Rollercoaster Lab

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New York University *

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PHYSICAL C

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Physics

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Feb 20, 2024

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docx

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Uploaded by ProfRain7042

Rollercoaster! Measuring Energy and Force on a Rollercoaster PURPOSE In this activity you will measure the potential energy at the top of a ramp, the kinetic energy at the bottom of the ramp, and the energy lost on the ramp. You will then use this value of kinetic energy to determine the height from which the car must roll in order to complete a loop and allow your car to successfully reach the end of the track. MATERIALS Each lab group will need the following : calculator, TI® graphing tape, masking clamp ruler, clear metric meter stick paper, carbon racetrack, extension set racetrack, sets PROCEDURE PART I: TRACK CHARACTERISTICS In Part I of the lab, you will measure the speed of a car as it rolls off the end of a curved track. 1. Set up the apparatus as shown in Figure 1 below. Line up the end of the molding track with the edge of the tabletop. If there is extra molding above the clamp at the top of the ring stand, have one of your lab partners hold it up, or find a way to prop it up so that it does not interfere with Part I of the lab. 1

2. Measure the vertical distance d y from the floor to the end of the track, and the height h at which you released the car above the bottom of the track and record your values in the data table for Part I on your student answer page. 3. Use a tape measure to measure the length of the track L in centimeters from the top of the track at height h to the end of the track (from point A to point B) and record your value in the data table for Part I on your student answer page. 4. Roll the car down the track and allow it to roll off the end of the track and land on the floor. Place a white sheet of paper on the floor at the location where the car landed. Place a piece of carbon paper on top of the white paper with the carbon side down. The next time you roll the car down the ramp and allow it to land on the floor, the car will make a mark on the white paper. You may want to tape the white paper to the floor. Depending on the way the car hits, you may have to make a decision about the actual point of contact. If it lands on the wheels and make 4 marks, use the center. If it hits on the front end use this mark. Other possibilities may require you to decide where the center of mass of the car hits. 5. Measure the horizontal distance dx from the point at which the hanging weight touches the floor to the point at which the car landed on the floor and record your value in the data table for Part I on your student answer page. 6. Repeat step 4 two more times, record your values in the data table for Part I on your student answer page. Use these values to find the average horizontal distance traveled by the car. 7. Answer the Analysis questions for Part I before moving on to the procedure for Part II. PART II: LOOP HEIGHT In Part I of the lab, you determined the speed and kinetic energy of the car as it came off the end of the track, the initial potential energy of the car at the top of the track, the energy lost by the car on the track, and the energy lost per centimeter of track. In Part II, you will predict the height from which the car must be let go on the track in order to make it just go completely around a loop of specific height. You will also predict the speed of the car at the end of the track and confirm this speed by predicting and measuring the speed of the car as it goes off the table and strikes the floor. 1. Clamp one end of the track to the top of the ring stand or other structure used to elevate the ramp. You may use the same set up and same height h as in Part I. If after making your calculations, you may need to increase the height, or you may need to start the car at some distance down the track. The exact distance h from which you release the car will be calculated after other measurements are made. 2. Add the circular loop onto the end of the track and adjust your apparatus so that the end of the track on the outside of the loop ends at the exact edge of the table. 2

3. Use a tape measure or meter stick to measure the same length of the track L in centimeters as in Part I from the top of the track at height h to the beginning of the loop. Measure the diameter of the circle (H) and calculate the circumference of the circle. Also measure any distance from the outbound side of the loop. 4. In the Analysis section for Part II of your student answer page, predict the minimum height h from which the car can be released in order to make it completely around the loop without ever losing contact with the track. Also predict the velocity of the car when it leaves the end or the track based on the amount of kinetic energy the car still posses as it reaches the edge of the track/table and becomes projectile. 5. Roll the car down the ramp and test the accuracy of your prediction. Do not wind the spring in the car, let the car roll freely using only its gravitational potential energy. 6. If the car does not make it around the loop without losing contact with the track, or if you think the car could be moving slower, adjust the height h from which the car is released and roll the car again. 3

Rollercoaster! Measuring Energy and Force on a Rollercoaster DATA AND OBSERVATIONS PART I: TRACK CHARACTERISTICS Mass m of your car = __0.039__ kg Length L of the track from the top of the ramp to the end of the track = _____154 ____ cm Trial # Initial Height of Car above Table h (m) Distance from Floor to Bottom of Ramp d y (m) Horizontal Distance d x (m) 1 0.51 0.76 0.93 2 0.51 0.76 0.985 3 0.51 0.76 0.92 ANALYSIS PART I: TRACK CHARACTERISTICS In Part I of the lab, we want to find the speed of the car as it leaves the end of the ramp so that we can then find the kinetic energy at the end of the ramp. As the car leaves the end of the ramp, it is moving horizontally and vertically at the same time. In the horizontal direction, it does not accelerate, but moves with a constant speed. In the vertical direction, the car accelerates at 9.80 m/s 2 downward as it falls. We can combine the horizontal and vertical motions of the car to find its speed, v, as it leaves the end of the track. 4

1. The time the car is in the air after it leaves the end of the ramp can be found using the motion equation d y = 1 2 gt 2 where d y is the vertical distance from the floor to the end of the ramp, and g is the acceleration due to gravity. Rearrange this equation for the time of flight t in terms of d y and g. Show your steps in the space below. Answer Here: Typeequationhere. 2. Using your equation for time above, substitute your values and find the actual time the car is in the air after it leaves the ramp. Answer Here: Typeequationhere. 3. Find the average horizontal distance dx the car travels before striking the floor. Show your work in the space below and be sure to include the proper number of significant digits. Answer Here: Typeequationhere. 5

4. Knowing the average horizontal distance dx your car traveled before striking the floor and the equation below, find the speed v of the car in m/s as it leaves the track. Answer Here: Typeequationhere. 5. Using the equation for kinetic energy below, find the kinetic energy in Joules of the car is it leaves the end of the track. Answer Here: Typeequationhere. 6

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