Level 10 - Tarzan Goes Sledding!

Transcription

1 Group #4 Name: Partner(s): Level 10 - Tarzan Goes Sledding! pivot clay ball hot wire H 88 cm table The Scenario: Tarzan is being chased (as usual). This time, however, it is snowing in the jungle. (Don't worry about how a snow storm hit the tropics - just assume it has.) Tarzan must swing from a vine and hit a sled that is resting on the snow at the bottom of the vine. After hitting the sled he will let go of the vine and start sliding along. But the situation is a bit trickier. Tarzan must stop sliding before plunging over the edge of a cliff. But if he stops short of the cliff, he will not be able to reach his next escape vine that is hanging off the edge of the cliff, and he will be caught. His plan is to swing from the correct height so that he hits the sled and slides exactly to the edge of the cliff. There he will grab hold of his next escape vine and slide down it to safety in a cave on the side of the cliff. Tarzan estimates the weight of the sled and then makes his jump. Will he make it? Of course he does - he's Tarzan - King of the Jungle!

2 2 But how will you fare? Place yourself in this scenario and use your physics and math knowledge to calculate your way to safety! Main Objective: Calculate the height from which Tarzan (a clay ball) must jump from such that he makes an inelastic collision with a sled at the bottom of his swing, and slides a predetermined distance to safety. Apparatus: A clay ball hanging on a fine cotton thread from a nearly frictionless pivot will be released from rest. When the ball gets to the bottom of its swing, it will make a perfectly inelastic collision with a sled. Simultaneously, at the bottom of its swing, the thread will be quickly cut with a hot wire. The combination of clay ball and sled will slide down the dynamics track. mass of sled = kg mass of clay ball = kg mass of thread = negligible final height = 88 cm min. release ht. = 100 cm max. release ht. = 185 cm thread length = 137 cm Your Group's Assigned Range: Slide the sled between 20 cm and 25 cm after the collision. Your zone is the "blue zone". Good luck!

3 3 Theory: In perfectly inelastic collisions, as in all collisions, momentum is conserved. The total momentum of the clay ball and sled before the collision must equal the total momentum of the clay ball and sled after the collision. If the collision is perfectly inelastic, then the final velocity of both objects will be identical. Assignment (to be completed by next week): 1. Use the assigned values above and determine the height (H) from which Tarzan must be released in order to end up in the "blue zone" (20-25 cm). * The deceleration of the sled will depend on the average friction present between the sled and the dynamics track. This value can vary from day to day because of changes in humidity, dust level in the lab room, etcetera.** * A 5 cm correction must be made in your predicted distance because the center of mass of the ball-sled system will shift forward about 5 cm after the initial collision. So the sled will slide about 5 cm LESS than your equations will predict. For example, if you calculate that the sled will slide 18 cm, then it will really slide about 13 cm. **The exact deceleration of the sled will be measured right before your lab. So solve for the height in terms of the deceleration (a). That way, when the deceleration value (a) is given to you in lab by the instructor, you can quickly "plug and chug" an answer for the release height (H). Attach pages that explain your group's reasoning and show your calculations (attach as many pieces of paper as needed). Put a box around your final answer for H.

4 4 2. Assume that the deceleration of the sled will be about 2.75 m/s 2 for this part. Calculate the expected impulse ( p) of the sled and the clay ball. Show your work below and put a box around final answers. Impulse of Clay Ball Impulse of Sled 3. When a collision occurs, the force is not constant throughout the collision. It changes value as the objects change shape and move. A typical force graph for an inelastic collision in a frictionless environment is shown below. A typical time scale over which this impulse force acts in a collision like this is 0.25 seconds (as shown). Using this time range for the collision, calculate the average force you expect the clay ball to apply to the sled. Then calculate the peak force as approximately one and a half times this amount. Show your calculation below and appropriately label the peak force on the y-axis of the graph below. F 0.25 s t

5 5 4. Now, in reality, once the sled starts to slide, you will have a small amount of kinetic friction opposing the motion. It should be roughly steady and point in the negative direction. Assume that the deceleration of the sled will be about 2.75 m/s 2 for this part. Ignore the mass of the clay ball here (we are focusing on the sled), and calculate the friction that would be needed to decelerate the mass of the sled alone at 2.75 m/s 2. Show your work below: 5. Considering that the sled will start moving shortly after the collision force starts to be applied, sketch the shape of the force graph you expect to get. (Hint: It will be a superposition of the impulse force in step 3 above and the force of friction just calculated in step 4.) Sketch the entire force graph from the time the collision starts until the sled stops moving - including a scale on each axis. F 0 t

6 6 6. Using the force graph above as your guide, predict the acceleration graph of the sled. Place your answer in the graph below, including a scale along each axis. a 0 t 7. Using the acceleration graph above as your guide, predict the velocity graph of the sled. Place your answer in the graph below, including a scale along each axis. v t

7 7 8. The area under the velocity-time graph should be equal to the total distance the sled slides.* Go back now and see how your predicted distance and the area under the velocity-time graph compare. Show your work below. If they are significantly different, check your calculations again. * Remember, units are important. The area under your velocity-time graph should be found using the scales you have set up along each axis. 9. Using the velocity graph above as your guide, predict the position graph of the sled. Place your answer in the graph below, including a scale along each axis. Assume the sled starts at position zero. x t

8 8 Analysis - To be completed while in lab after your solution has been tested and data has been collected. 1. Highlight the area under your velocity-time graph where there is meaningful data (i.e. from the time of the collision until the sled stops moving). Use the statistics mode of the Science Workshop software to integrate the area. Enter your answer in the chart below. 2. Now use the statistics mode and determine the total distance the sled moved according to your position-time graph. If the motion sensor was zeroed properly, this should be the total distance the sled traveled. Enter the answer in the chart below. Area Under v-t Graph Total Distance Traveled Your comments about the above chart: 3. Highlight a small interval of data on your position time graph and use the statistics mode to do a linear curve fit. The slope of the curve-fitted line will be indicated with the variable a 2 that shows up in the statistics window. Record this value in the chart below. Also use the analysis feature of the software (i.e. the crosshairs) to determine the approximate time at the center of this interval you have chosen. Record this in the chart below also.

9 9 4. Now use the crosshairs on your velocity graph to measure the velocity at the same time. Record this value below. 5. Repeat steps three and four choosing new data intervals up and down your position graph. Record your results in the chart below. Time Slope of x-t Graph Velocity Your comments about the above chart: 3. Highlight the positive pulse on your acceleration-time graph and integrate the area under it. Record in the chart below. Compare this to the maximum velocity on your velocity-time graph. Record this in the chart below also. Area Under Positive Pulse on Accel.-time Graph Maximum Velocity

10 10 4. Now highlight the area of the acceleration-time graph where the acceleration is negative. Integrate it. How does your answer compare with the area under the positive pulse on your acceleration-time graph found previously? Explain. Area Under Positive Pulse on Accel.-time Graph Area Under Negative Part of Accel.-time Graph Explanation: 5. Highlight the positive pulse on your force-time graph. Integrate the area using the statistics feature of the software. Record below. Now enter the mass of the sled and the maximum velocity of the sled in the chart. Multiply the mass times the velocity to determine the impulse of the sled caused by the collision. How does this compare to the area under the positive pulse on your force-time graph? Explain. Area Under Pos. Pulse on F-t Graph Impulse of Sled Mass of Sled Max. Velocity of Sled Explanation:

11 11 Questions - To be completed after the lab When answering these questions, be sure to refer to your data graphs taken in lab when you ran your solution. 1. How far did your sled end up sliding? Was your attempt successful? Explain: 2. If your attempt was not successful, have you determined what went wrong? What have you narrowed it down to? Explain. Also, show any corrections in your solution below (attach as many pieces of paper as needed).

12 12 3. The tension in the thread was not considered in the lab. At what point would the tension in the thread be greatest? Calculate the maximum tension that would have existed in the thread while the clay ball was swinging in your solution. Show your work below (including a free-body-diagram) and put a box around your final answer: 4. Calculate the kinetic energy in your system right before the collision. Then calculate the kinetic energy right after the collision. Are they the same? Why or why not?

13 13 5. The sled stopped moving mainly because of friction. So where did all of the original kinetic energy of the sled go? Answer in detail including the specific process that occurred on the molecular level. 6. Once friction became the dominating force affecting the motion of the sled, did the sled's kinetic energy dissipate as heat at a steady rate? Explain. Give evidence to support your argument by referring to one or more of your real data graphs.

14 14 7. Overall, how did your predicted force vs. time, acceleration vs. time, velocity vs. time, and position vs. time graphs match up with the true data graphs? Keep in mind that you assumed the deceleration of the sled would be 2.75 m/s 2 to predict your graphs, and that's not necessarily what the deceleration was. Considering this, rate how well you think your graphs matched using a scale of 1 (terrible) to 5 (fantastic). Force vs. Time Acceleration vs. Time Velocity vs. Time Position vs. Time Score