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Name (printed) _______________________________ First Day Stamp LABETTE A CALCULATION OF PERSONAL POWER INTRODUCTION My dad gave me a car three days after I turned sixteen. I was ecstatic. I couldn’t contain myself. My very own car – I couldn’t believe it. And even though he towed it home, it was the most beautiful two tons of metal I think I had ever seen. He said if I could get it to run, it was mine. The ‘62 Pontiac Grand Prix had almost 100,000 miles and an engine that had died, but after I got it to run I was amazed at its incredible power – 303 horsepower. No sixteen-year-old boy should be allowed to tame that much power. Oh, the stories I could tell. You might wonder how much 303 horsepower really is and how it compares to your own personal power. It’s a lot by today’s automotive standards. A standard mid-size American car probably has around half the power of my old Grand Prix (and probably gets three times the mileage). How it compares to your own personal power is an interesting question. I’ll have you do three experiments to determine your personal power: one in which you do work with your biceps (curling a dumbbell), one in which you do work with your triceps (doing pushups), and one in which you do work with your legs (climbing stairs). It seems that determining personal power using this last method is somewhat of a tradition at Tam. I ran across an old article from the Tam News a few years ago when I was moving some furniture in my classroom. It was an article from the March 8, 1940 issue, written about the annual personal power competition in physics. The way the students measured their power was to time themselves running up a set of stairs as quickly as possible. Moving up the stairs caused them to change their gravitational potential energy and running increased the rate of that energy change. We’ll do the same thing, using the stairs outside the physics classroom. Students always ask if they can skip steps. The answer is yes, because all you’re trying to do is increase your distance above the Earth as quickly as possible. The method doesn’t matter. Students also usually wonder if they can get a running start. I think this is fine. In fact, you want your speed at the bottom to be the same as your speed at the top so that there is no change in your kinetic energy, only your potential energy. So, on your marks, get set, GO! The school record for boys is 2.16 hp by Elmo Maggiora (class of 1938) and for girls it’s 1.41 hp by Helen Wendering (class of 1933). PURPOSE To calculate your own personal power. PROCEDURE (PART 1 - BICEPS) 1. Record the weight of the dumbbell you will use. 2. Record the vertical distance the dumbbell moves as you curl it. (Make sure you don’t move your shoulder – only your elbow). 3. Record the number of curls you can do in 30 seconds. DATA (PART 1 - BICEPS) 1. Weight of dumbbell in pounds: ___________ 2. Weight in Newtons: ___________ (1 pound = 4.45 N) 3. Vertical distance of curl: ___________ 4. Number of curls in 30 s: ___________ Figure 13.5: Alex MacDonald, Class of 2004 1 QUESTIONS/CALCULATIONS (PART 1 - BICEPS) SHOW ALL WORK 1. Calculate the total work done in 30 seconds of curling. 2. Calculate your personal power using biceps and express it in both watts and in horsepower. (1 horsepower = 746 watts) PROCEDURE (PART 2 – BACK AND TRICEPS) 1. With either your knees or toes on a scale, place yourself in the up part of the pushup position. Then do the same thing except put yourself in the down part of the pushup position. Average these two measurements and subtract this weight from your body weight. Record this difference as the weight you will be lifting during the pushup. 2. Record the vertical distance your shoulders rise as you do a pushup. 3. Record the number of full pushups (all the way down) you can do in 30 seconds. DATA (PART 2 - TRICEPS) Figure 13.6: Eric Andrews, Class of 2009 1. Weight lifted during pushup (lbs): ___________ 3. Vertical distance of pushup: ___________ 2. Weight lifted during pushup (N): ___________ 4. Number of pushups in 30 s: ___________ QUESTIONS/CALCULATIONS (PART 2 – BACK AND TRICEPS) SHOW ALL WORK 1. Calculate the total work done in 30 seconds of pushups. 2. Calculate your personal power using triceps and express it in both watts and in horsepower. 2 PROCEDURE (PART 3 - LEGS) 1. Record your weight 2. Measure the height of a stair outside the back door of the physics classroom. 3. Have your partner use a stopwatch to measure the time required for you to run at full speed up the flight of stairs outside the back door of the physics classroom. In order for the transferred energy to be exclusively gravitational potential energy, you should be moving at the same speed when you cross the top stair as you are moving when you start at the bottom stair (not stopped and not sprinting). So approach the bottom step at a fast walk and then go to full speed as soon as you reach the first step. DATA (PART 3 - LEGS) 1. Weight in pounds: ___________ 2. Weight in Newtons: ___________ 3. Height of step: 4. Total height climbed: ___________ ___________ Figure 13.7: Beth Behrs, Class of 2004 5. Time to climb stairs: ___________ QUESTIONS/CALCULATIONS (PART 3 - LEGS) SHOW ALL WORK 1. Calculate the total work done in climbing the stairs. 2. Calculate your personal power using legs and express it in both watts and in horsepower. 3. Determine the following ratios (rounded to the nearest integer) of power: TRICEP TO BICEP LEG TO TRICEP LEG TO BICEP Move ahead 3 100% CORRECT For each of the following questions, give clear and complete evidence for your choice in the space provided. 1. _____ When a force is applied, work a. must always be done b. may be done c. is never done 2. _____ A box weighs 50 N and moves at constant speed across a horizontal frictionless surface. How much work is done on the box over the distance of 4.0 meters? a. 0 J b. 200 J c. 1960 J 3. _____ A 50-N object was lifted 2.0 m vertically and is being held there. How much work is being done in holding the box in this position? a. more than 100 J b. 100 J c. less than 100 J, but more than 0 J d. 0 4. _____ Average walking speed is about 2 m/s. A sprinter can reach 8 m/s. How much more kinetic energy does a person’s body have when sprinting compared to walking? a. two times more b. four times more c. eight times more d. 16 times more 5. _____ A person lifts a 10 kg block to a table top in 2.0 seconds. He lifts an identical block a second time in 1.5 seconds. What is true about his work and power during the lifting of the second block? a. work same, power same b. work more, power same c. work same, power more d. work more, power more 6. _____ A 50-kg physics student climbs a flight of stairs in 7.5 seconds. Each of the 60 steps is 20-cm high. What is her power? a. 80 W b. 133 W c. 600 W d. 784 W e. 8000 W 7. _____ A 9000-W motor lifts a 4500-kg elevator to a height of 12 m. How long does it take to do this? a. 6.0 s b. 24 s c. 38 s d. 59 s 4 QUESTIONS AND PROBLEMS WORK AND POWER Do the following questions and problems from the Giancoli book in the space provided below. Pages 160 – 164 Question 2; Problems 3, 5, 10, 58, 64, 66, 87 Move ahead 5 100% CORRECT LABETTE THE PHYSICS OF SIMPLE MACHINES PURPOSE To build a simple machine and to analyze its physical features. PROCEDURE 1. 2. 3. 4. Build a simple pulley system as illustrated in class. Use a spring scale to measure the weight that will be lifted (using all the weights provided). Use a spring scale to measure the force required to lift the weight using the pulley system. (You must be moving the pulley system when you make this measurement.) Measure the distance you must pull on the pulley system in order to lift the weight 0.10 m. (Round this to the nearest integer multiple of 0.10 m.) DATA Resistance Force: ___________ Effort Force: ___________ Resistance Distance: ___________ Effort Distance: ___________ QUESTIONS/CALCULATIONS SHOW ALL WORK 1. Calculate the work input. 2. Calculate the work output. 3. Calculate the actual mechanical advantage. 4. Calculate the ideal mechanical advantage. 5. Calculate the efficiency of the machine. 6. Calculate the amount of heat produced? 6 7. Give some rationale for the reason why this machine should have the ideal mechanical advantage that it has. (Hint: This is not about comparing effort and resistance distances. It’s about looking at the number of supporting strings.) 8. Let’s say that instead of using two double pulleys, you used two triple pulleys. Assume the friction per individual pulley wheel is the same as before. Show careful calculations for the new effort force? QUESTIONS AND PROBLEMS SIMPLE MACHINES 1. A pulley system lifts a 1345-N weight a distance of 0.975 m. A 375-N force is exerted through a distance of 3.90 m. a. If the machine were ideal, how much force would have needed to be applied to lift the 1345 N weight? b. What is the efficiency of the system? c. How much heat is produced? d. How much force would need to be applied to this actual pulley system in order to lift a 2000 N weight? 2. A 1000-N piano is raised a distance of 5.00 m using a set of pulleys. It requires pulling 20.0 m of rope. a. How much effort force would need to be applied if this were an ideal machine? b. If the machine were 75% efficient, how much effort force would be used? c. What is the ideal mechanical advantage and the actual mechanical advantage? 3. An inclined plane is 18 m long and reaches a height of 4.5 m high. a. What force parallel to the ramp is required to slide a 25-kg box to the top of the ramp if friction is neglected? b. What is the IMA of the ramp? c. What is the AMA if it actually requires a parallel force of 75 N to push the box? d. What is the efficiency of the machine in this case? 7 4. A 10-m long inclined plane, whose maximum height is 2.0 m has an efficiency of 70%. a. How much force must be applied to a 50-kg box to move it along the plane? b. What is the actual mechanical advantage of the inclined plane? c. How much heat is produced in moving the block up the plane? d. How much force would have to be applied if the plane were an ideal simple machine? 5. A ramp is used to move a refrigerator into the back of a truck. The refrigerator has a weight of 1127 N. The ramp is 2.10 m long and rises 0.850 m off the ground. The mover pulls the dolly with a force of 496 N up the ramp. What is the efficiency of the machine? 6. A pulley system has an efficiency of 70%. When a student uses it to lift an engine out of a car, she pulls 10 m for every 1-m that the engine is lifted. How much force does she have to apply in order to lift the 2000-N engine? 8 Move ahead 100% CORRECT For each of the following questions, give clear and complete evidence for your choice in the space provided. 1. _____ Two cars, with the same mass, but initially at different altitudes, both increase their altitude by 1,000 m. Which one (if either) has the greater increase in gravitational potential energy? a. the lower altitude car b. the higher altitude car c. both the same 2. _____ 2.0 J of energy are used to stretch a rubber band 3.0 cm. If 4.0 J of energy were used to stretch the same rubber band, how much would the stretch increase to? a. less than 6.0 cm b. 6.0 cm c. more than 6.0 cm, but less than 12 cm d. 12 cm 3. _____ If a pole-vaulter were somehow able to increase his fastest running speed to double, how much higher should he be able to vault himself? a. less than twice as high b. twice as high c. more than twice as high 4. _____ If a person using a slingshot stretched the elastic twice as far and then shot a rock, how much faster would the rock leave the slingshot? a. less than twice as fast b. twice as fast c. more than twice as fast 5. _____ If a person using a slingshot stretched the elastic twice as far and then shot a rock straight up, how much higher would the rock go? a. less than twice as high b. twice as high c. more than twice as high 6. _____ A person on the edge of a roof throws a ball downward. It strikes the ground with 100 J of kinetic energy. The person throws another identical ball upward with the same initial speed, and this too falls to the ground. Neglecting air resistance, the second ball hits the ground with a kinetic energy of a. 100 J b. 200 J c. less than 100 J d. more than 200 J 9 Move ahead 100% CORRECT QUESTIONS AND PROBLEMS CONSERVATION OF ENERGY Do the following questions and problems from the Giancoli book in the space provided on the next two pages. Pages 160 – 166 Question 10, 11, 19; Problems 37, 39, 42, 49, 52, 54, 55, 76 10 11