Jumping Up. PY205m. apply the Energy Principle to the point particle system of the jumper, and

Transcription

1 Jumping Up PY205m 1 Purpose In this lab you will review the Energy Principle and the Momentum Principle by fully analyzing what happens in a jump upward from a crouching position: apply the Energy Principle to the real system of the jumper, apply the Energy Principle to the point particle system of the jumper, and apply the Momentum Principle in order to determine the short time of contact with the floor. 2 Experimental Observations Equipment: meter stick and the experiment requires three people. Have each person in the group crouch down, then jump as high as possible, starting from rest. Jump HARD!! While the jumper is crouched down, measure the height of the estimated location of the jumper s center of mass above the floor. Record this as y 1 for that jumper. Have the jumper stand up in a stretched position, approximating the position the jumper will have just as the feet lose contact with the floor in the jump. Measure and record the height y 2 of the estimated location of the jumper s center of mass at this take-off point. Now have the jumper crouch down again and jump upwards as hard as possible, starting from rest. Measure and record the height y 3 of the estimated location of the person s center of mass at the highest point of the jump. Estimate the mass m of the jumper. Note that 1 kg is 2.2 pounds. Record this data for each jumper. CHECKPOINT: Compare your data with another group to make sure it is reasonable. 1

2 3 Analysis of Experimental Observations (on Whiteboards) Note: Do NOT plug in any numbers! Use m for the mass of the jumper and y 1, y 2, and y 3 for the three key heights of the center of mass. 3.1 Energy Principle of Real System Be careful of signs! Using the Energy Principle for the real system for the jumper alone, going from crouch (y 1, just before starting to jump) to the highest point of the jump (y 3 ), determine how much chemical energy is expended. Initial and kinetic energy of the jumper. Force exerted on the jumper by the Earth. Net displacement of the point of application of the gravitational force. (the gravitational force acts at the center of mass) Work done on the jumper by the force exerted by the Earth. Work done on the jumper by the force of the floor on the bottom of the feet. Write the Energy Principle for this situation and choice of real system. Be sure to include the term E internal, the change of internal energy of the jumper. Be careful of signs. Solve for the internal energy change in the jumper in terms of m, g, y 1, y 3. Answer the following questions: Why is W floor = 0? Why is E internal negative? CHECKPOINT: Compare your results with another group. Record your results and answers to the follow-up questions (you will need to answer these questions in WebAssign later) 2

3 3.2 Energy Principle for Point Particle System Using the Energy Principle for the point particle system for the jumper alone, going from lift-off (y 2, just after feet leave the floor) to to the highest point of the jump (y 3 ), determine the speed v 2 of the jumpers center of mass at lift-off. Initial translational kinetic energy of the jumper (K trans,2 is unknown) Final translational kinetic energy of the jumper Net force exerted on the point particle system Net displacement of the point particle system Work done on the point particle system by the net force Write the Energy Principle for this situation and choice of point particle system. Be careful of signs. Solve for the translational kinetic energy at lift-off. Solve for the speed of the jumpers center of mass at lift-off. CHECKPOINT: Compare your results with another group and record your results 3.3 Energy Principle for Point Particle System Using the Energy Principle for the point particle system for the jumper alone, going from the crouch (y 1, just before starting to jump) to the lift-off point of the jump (y 2, just before feet leave the floor), determine the magnitude (F floor ) of the force that the floor exerts on the bottom of the jumpers feet. Assume this force is approximately constant while the feet are in contact with the floor. Initial translational kinetic energy of the jumper Final translational kinetic energy of the jumper (get from Section 3.2) 3

4 Net force exerted on the point particle system Net displacement of the point particle system Work done on the point particle system by the net force Write the Energy Principle for this situation and choice of point particle system. Be careful of signs. Solve for the magnitude of the force exerted by the floor in terms of m, g, y 1, y 2, y 3 This tells how strong the floor must be. If the floor cannot support a force this large, it will break. Note that F floor is larger than the weight mg of the jumper. Answer the following questions: Why does the force of the floor, F floor, appear in this analysis but not in the analysis of the real system, in Section 3.1? Why is there no term E internal in this analysis? CHECKPOINT: Compare your results with another group. Record your results and answers to the follow-up questions (you will need to answer these questions in WebAssign later) 3.4 Momentum Principle for the Real System Using the Momentum Principle for the real system for the jumper alone (or the point particle system; the momentum principle is the same for both systems), going from the crouch (y 1, just before starting to jump) to lift-off (y 2, just after feet leave the floor), determine the amount of time t the jumper s feet are in contact with the floor. Assume the force of the floor F floor is approximately constant while the feet are in contact with the floor. Initial momentum of the jumper Final momentum of the jumper (write in terms of the speed v 2 ) Net force exerted on the system (write in terms of F floor ) Write the Momentum Principle for this situation and choice of system. Be careful of signs. Solve for the amount of time that the jumper s feet are in contact with the floor in terms of m, g, v 2, F floor Note that the Momentum Principle always involves the net force, the vector sum of all the forces acting on the system. Also note that F floor must be larger than mg in order to increase the upward momentum. CHECKPOINT: Compare your results with another group and record your results 4

5 4 Numerical Results Calculate numerical values for each jumper and enter the results into WebAssign. Section 3.1: internal energy change Section 3.2: lift-off speed Section 3.3: magnitude of average force of floor and weight of jumper (note that the floor must support more than the jumpers weight) Section 3.4: amount of time feet are in contact with floor Give correct SI units for each quantity. CHECKPOINT: Recorder should enter experimental data and results into WebAssign. Answer the follow-up questions in WebAssign as a group. October 29,