05 Fan Car - Lab Report 5

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Dec 6, 2023

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Fan Cart – Lab Report Name: Sabina Veysalova Section:1 Nina Mangini Andrew Simon Ephram Duku Courtney Solensky Procedure: Using the scale at your workstation, find the mass of the cart + fan: Mass = .569kg Note that when the fan is running, a constant force is applied to the fan-cart, as shown below. Draw a free body diagram for the cart in this situation. Include all forces acting on the cart except friction. We will assume friction is negligible. Indicate the direction of acceleration below or to one side of your free body diagram. Free Body Diagram: Part 1: Determining the Force of the Fan Use Capstone to determine the acceleration of the cart moving to the left, then turn the cart around and measure the acceleration of the cart moving to the right (don’t worry about the uncertainty). Remember that acceleration is the slope of a velocity time graph. Fan cart 1

It will take a moment for the fan to reach full power. Wait until the fan is spinning at top speed to release it. ¿ a ¿ = 0.5 m/s 2 a ¿ = 0.5 m/s 2 Should these accelerations be the same? Explain. Yes, the change in direction doesn’t change in acceleration. Calculate the average acceleration caused by the fan. a avg = 0.5 m/s 2 You will use this average acceleration to determine the force exerted by the fan. Why do you think measuring the acceleration in both directions and using their average is better than measuring two accelerations in one direction and using their average? - Measuring the acceleration in both directions and using their average is better than measuring two accelerations in one direction and using their average because it helps to reduce the effect of any external forces that mat be acting on the cart in a particular direction. By measuring the acceleration in both directions and taking their average, we are effectively cancelling out any external forces that are acting on the cart in one direction. This helps to provide a more accurate measurement of the force exerted by the fan. Using your free-body-diagram and Newton’s 2nd law, determine the force exerted the fan-cart. Show your work: F fan = 0.2845 N Work: Mass x acceleration Part 2: Adding Mass If you add mass to the cart, would you expect the acceleration to: INCREASE DECREASE STAY THE SAME? (Don’t change your answer after the measurement; it won’t be marked wrong.) 2

Add a mass bar to the cart and measure the acceleration as in Part 1 above: Mass of cart + mass bar = 1.07 kg ¿ a ¿ = 0.3 m/s 2 a ¿ = 0.3 m/s 2 Was your prediction correct? If not, what did you observe? Our prediction was correct, it did decrease. Using the same procedure as Part 1, calculate the force the fan exerts on the cart. (Don’t forget, you added mass to the cart.) Show your work. F fan = 0.321 N Work: F 0.569 x 0.3 If your force measurements from Parts 1 and 2 were not consistent, let your professor know. In the questions that follow, go ahead and use the force you found in Part 1. It is probably a little bit more accurate (because less mass results in less rolling resistance in the wheels). Part 3: It’s All Uphill From Here! Remove the bar mass from your cart. 3

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Prediction 3A: Imagine you place the cart on a sloped track such that the fan pushes the cart up the ramp, as shown in the figure above. Also imagine that the angle of the track has been set such that the cart remains stationary while the fan is running. What does this tell you about the forces acting on the cart? - If the cart remains stationary while the fan is running, this indicates that the force of the fan pushing the cart up the ramp is balanced by the force of gravity acting on the cart, which is pulling the cart down the ramp. This means that the net force acting on the cart is zero, and that the cart is in a state of equilibrium. Now imagine that you give the cart a short push so that it travels up the (essentially frictionless) ramp. Using the reference frame in the figure, sketch your predictions for the velocity vs time and acceleration vs time graphs on the next page. Only consider the motion of the cart after you have let go. Draw your sketch on the axes provided on the next page. Time (s) Velocity (m/s) Time (s) Acceleration (m/s2) Prediction 3B: Using the same configurate as Prediction 3A, what if the cart started at the top of the track with the fan on and you gave it a push down the track? Sketch your predictions for the velocity vs time and acceleration vs time graphs. Only consider the motion of the cart after you have let go. 5

Time (s) Velocity (m/s) Time (s) Acceleration (m/s2) Experiment: 6

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x y To test your predictions, you will need to determine the correct angle to place the track so that the cart remains stationary with the fan running. Draw a free body diagram for the cart if the track is placed on an incline as shown in the figure above. Use the given reference frame (x-axis parallel to the incline and y-axis perpendicular to the incline.) Remember, the fan is pushing the cart up the ramp and friction is negligible. Free body diagram: Use your knowledge of Newton’s 2 nd Law to determine the angle at which to place the track so that the fan cart will not accelerate. Remember, you must use the component form of Newton’s 2nd law. Solve algebraically for θ and show your work for each step. Do not plug in numbers until the final step or you will lose points. θ = ___92____ ° θ = sin^(-1)(f/(mg)) = sin^-1 ( 0.2845 )/(9.8)( .569) = (16.52896)/(5.5762) = 92.16878675 Now that you have the angle of the track, use trigonometry to determine how high to elevate one end of the track from the other, Δh . Show your work. JackSta 8

Length of track = ___120________ cm Δh = ___3.5_______ cm Move one jack stand to the end of the track as shown in the figure above. Measure the height h 1 . From the information above, calculate h 2 and set the height of each end of the track appropriately to get the proper angle. h 1 = _____5.5_____ cm h 2 = ______6____ cm Once you are finished, you may use the electronic angle finder to verify the angle. Place the cart on the track, but DO NOT TURN ON THE FAN until your professor is supervising. Did the cart remain stationary? YES NO Professor’s initials: _____Horne____ Now that you have the track at the proper angle that causes the cart to remain stationary, place the cart near the bottom of the track as shown in Prediction 3A. Turn the fan on, begin taking data and give the cart a big enough push so that it travels up the track and must be caught (before falling off the end). Remember, low friction carts are not truly frictionless (also the angle of the track being off slightly) can mask what is really happening. So, if the cart’s velocity graph appears to be close to horizontal, go ahead and consider its velocity to be constant. How do your results compare to your predictions? Our acceleration graph was wrong as there was a slight incline with the push of the cart which then proceeded to level out. Our velocity graph was also wrong as it displayed that the velocity was a constant 0 compared to our graph which was a incline to leveling off. Next place the cart near the top of the track as shown in Prediction 3B. Turn the fan on, begin taking data and give the cart a big enough push so that it travels down the track and must be caught (before falling off the end). How do your results compare to your predictions? JackSta nd Table 9

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Our velocity graph matches the prediction graph that we created. However, the acceleration had a slight decrease before leveling off, compared to our graph which disp;layed a constant acceleration. Conclusions: In both instances the fan was causing a force on the cart and yet the cart traveled at a fairly constant velocity. Is this consistent with Newton’s 2nd law? Explain. - Yes, this is consistent with Newton’s second law of motion. According to the second law, the net force acting on an object is directly proportional to its acceleration, and the direction of the acceleration is in the direction of the net force. Mathematically, F_net=ma, where F_net is the net force, m is the mass of the object, and a is the acceleration. In the case of the fan and cart moving at a constant velocity, this means that the net force acting on the cart is zero. If the force of the fan pushing the cart forward is equal in magnitude to the forces opposing the cart’s motion, such as friction or air resistance, then the net force acting on the cart is zero. Identify two (2) potential sources of error in this lab. Are these systematic or statistical errors? What could be done differently (if anything) to minimize these sources of error? Be as specific as possible. For example, “human error” is not specific; it does not say what the humans did wrong. It is OK to mention errors that resulted due to human involvement. - Friction, friction can cause the cart to slow down and may not allow it to move at a constant velocity. This can lead to errors in measuring the acceleration of the cart. Friction can also affect the force measurements, as it can cause the cart to require more force to move it than expected. - Air resistance, air resistance can also affect the motion of the cart, especially at higher speeds. This can cause errors in measuring the acceleration of the cart, as well as the force measurements. What’s the point?!?!?! In a few sentences, describe what you think was the point of doing this lab. (What did you learn? What physics principles were tested? Etc.) - The point of doing the lab of the fan cart was to explore the relationship between force, mass, and acceleration, which is a fundamental principle of physics known as Newton’s 10

second law of motion. By measuring the acceleration of the cart and using this to calculate the force exerted by the fan, we were able to test this principle and demonstrate how it can be applied in real-world situations. Do-It-Yourself! In a few sentences, propose an additional experiment that could further test the results or physics principles of today’s observations. Explain 1) what you will measure, 2) how you will measure it, and 3) what you might expect the results of the experiment to be. Do not simply restate today’s experiment, but change it from a bike to a car, etc. It should be a fundamentally new experiment that tests some aspect of today’s investigation - one additional experiment that could further test the principles of today’s investigation would be to use the fan cart to study the effect of changing the mass of the cart on its acceleration. In this experiment, we would measure the acceleration of the cart while keeping the force of the fan constant but changing the mass of the cart. We could do this by adding weights to the cart and repeating the measurements. We would expect that as the mass of the cart increases, the acceleration of the cart would decrease, as the force required to move a heavier object is greater than that required to move a lighter object. By testing this relationship, we can further investigate the physics principles underlying Newton’s second law of motion and gain a deeper understanding of how force, mass, and acceleration are interrelated. 11

05 Fan Car - Lab Report 5

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