Conservation of Linear Momentum and Parts of Wall Jib Crane - Research Paper Example

Name: Course: Professor: Institution: Date: Experiment 1: Conservation of Linear Momentum in In-elastic collision Objective This lab experiment was carried out with the aim of testing for the conservation of linear momentum by observation of collisions between two trolleys and measuring the energy changes. Introduction When two or more objects hit each other, a collision is said to occur between the objects. After collision, each object experiences a force for a very short period of time. Normally, this force changes the momentum of the colliding bodies, or it imparts an impulse. If the system of particles involved in the collision is isolated, then the momentum is conserved, and the total momentum remains constant in the system (Lerner, 1996). Collisions can be classified as elastic, inelastic or completely inelastic, and the procedure involved in the analysis of collisions depends on these three. In elastic collisions, kinetic energy is conserved while in inelastic collision, this energy is lost through conversion into other forms of energy. However, momentum is conserved in both elastic and inelastic collisions. In completely inelastic collision, the objects stick together even after collision. In some cases, a collision in which kinetic energy is gained can be described as super-elastic. The study of linear momentum in colliding objects helps in the prediction of bodies that collide in nature. Procedure Two trolleys were selected, labeled and their length measured and recorded. Non-elastic colliders and masses were then fitted on both trolleys and weighed again. Two lightgates were set-up at 0.6m apart, even about the middle of the air track and each of the two connected to two event timers zeroed in MODE B. The light gates were labeled as 1 and 2 corresponding to the left hand and right hand lightgates respectively. After ensuring that both trolleys could pass through the lightgates without any impact, the first trolley was set to the left of lightgate 1 while the second one placed between the two lightgates, and the blower turned on at full speed. The two trolleys were then pushed towards each other at an even speed to ensure that both trolleys could travel through lightgate 2 after collision. The time taken by the trolleys to pass through was recorded on each event timer after collision and recorded in table 2(a). The steps above were repeated to obtain the results recorded in table 2 (b) for Kinetic energy. Results and Discussion Table 1: In-elastic Collisions, Momentum Trolley 1 length 13.2 m Trolley 2 length 13.2 m Trolley 1 mass 0.12 (Kg) Trolley 2 mass 0.12 (Kg) Lightgate 1 Time T1 (s) Lightgate 2 Time T2 (s) Velocity of Trolley 1 V1 (m/s) Velocity of Trolley 2 V2 (m/s) Momentum of Trolley 1 P1 (Kgm/s) Momentum of Trolley 2 P2 (Kgm/s) Momentum Ratio 203.7 198.3 0.0648 0.0666 0.0078 0.0080 0.97 287.3 279.1 0.0459 0.0473 0.0055 0.0057 0.97 228.2 219.9 0.0578 0.0600 0.0069 0.0072 0.96 305.2 291.9 0.0433 0.0452 0.0052 0.0054 0.96 196.6 189.02 0.0671 0.0698 0.0081 0.0084 0.96 104.3 109.97 0.1266 0.1200 0.0152 0.0144 1.05 The ratio of momentum a constant (1). This implies that momentum before collision equals to momentum after collision, and therefore momentum is conserved in this type of collision. There is no any dissipative force in the event of elastic collision and the momentum is still maintained after the action. A plot of momentum of trolley 1 against the momentum of trolley 1 produced the results shown in the figure 1 below: Figure 1: Graph of momentum before collision vs. momentum after collision The line of this graph shows a linear correlation, even though the line is not very straight. This may have resulted from measurement errors that occurred during the experiment and rounding off the values in the calculation part. In a perfectly elastic collision, this line is expected to be linear. In the second part that involved measurement of kinetic energy, the results presented in table 2(b) below were obtained. Table 2: In-Elastic Collision, Kinetic Energy Lightgate 1 Time T1 (s) Lightgate 2 Time T2 (s) Velocity of Trolley 1 V1 (m/s) Velocity of Trolley 2 V2 (m/s) Kinetic energy of Trolley 1 KE1 (J) Kinetic energy of Trolley 2 KE2 (J) Kinetic energy Ratio 139.44 654.8 0.0947 0.0202 0.0005 2.438E-05 0.0453 170.94 751.64 0.0772 0.0176 0.0004 1.850E-05 0.0517 159.02 725.38 0.0830 0.0182 0.0004 1.987E-05 0.0481 149.93 656.32 0.0880 0.0201 0.0005 2.427E-05 0.0522 95.44 436.6 0.1383 0.0302 0.0011 5.484E-05 0.0478 138.5 701.81 0.0953 0.0188 0.0005 2.123E-05 0.0389 From these results, it can be observed that the kinetic energy ratio is much lower, implying that the kinetic energy before and after collision are not equal. The kinetic energy after collision is much lower than the kinetic energy before collision, meaning that there is loss of kinetic energy during the collision of the two trolleys. Some kinetic energy is converted to sound, heat energy and potential energy during the process of in-elastic collision. This is the characteristic that is used to determine if a certain collision is elastic or inelastic, by calculating the kinetic energy after and before collision. In in-elastic collision, kinetic energy is not conserved. The graph in figure 2 below is a plot of kinetic energy before collision against kinetic energy after collision. Figure 2: Graph of Kinetic energy before collision vs. kinetic energy after collision Similarly, it can be observed from the graph in figure 2 that there is no linear relation between the two values, and that at any particular moment, the value of kinetic energy before collision is higher than the value of kinetic energy after collision. Conclusion During in-elastic collision, momentum of the two colliding bodies is maintained. On the other hand, the kinetic energy in the system is not conserved, but instead, it is transformed to other forms of energy such as sound and heat. Experiment 2: WALL JIB CRANE Objectives The first objective for this lab was to determine the experimental values of the forces in the principal parts of the jib crane. The second objective was to study the effect of altering the length of the tie to change the geometry, and finally, the last objective was to compare the results with the forces obtained from graphical solutions using a polygon or a triangle of forces. Introduction The Wall Jib equipment was used sometime back at warehouses for unloading wagons before the fork lift trucks and lorries with on board hydraulic crane were advanced. One advantage of this crane for its popular application was that it could be swung against a wall side of a building when it is not in use. It was also a relatively cheap support. Although today wall jib cranes are obsolete, it has been used for several years to introduce students to studies of accelerated linear motion, especially dependence of acceleration on the force that causes the motion (Prakash, 1997). The self-evident confluence of four forces at the jib end illustrates a real situation of a triangle of forces. This apparatus can be used in the derivation of Newton’s second law of motion. In this experiment, the forces in the Jib Crane members were measured using different weights, and comparing the results with values obtained by graphical solutions. Procedure The Jib Crane was set with a tie of 400mm long, a jib of 530mm long and the distance from tie anchor to jib pivot set at 380mm. The load cord anchor was then fixed at 150mm length above the jib pivot, passing it over the pulley and to the load hunger. It was ensured that there was enough length adjustment for compensation of change in the spring balances. After checking that the hooks for the tie and cord anchor were aligned vertically with respect to jib wall pivot, the four length measurements were recorded in table 1. The “no load” readings of the spring balances were also recorded down as they supported the dead weight. A load of 15 N was then fixed on the hunger and the four lengths readjusted to their original measurements, and the final readings on the spring balance recorded down. This was repeated for loads of 10 N and 5 N. Results and Discussion The table 1 below shows the results obtained from carrying out this experiment. Table 1: Force on the Wall Jib Crane members as observed from the spring balances on the Tie and Jib Length of tie (mm) Length of Jib (mm) Jib Pivot to: Load (N) Tie Force (N) Jib Force (N) Tie (mm) Load anchor (mm) 400 530 380 150 0 0 0 400 530 380 150 15 12.74 32 400 530 380 150 10 6.86 20 400 530 380 150 5 3.92 10 Changing the tie length has an effect on the compression force experienced on the jib length. Increasing the tie length increases the compression force in the jib length as well as the tensional force in the cord length, and vice versa. The pictures in figure 1 below show the space diagram, the free body diagram, the force diagram and the force polygons constructed to a scale of 5mm representing 1 Newton. Figure 1: Space diagram (a), Free body diagram (b) and Force diagram (c) Figure 2(a): Solution by construction of a polygon of forces of the Wall Jib Crane (Load = 15N) Figure 2(b): Load = 10 N Figure 2(c): Load = 5 N Discussion The table below compares the magnitudes of measured and graphically determined forces in the members of the Wall Jib Crane. Measured values Values from a force polygon LOAD (N) Tie Force (N) T1 Jib Force (N) J1 Tie Force (N) T2 Tie Force (N) J2 15 12.74 32 10 30.8 10 6.86 20 6.5 21 5 3.92 10 3.2 10.2 Calculation of Errors Test 1 (load = 15 N) Tie force: % error = = = 21.5% Jib force: % error = = = 3.75% Test 2 (Load = 10 N) Tie force: % error = = = 5.25% Jib force: % error = = = 5% Test 3 (Load = 5 N) Tie force: % error = = = 18.4% Jib force: % error = = = 2% The results obtained by graphical solution closely agree with the results obtained by the spring balances on the tie and jib members for the three test loads. However, the values measured by the spring balance are generally slightly higher than the values obtained by graphical solutions, hence, the errors above. This difference results from the weight of the crane members. In the construction, the weight of the members of the crane have been neglected. Conclusion This experiment enables the determination of magnitude of forces in the members of the jib crane and confirming the results with graphical solutions obtained from a force parallelogram. The results obtained by graphical solutions were in agreement with experimentally measured values. This experiment provides a good knowledge on the study of application of a polygon of forces in a real life situation. References Read More

Table 2: In-Elastic Collision, Kinetic Energy Lightgate 1 Time T1 (s) Lightgate 2 Time T2 (s) Velocity of Trolley 1 V1 (m/s) Velocity of Trolley 2 V2 (m/s) Kinetic energy of Trolley 1 KE1 (J) Kinetic energy of Trolley 2 KE2 (J) Kinetic energy Ratio 139.44 654.8 0.0947 0.0202 0.0005 2.438E-05 0.0453 170.94 751.64 0.0772 0.0176 0.0004 1.850E-05 0.0517 159.02 725.38 0.0830 0.0182 0.0004 1.987E-05 0.0481 149.93 656.32 0.0880 0.0201 0.0005 2.427E-05 0.0522 95.44 436.6 0.1383 0.0302 0.0011 5.484E-05 0.0478 138.5 701.81 0.0953 0.0188 0.0005 2.123E-05 0.0389 From these results, it can be observed that the kinetic energy ratio is much lower, implying that the kinetic energy before and after collision are not equal.

The kinetic energy after collision is much lower than the kinetic energy before collision, meaning that there is loss of kinetic energy during the collision of the two trolleys. Some kinetic energy is converted to sound, heat energy and potential energy during the process of in-elastic collision. This is the characteristic that is used to determine if a certain collision is elastic or inelastic, by calculating the kinetic energy after and before collision. In in-elastic collision, kinetic energy is not conserved.

The graph in figure 2 below is a plot of kinetic energy before collision against kinetic energy after collision. Figure 2: Graph of Kinetic energy before collision vs. kinetic energy after collision Similarly, it can be observed from the graph in figure 2 that there is no linear relation between the two values, and that at any particular moment, the value of kinetic energy before collision is higher than the value of kinetic energy after collision. Conclusion During in-elastic collision, momentum of the two colliding bodies is maintained.

On the other hand, the kinetic energy in the system is not conserved, but instead, it is transformed to other forms of energy such as sound and heat. Experiment 2: WALL JIB CRANE Objectives The first objective for this lab was to determine the experimental values of the forces in the principal parts of the jib crane. The second objective was to study the effect of altering the length of the tie to change the geometry, and finally, the last objective was to compare the results with the forces obtained from graphical solutions using a polygon or a triangle of forces.

Introduction The Wall Jib equipment was used sometime back at warehouses for unloading wagons before the fork lift trucks and lorries with on board hydraulic crane were advanced. One advantage of this crane for its popular application was that it could be swung against a wall side of a building when it is not in use. It was also a relatively cheap support. Although today wall jib cranes are obsolete, it has been used for several years to introduce students to studies of accelerated linear motion, especially dependence of acceleration on the force that causes the motion (Prakash, 1997).

The self-evident confluence of four forces at the jib end illustrates a real situation of a triangle of forces. This apparatus can be used in the derivation of Newton’s second law of motion. In this experiment, the forces in the Jib Crane members were measured using different weights, and comparing the results with values obtained by graphical solutions. Procedure The Jib Crane was set with a tie of 400mm long, a jib of 530mm long and the distance from tie anchor to jib pivot set at 380mm. The load cord anchor was then fixed at 150mm length above the jib pivot, passing it over the pulley and to the load hunger.

It was ensured that there was enough length adjustment for compensation of change in the spring balances. After checking that the hooks for the tie and cord anchor were aligned vertically with respect to jib wall pivot, the four length measurements were recorded in table 1. The “no load” readings of the spring balances were also recorded down as they supported the dead weight. A load of 15 N was then fixed on the hunger and the four lengths readjusted to their original measurements, and the final readings on the spring balance recorded down.

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