In preparation for a visit to an amusement park you measure your mass to be 53 k
ID: 2077962 • Letter: I
Question
In preparation for a visit to an amusement park you measure your mass to be 53 kg. You then pace off 100 m on the track. You find that you take 128 steps in the 100 m distance. What is the length of one of your steps? Now you are at the park. You are going to analyze a circular ride. On this ride you sit in a seat to the end of long chain and swung in a circle. Here are the measurements that you make. While the ride is operating, you pace off the diameter of the circle made by the swings. The diameter is 13.0 paces long. Additionally, you record the time it takes for a swing to make on completer revolution. You collect the following data: First timing: 7.12 seconds Second timing: timing: 7.11 second You also measure the angle that the chains make with the vertical while in full operation and find it to be 17.4 degrees. With all of this information you should now be able to answer the following questions. What is the period of rotation for the ride while in full operation? What is the radius of the swing's circle while the ride is in full operation? Calculate the maximum speed for the rider. Calculate the centripetal force acting on you as a rider while the ride is in full operation. Tension is the vector sum of centripetal force and weight. What is the tension in the chains of the swing at maximum speed? Using trig, calculate the angle the chain should make with the vertical. Give your answer in degrees, no units necessary in the answer field. Compare your calculated angle to the measured angle. Determine the percent difference using the measured angle as the experimental value and the calculated angle as the actual angle. Express your percent difference as an absolute value unitless decimal (hopefully, less than one)Explanation / Answer
1) length of one of your step = 100/128 = 0.781 m
2) a) period of rotation is the time taken to complete one rotation.
period = (7.12+7.19+7.11)/3 = 7.14 s
b) radius of the swing's circle = 13 pace/2 =9.91 m/2 = 4.95 m
c) Maximum angular speed, w = s/rt = 2 x 3.14 x 4.95/ 4.95 x 7.11 =0.883 rad/s
Maximum linear velocity, v = wr = 0.883 x 4.95 = 4.37 m/s
d) centripetal force, f = mv2/r = 53 x 4.372/4.95 = 204.67 N