Work Energy- Section 008 PDF

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1 ! ! ! ! ! ! ! ! ! ! ! Work Energy- Post Laboratory

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2 Objective/Description: The purpose of this laboratory was to investigate and prove the validity of the work energy theory. The equipment used in this experiment included the air track, large glider, a force sensor, strings connected with rubber bands attached to it or loops, the kg masses with hooks, as well as the photogate/smart pulley. In this experiment, the glider was placed on the horizontal air track while attached to a string connected to various rubber bands. The last rubber band was attached to a force sensor, which was clamped to a rod near the floor. The glider then had to be pulled back, causing the rubber bands to be stretched and then the glider was pulled away. The program was also used to find the total area under the curve from one point to the next. The velocities calculated by the program were then used to determine the change in kinetic energy throughout the movement of the glider. The second experiment was focused on applying the 𝑊 = ∆𝐾𝐸 theorem go a system involving two masses. The theorem is first applied to the masses separately and then to the entire system. Theory: Work is defined as the change in kinetic energy. When a point mass (m) is acted on by a force (F). The position, velocity, acceleration of that mass are r ,v, a, and time (t). To find the work performed in a mass can be integrated over the initial and final positions of the object. In the equation, the left side of it can be used to determine the work done on mass as it moves from r1 to r2. As mass moves from r1 to r2, the total work done on m between those points in equal to the change in kinetic energy between those points, thus 𝑊 = ∆𝐾𝐸 . The area under the curve is known as the integral of a function. The total work done should be equal to the total change in kinetic energy, but the internal work, or forces between the particles in the system has to be taken into consideration as well. To determine the force to calculate the work done, the tension force within the string is used, which can be calculated using Newton’s second law to get the ' ') * , where 𝑀- .is.50g.and.𝑀7 .is.the.mass.of.the.glider.. formula 𝑇 = '(+' (

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Procedure: In the first experiment, the tension of a rubber band was measured as it was stretched while the glider it was attached to was pulled back along the air track. Capstone then recorded all the information in a force vs. distance(x) graph. The area under the curve of the graph could then be used to determine the work done on the rubber band. In the second experiment, a 50g mass was hung from a string that was strung through the wheel of the smart pulley, causing the system to be frictionless. The mass would then accelerate downward in the –y direction, which then caused the glider to also accelerate but in the 0x direction. The positions of both objects were then used to calculate the total work of the system and the velocities were used to determine the change in kinetic energy.

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3 Data and Calculations: Table 1. The change in KE with rubber bands ∆𝐾𝐸 (change in KE in the Trial W (area under the force curve) N*m velocity graph) J 1 0.07 0.0551 2 0.06 0.0572 3 0.07 0.0605 Mass: 0.4554kg

𝑊 − ∆𝐾𝐸 (J) 0.0149 0.0028 0.0095

1 1 ∆𝐾𝐸 = 𝑚𝑣F7 − 𝑚𝑣G7 2 2 -

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-

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Trial 1: ∆𝐾𝐸 = 7 0.4554 1.39 7F − 7 0.4554 1.30 7G = 0.0551𝐽 Trial 2:.∆𝐾𝐸 = 7 0.4554 1.44 7F − 7 0.4554 1.35 7G = 0.0572𝐽 Trialc3: ∆𝐾𝐸 =

7

-

0.4554 1.52 7F − 7 0.4554 1.43 7G = 0.0605𝐽

Table 2. The change in KE with two particles Trial Tension (N) Work done on M1 (J) 1 0.442 2 0.442 3 0.442 M1: 0.05kg M2: 0.4554kg ' ' *

𝑇 = '(+') à 𝑇 = (

)

0.0928 0.0884 0.1105

Work done on M2 (J) 0.00281 0.00268 0.00335

Work done on the system (Nm) 0.9382 0.8935 1.1169

W

(O.OPQ*∗O.SPPSQ* )(U.V-) ) X

(O.OPQ* +O.SPPSQ*)

= 0.442𝑁

𝑊'- = 𝑇(∆𝑥) Trial 1: 𝑊'- = 0.442𝑁 0.53𝑚 − 0.32𝑚 = 0.0928𝐽 Trial 2: 𝑊'- = 0.442𝑁 0.55𝑚 − 0.35𝑚 = 0.0884𝐽 Trial 3: 𝑊'- = 0.442𝑁 0.58𝑚 − 0.33𝑚 = 0.1105𝐽 𝑊'7 = (𝑀7 − 𝑇)(∆𝑥) Trial 1: 𝑊'7 = (0.4554kg-0.442N) 0.53𝑚 − 0.32𝑚 = 0.00281J Trial 2: 𝑊'7 = (0.4554kg-0.442N) 0.55𝑚 − 0.35𝑚 = 0.00268J Trial 3: 𝑊'7 = (0.4554kg-0.442N) 0.58𝑚 − 0.33𝑚 = 0.00335J

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∆𝐾𝐸

0.0822 0.0948 0.1096

4 𝑊\]^_` = (𝑀7 𝑔)(∆𝑥) Trial 1: 𝑊\]^_` = 0.4554𝑘𝑔.𝑥 Trial 2:.𝑊\]^_` = 0.4554𝑘𝑔.𝑥 Trial 3: 𝑊\]^_` = 0.4554𝑘𝑔.𝑥 1 1 ∆𝐾𝐸 = 𝑚𝑣F7 − 𝑚𝑣G7 2 2 Trial 1:.∆𝐾𝐸 =

Trial 2:.∆𝐾𝐸 = Trial 3:.∆𝐾𝐸 =

7

7 7

0.5011𝑘𝑔

0.5011𝑘𝑔 0.5011𝑘𝑔

U.V-c

0.53𝑚 − 0.32𝑚 = 0.9382𝑁𝑚

d) U.V-c d) U.V-c

0.55𝑚 − 0.35𝑚 = 0.8935𝑁𝑚 0.58𝑚 − 0.33𝑚 = 1.1169𝑁𝑚

d)

O.U7c 7 d

O.Uec d

F 7 F

-.OOc 7 d

−

F

− −

7

7 7

0.5011𝑘𝑔

0.5011𝑘𝑔 0.5011𝑘𝑔

O.e7c 7 d

O.ePc d

7

= 0.0948𝐽 G

O.ePc 7 d

= 0.0822𝐽

G

= 0.1096𝐽

G

Error Analysis: The main source of error in this lab could have been due to systematic errors like the force glider not being constant due to the force form the string not being uniform as well as air resistance. Even though there is not much error that can be done, the values of the KE and the W for both experiments are not similar which indicates that there might have been some errors done to the system. This could be due to not properly using the equipment such as the bumper on the air track that the glider would bump to as a results of the pulling the glider. Questions: Section 2: 1. In this experiment, the internal forces are those forces that are happening between the mass and the string attached to the rubber band as well as the forces present between the two masses as they’re moving. As example of internal work would bean inelastic collision between particles that result in a loss of energy, leading to less internal work. Section 3.1: 1. The force on the glider is not constant because force from the string is not uniform. The mass of the rubber bands and string are also not considered, which could throw off any calculations. Section 3.6: 1. The values of the KE are a bit larger than the calculated work, the values of the W are generally smaller than the values of KE. 2. Air resistance and friction contribute to the systematic errors that affect the runs, being that system may not be completely frictionless. Section 4.2: 1. There is a minus sign before the T in the equation because of the pulling force is going downward and T is going upward, the externa forces on M1 are gravity and normal force. 2. The T’s cancel out when the work done on M1 and M2 are added when determining the total work of the system. !

5 Section 4.5: 1. The work done on M1 is close to the change in kinetic energy. It seemed like the values of the last two trials were similar throughout the experiment. The velocity vs. distance curve was a straight line with a little bit of curvature due to air resistance and the broken bumper on the air track. The motion of the masses is proportional to the acceleration because of gravity, while air resistance is proportional to velocity. Conclusion: In conclusion, the experiment proved that the work-energy theorem is valid. Based on what was done in this experiment it can be determined that there is more than one way to calculate the same value whether it is the total work done or kinetic energy. Even though the values of the KE and W were not the same, the different values of work are similar and there is a relationship between them, based on how close the values are to each other. When the change in KE was subtracted from W the values were positive and small which is a good indicated that energy was neither created nor destroyed.

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