Loss of Kinetic Energy Name: _______________________________________ Date: ______________ INTRO: Kinetic energy (K.E.) is the energy of objects in MOTION. If an object is not moving it has no K.E. Gravitational potential energy (P.E.) is the energy of POSITION. If you pick up an object and raise it higher, you do WORK on it and give it more P.E. Combining the ideas of CONSERVATION OF MECHANICAL ENERGY & the WORK-ENERGY THEOREM we understand that the work done to raise an object is equal in value to the increase in its P.E. Also when an object falls from a particular height its P.E. is converted into K.E. So if we picked up a ball and did 100 Joules of work on it, by how much did we raise its P.E.? 100 Joules! If we dropped the ball and it fell back to the floor where it came from, how much K.E. would it have right before it hits the floor? 100 Joules! This is all assuming of course no FRICTION acting on the system. WORK = P.E. = K.E. (in the absence of friction) In lab today we’ll test to see how the P.E. of a ball changes to K.E., and how K.E. is lost as the ball bounces back up. PROCEDURE: 1) Take a golf ball or other ball provided and find its mass. Convert your answer to Kg. Mass is _____ g = ________ Kg 2) Now find the gravitational P.E. if you lift the ball exactly one meter off the floor. Use 9.8 as the value for “g”. P.E. = mgh What is the P.E. of the ball? ________ Joules 3) If you drop it, what should be the K.E. of the ball just as it hits the floor? THE SAME VALUE YOU JUST GOT FOR P.E. which was ______ Joules. Use the formula below to find the SPEED of the ball just as it hits the floor… Since K.E. = P.E. and K.E. = ½ mv2 you solve for v by using your number of Joules for P.E., dividing by 0.5 and by the mass, then finding the square root of your answer to get velocity. V = √P.E. value/(0.5)(mass) 4) Take your ball, hold it up exactly one meter (using a meter stick), and drop the ball. See how high it bounces & record. ______ cm = ______ m 5) Did the ball bounce up 1 meter high? ____ This is because K.E. was LOST as the ball hit the floor. Whenever frictional forces interfere energy is lost in a process. This is why there are no 100% efficient machines, because there is some friction in all of them. 6) You can calculate the speed with which the ball left the floor by the equality K.E. = P.E. so 1/2 mv2 = mgh Notice that mass cancels That leaves us with 0.5v2 = gh Use 9.8 as “g” and the height to which your ball bounced as “h” and calculate v. V = _______ m/s Compare this value with the value the ball had as it struck the floor. It is significantly less, isn’t it? _____ ANALYSIS & QUESTIONS 1) The ball lost K.E. as it hit the floor. The best evidence for this is that a) the ball was going faster as it bounced up b) the ball changed mass as it hit the floor c) the ball didn’t bounce as high as the distance from which it was dropped d) P.E. really isn’t equal to K.E. 2) The energy lost by the ball a) was exactly half its original K.E. b) went into work done on the floor to make it vibrate c) was almost all its original K.E. 3) A ball is sitting still on a counter exactly 1 meter high. The ball has ____ J of K.E. a) 100 b) 1000 c) 0 d) depends on the mass of the ball 4) The moon has 1/6 the value of “g” compared to earth. A ball on the moon would have ____ the P.E. compared with a ball the same height above the ground on earth. a) equal b) 1/6 c) 6 times d) infinitely more 5) T/F If you doubled the mass of an object you would double its P.E. 6) T/F If you doubled the height to which you carried an object, you would cut its P.E. in half. 7) T/F P.E. is directly proportional to “g”. 8) T/F Regardless of the mass of ball dropped, each ball would have the same speed as it hits the ground if dropped from the same height (if we ignore air resistance). 9) T/F If we do 500 J of work on an object to raise it, we have increased its P.E. by 500 J. 10) A toy company says it’s created a ball that bounces higher than from where it was dropped. Why should you question such a claim? 11) Student A has a mass of 60 kg. How much P.E. do they have when they climb a hill of height 30 meters? a) 13,400 J b) 15,300 J c) 16,240 J d) 17,640 J 12) Student B steps off a diving board of height 3 m. How fast will she be going when she hits the water below? (you don’t need her mass to calculate, just use P.E.=K.E.) a) 7.7 m/s b) 6.8 m/s c) 9.8 m/s d) 8.6 m/s 13) Student C is at the water park, sliding down a frictionless water slide a vertical distance of 25 m. What is their speed as they hit the water? (hint: it’s the exact same question as #12; it doesn’t matter if the person is falling, sliding, swinging, etc. as long as you ignore frictional forces) a) 13.4 m/s b) 16.4 m/s c) 18.8 m/s d) 22.1 m/s 14) A ball is dropped from 1 meter and bounces up to 80 cm. What percentage of its K.E. is lost? (there are several ways to find the answer, including one very simple way) a) 80 % b) 20 % c) 12.4 % d) 16.6 % *Be sure and show students (if you haven’t already shown them) that mass is CANCELLED when solving for speed of a falling object. PE=KE so mgh=1/2mv2; this simplifies to gh=1/2v2 and applies to any object falling, swinging on a rope, sliding down a frictionless slide or ski hill, etc. The use of conservation of mechanical energy is one of the most helpful formulas we use in simple physics. ANSWERS TO QUESTIONS: 1) c) 2) b) even though work isn’t technically done unless something moves, the floor does move back & forth or vibrate, because you can HEAR the ball hit 3) c) 0 J of KE because it’s not moving 4) b) 1/6; “g” and PE are directly proportional 5 & 7 are true b/c PE is directly proportional to m, g, & h. 6 is false for the same reason. 8. TRUE; mass cancels b/c mgh=1/2mv2 9. TRUE; work-energy theorem says W = PE 10) Their claim is false; energy is always lost in collisions unless they are perfectly elastic, & a ball hitting a surface doesn’t have this kind of collision 11) d) PE=mgh so (60 kg)(9.8)(30 m) = 17,640 J 12) a) use gh=1/2v2 and solve for v 13) d) see answer for #12 14) b) 20%; the easiest way to answer is to say that the ball bounced to 80% of its original height (or you can think of it as 80% of its original PE since m & g didn’t change). If it maintains 80%, it lost 20 %. 15) c); calculate the KE it was SUPPOSED to have, then use the KE equation to calculate the KE it DOES have, and SUBTRACT the lesser from the greater. This loss of KE equals the work done by the air. 98 J – 64 J = 34 J lost b/c of work done by air