of both of the carts was 0 m/s. The final momentum for trials 1-3 were 16.13, 0.257, and 16.1 kg(m/s); the systems did not retain a total of zero momentum after motion was induced. Experiment 3 demonstrated the relationship between force, momentum, and velocity. The graphs of momentum and velocity were proportional because of the formula p = mv and the mass was constant. The relationship between the force and momentum graph was that a change in momentum signified that the elastic cord was exerting force on the cart. This was difficult to see at first because of the flat regions along the force graph however upon further examination there is still a small but constant force on the cart during the flat region after the collision. The calculated impulse, -0.188 N(s) is theoretically equal to the change in the momentum from the graph, -0.14 kg(m/s) however in this experiment we measured a difference of 0.044 kg(m/s) between the values. This may be explained by the cart getting stuck over the string on its return trip as that would affect the force values and therefore the impulse....