Chemistry lab 12

Abstract:
Theoretically, this experiment is used to address the Newton’s Second Law of Motion which is the net force is product of the mass and the acceleration of the object. However, the performance’s result would be measured acceleration instead the net force.
During this experiment, the objects are two weight hangers with a same origin mass which is 5g and later have total mass is around 2000g. The experiment is performed by transferring mass from one to another hanger and calculates the time the right hanger takes to hit the ground. Then, students start to calculate the measured acceleration and predicted one. Objectively, the measured acceleration should precisely the same to the predicted one. If yes, the experiment is successfully done and if no, there would be some possible error involved.
Purpose: To investigate Newton’s Second Law of Motion by measuring the acceleration of given mass caused by given net force.
Procedure:
1. Mount the pulley on one of the bars on the table, using a clamp. The pulley must overhang the table with the pulley disk in a vertical plane. Connect each end of a piece of string to a 50 g weight hanger and drape the string over the pulley. The string length should be such that, when one hanger hits the floor, the upper part of the other hanger is near the pulley, without touching the pulley. (You may find that the lab assistant has already set up the apparatus as described here. If so, double check the setup.)
2. Place equal masses of approximately 1000 g on each weight hanger. These masses should include four 5 g masses at the top of the left hanger. Hold back the 1 g and 2 g masses from the weight sets and do not initially use them on the hangers. Move the weights up and down carefully to be sure that there is no obstruction until the weight hits the floor on each side. Make sure that the pulley disk is still in a vertical plane (to prevent the string from rubbing the walls of the groove in the pulley disk).
3. Lower the left weight hanger until it touches the floor. Then pull downward very slightly on the right weight hanger, release it, and watch it descend at a constant velocity (i.e. with acceleration = 0). It will be impossible to make an accurate observation, unless the initial velocity is very small. Repeat and make additional observations, if necessary. If the right-hand weight hanger is slowing down, add a small mass to that hanger (l or 2g will probably be sufficient) and make further observations. Some laboratory instructors may ask the students to adjust the added mass to the nearest 0.5g. No slotted weights this small are available, but a short piece of wire with a mass of 0.5 g will be provided. If the right weight hanger speeds up instead of slowing down, add the small mass to the left hanger instead. Continue these adjustments and observations until the right weight hanger can be made to descend with a very slow and constant velocity. This procedure compensates for friction and for slight calibration errors in the larger masses. Some laboratory instructors may ask to check your apparatus at this point.
4. Determine the total mass at the left hanger, including the slotted weights and the hanger itself. Record this mass on the first line of the data sheet as m1. Record the total mass at the right hanger as m2. The acceleration for the first line is zero; and Δm is zero by definition. Note that equation (4) does not apply, since the initial velocity was not zero.
5. Calculate predicted values of the acceleration for m = 5 g, 10 g, 15 g, and 20 g, using equation (2). The total of m1 + m2 should be the same in each case as on the first line of the data sheet.
6. Transfer a 5g mass from the left weight hanger to the right weight hanger. (Δm = 5g)
7. Press down lightly on the left weight hanger and hold it against the floor. Measure the distance from the floor to the bottom of the right weight hanger and record it as s.
8. Simultaneously, release the left weight hanger and start the stopwatch. When the right weight hanger hits the floor, stop the stopwatch. Record its reading on the second line of the data sheet as t. Before the timing operation, the left weight hanger should be held down only by touching the top weight with one finger. If the top of the weight hanger were held with two fingers, the weight hanger could easily be given an unintended initial velocity. Note that one laboratory partner at each table must both release the weight hanger and operate the stopwatch. If one partner releases the weight hanger and the other partner operates the stopwatch, reaction-time errors will be excessive. The partner operating the stopwatch should be holding the stopwatch next to his ear and squatting down to observe the right hanger approaching the floor. He should try to hit the stop button at the same moment the right hanger hits the floor. Most stopwatches make either a clicking sound or an electronic beep when the stop button is pushed. If the sound of the stopwatch button occurs before or after the bang of the right hanger on the floor, this step of the experiment should be repeated. While one laboratory partner is operating the stopwatch and observing the right weight hanger, the other partner (or one of the other partners) should cup his hands under the rising left hanger (without touching the hanger) to catch any weights that might fall off.
9. Calculate the actual acceleration ameas, using equation (4). Compare this value to the value predicted in step 5, and calculate the percent difference.
10. Transfer an additional 5 g mass from the left hanger to the right hanger (so that Δm = 10 g). Repeat steps 7, 8, and 9. (If you do not remeasure s at every step, you should measure it at the beginning of the first step and the end of the last step to be sure that s has not changed due to the string stretching or a pulley clamp slipping.) Repeat again for the total value of Δm equal to 15 g and to 20 g.
Calculation:
1. Total mass: m1 + m2
a. Trial #1: 998g +1008g = 2006 (total mass is equivalent for four trials)
2. Measured acceleration (ameas) =
a. Trial #1: = 3.66 cm/s².
b. #2: 9.02 cm/s².
c. #3: 16.1 cm/s².
d. #4: 19.1 cm/s².
3. Predicted acceleration (apred) =
a. Trial #1: = 4.89 cm/s².
b. #2: 9.77 cm/s².
c. #3: 14.7 cm/s².
d. #4: 19.5 cm/s².
4. Percent of difference =
a. Trial #1: *100 = 25.1%.
b. #2: 7.68%.
c. #3: 10.1%.
d. #4: 2.05%.
Answer to questions:
1. Equation (l) can also be obtained by drawing separate free body diagrams for the two masses in the system, applying Newton's Laws to each body to get 2 equations with T (string tension force) and a as unknowns, and solving the 2 equations simultaneously. Write the 2 equations and solve them simultaneously to obtain formulas for T and a in term of m1, m2, and g.

Equation 1:

F = ma.
Fnet1 = T – m1g = m1a
Fnet2 = m2g – T = m2a
T = m­1 ( + g) – m2 (g – ).
2. This experiment has stressed Newton's Second Law of Motion, F = ma. State Newton's first and third laws of motion (copy from your textbook if you wish). Were these laws used implicitly in analyzing the system used in this experiment? If so, how?
Newton’s First Law of Motion is a body remains at rest or in motion with a constant velocity unless acted upon by an external force. Newton’s Third Law of Motion is for every action, there is an equal and opposite reaction. The Newton’s First Law is applied during the second step in procedure when two hangers were stationary and no force was applied on them. Then, there is no Newton’s Third Law was presented during this experiment.
3.
a. How do we know Tl = T2?
T1 and T2 are the same in magnitude but different in direction. If we take direction of (a) is positive then, T1 is positive and T2 is negative value of T1.
b. How do we know T2 = T3?

c. How do we know T3 = T4?
d. How do we know Tl = T4?
Discussion:
First, this experiment has presented Newton’s Second Law of Motion; the acceleration is dependent on the net forces and the mass of the object. The net force for this experiment includes tension, gravitational force, and small friction of the cord. Then, the mass is transferring but the total mass is constant. For four trials, the percentage differences are 25.1%, 7.68%, 10.1% and 2.05% which show that the measurements and predictions were précised by numbers of trials. However, the result from trial #1 is not accurate to be taken in account for the purpose therefore; the experiment could involve some possible errors.
Second, the possible errors for this experiment could be the human error because the mass is calculated and the distance from the hanger to the floor is constant. Therefore, the error could only be the timing when releasing the hanger and when stop the stopwatch after the right hanger touches the ground. Plus, student could have applied force to the left hanger instead of just releasing it.
Finally, the purpose and theory for this experiment is verified which means the acceleration is dependent on the net force act on the object and how much weight the object has. The acceleration is increased whether the mass increases or faster the time. This experiment is straightforward and the procedure is very easy to follow. Plus, the set-up is simple therefore, there is no recommendation for this experiment.