Physics lab report 2

Lab 2: Linear Motion By: Paige Williams, Garcelle Dessables,Tynae Drain, Kamren Dutton

Purpose Statement: The purpose of this lab was to study the concept of linear motion. This was done by attaching string to the cart which will be placed over the pulley and attached to a suspended mass. The suspended mass will generate the motion via gravity. We will calculate the ideal and experimental acceleration of the cart and compare the two. We will also determine the final velocity of the cart and evaluate the impact of different masses on the hanger’s motion. Materials: Track, track stop, cart, string, hanger, stopwatch, electronic balance, pulley and masses. Procedure: For this experiment, we began by assembling our cart, track and pulley mechanism. After placing our cart on the track and securing our wheel to the track, we measured out our string, ensuring that it was long enough for there to be a total distance of 80cm between the cart and the stop at the end of the track. Before conducting the experiment, both the cart and the hanger were weighed. One end of the string was tied around the cart and the hanger was tied to the other end. We conducted this experiment by pulling the cart back back to around 110cm and placing 50 grams on the hanger. When everything was set, the cart was released and the time it took for the cart to hit the stopper(ensuring that the hanger did not touch the floor) at the end of the track was

Analysis: In this section of the lab, the ideal acceleration(column 3) is going to be calculated using . The data used for the calculations in column 3 come from the ? ℎ𝑎??𝑖?? = ? ?𝑎?? ? ℎ𝑎??𝑖?? +? ?𝑎?? × ? mass of the cart, the hanger and gravity which is given(9.81m/s). Column 4 uses to calculate ideal velocity. The data used for this secction was the 𝑣 ? 2 = 𝑣 𝑖 2 + 2𝑎(𝑥 ? − 𝑥 𝑖 ) distance from the stopper to the initial position of the cart( ) and the speed of the cart ∆𝑥[??] from the trials. Column 1 uses . This equation uses the distance from (𝑥 ? − 𝑥 𝑖 ) = 𝑣 𝑖 ? + 1 2 𝑎? 2 the stopper to the initial position of the cart( ), the speed and initial velocity. Finally ∆𝑥[??] column 2 used equation . The data used was the speed and the ideal acceleration. 𝑣 ? = 𝑣 𝑖 + 𝑎? Table 2: Trials 𝑎 ?𝑥𝑝[ ? 2 ? ] 𝑉 ? ?𝑥𝑝[ ? ? ] 𝑎 𝑖??𝑎? [ ? 2 ? ] 𝑉 ?, 𝑖??𝑎? [ ? ? ] 1 0.66 1.08 0.88 0.93 2 0.55 1.52 1.04 1.11 3 0.68 1.71 1.20 1.29 4 0.87 1.80 1.34 1.46 5 1.17 1.84 1.49 1.63 6 1.77 1.62 1.69 1.79 7 1.89 1.60 1.74 1.89 8 2.06 1.58 1.80 2.02 9 2.11 1.64 1.89 2.14 10 2.27 1.59 1.89 2.25

Trial Percent Error acceleration Percent error velocity 1 34% 8% 2 45% 52% 3 32% 71% 4 13% 80% 5 17% 84% by 6 4.7% 9.49% 7 8.62% 15.3% 8 14.4% 21.7% 9 11.6% 23.3% 10 20.1% 8%

Equation 3: 𝑣 ? 2 = 𝑣 𝑖 2 + 2𝑎(𝑥 ? − 𝑥 𝑖 ) V(f)=3.0 ? ? 3. 0 = 0 + 2𝑎(1) → 3. 0 = 2𝑎 → 1. 5 = 𝑎 Equation 2: ? ℎ𝑎??𝑖?? = ? ?𝑎?? ( ? 𝑎 −1) ? ℎ𝑎??𝑖?? = 0.503?? 9.81?/? 2 1.5?/? 2 −1 ∼ 0. 091??/ ∼ 91? 3) If the tracks were not on a level surface how would the experimental results be affected? Consider if the tracks were sloped up and sloped down individually. If the tracks were not on a level surface then the acceleration would be inaccurate. In order for there to be no error the tracks have to be on a leveled surface. 4) Why do we use equations 1 and 3 as the ideal values for acceleration and final velocity? Equations 1 and 3 are used for the ideals values of acceleration and final velocity to display what the results are supposed to look like, 5) Why do we use equations 2 and 4 as the experimental values for acceleration and final velocity? The purpose of equations 2 and 4 are to display our actual calculation compared to the ideal. 6) I’m willing to bet that your experimental acceleration is lower than your ideal acceleration. What do you think is missing from the analysis model that is present in the real world? In the real world we would most likely have an issue with factors like wind/air resistance. Any natural factor that would keep the car from moving at optimum. If this experiment were to be conducted in the real world, it would not be as reliable or accurate. When the experiment is done in the lab we are able to control our environment more. 7) Did you find a trend when you plotted hang mass versus experimental error? If so, what is a possible functional form for this trend(e.g. Linear, quadratic, logarithmic, etc.). Why or why not would there be a trend?

There was no trend due to the constant increase and decrease of our percent error. Conclusion: In conclusion, this lab allowed us to explore linear motion by studying the motion of a cart on a track. By studying the motion of the cart in relation to the mass of the hanger, we were able to calculate the ideal and experimental accelerations and final velocity.