Page 1. Clicker Question 9: Physics 131: Lecture 15. Today s Agenda. Clicker Question 9: Energy. Energy is Conserved.

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1 Physcs 3: Lecture 5 Today s Agenda Intro to Conseraton o Energy Intro to some derent knds o energy Knetc Potental Denton o Mechancal Energy Conseraton o Mechancal Energy Conserate orces Examples Pendulum Clcker Queston 9: Two dry ce pucks slde on a horzontal, rctonless surace. Puck A, whch s kg, moes at speed 7 m/s n the poste x drecton and Puck B, whch s kg, moes at speed 8 m/s n the negate y drecton as shown n the gure. The pucks collde near the star n the gure. Ater the collson Puck B s mong n the poste x drecton, whle Puck A s mong n the drecton that makes 45 wth the poste x-axs as llustrated. What s the speed o Puck A ater the collson? (a) m/s (b) m/s (c) m/s (d) 4 m/s (e) 4 m/s Physcs 0: Lecture, Pg Physcs 0: Lecture, Pg Clcker Queston 9: Intal: MA = kg, = 7 m/s MB = kg, = 8 m/s Energy Very mportant dea n physcs Knght splts ths nto two chapters: Ch 0: How to use conseraton o energy Ch : How to thnk about t conceptually Physcs 0: Lecture, Pg 3 Physcs 0: Lecture, Pg 4 Energy s Consered Energy s Consered meanng t can not be created nor destroyed Can change orm Can be transerred Total Energy does not change wth tme. Knetc Energy An object n moton has energy Energy o moton s called Knetc energy True or any object wth elocty and mass m. K m Ths s a BIG deal! Physcs 0: Lecture, Pg 5 Physcs 0: Lecture, Pg 6 Page

2 Clcker Queston : Ater a bomb at rest explodes nto two unequal ragments, the more masse ragment has (a) the same knetc energy than the less masse ragment. (b) less knetc energy than the less masse ragment. (c) more knetc energy than the less masse ragment. Potental energy Potental energy: Stored energy Energy depends on the poston or conguraton o an object. Examples Potental energy due to graty Potental energy o a sprng. U = mgy Physcs 0: Lecture, Pg 7 Physcs 0: Lecture, Pg 8 Gratatonal Potental Energy or Free Fall The gure shows a beore-and-ater representaton o an object n ree all. One o the knematcs equatons rom Chapter, wth a y = g, s: Gratatonal Potental Energy on a Frctonless Surace a g sn as y g sn sn gy g y y Rearrangng: gy gy Multplyng both sdes by ½m: m mgy m mgy We can thnk o ths n terms o energy! Physcs 0: Lecture, Pg 9 y sn O H y s y s sn m g y g y y gy gy mgy m Physcs 0: Lecture, Pg 0 mgy Ths works or any rctonless surace! Gratatonal Potental Energy on a Frctonless Surace Conseraton o Mechancal Energy When only graty s actng on an object t conseres mechancal energy E E mech mech Can approxmate any surace as a bunch o small nclnes! K U g K U m mgy m mgy g Physcs 0: Lecture, Pg Physcs 0: Lecture, Pg Page

3 Conseraton o Mechancal Energy K U K + U Clcker Queston : Three balls are thrown rom a cl wth the same speed but at derent angles. Whch ball has the greatest speed just beore t hts the ground? A. Ball A. B. Ball B. C. Ball C. D. All balls hae the same speed. Physcs 0: Lecture, Pg 3 Physcs 0: Lecture, Pg 4 Clcker Queston 3: A hockey puck sldng on smooth ce at 4 m/s comes to a -m-hgh hll. Wll t make t to the top o the hll? A. Yes. B. No. C. Can t answer wthout knowng the mass o the puck. D. Can t say wthout knowng the angle o the hll. Clcker Queston 4: A quarter s dropped rom rest rom the th loor o a ery tall buldng. The speed o the quarter s just beore strkng the ground. From what loor would the quarter hae to be dropped rom rest or the speed just beore strkng the ground to be approxmately? Ignore all ar resstance eects to determne your answer. a) 4 b) 5 c) 0 d) 7 e) 0 Physcs 0: Lecture, Pg 5 Physcs 0: Lecture, Pg 6 Clcker Queston 5: A ball s shot upwards o a cl o heght 00.0 m wth a speed o 45.0 m/s. What speed wll the ball hae when t s halway down the cl at heght 00.0 m? a) 77. m/s b) 63. m/s c) 5.3 m/s d) 94.4 m/s e) 35.9 m/s Force due to a sprng When to compress a sprng, the sprng pushes out on your hand. When you stretch a sprng, the sprng wll pull back on your hand. Sprng orce always opposes the orce you apply. Physcs 0: Lecture, Pg 7 Physcs 0: Lecture, Pg 8 Page 3

4 Force due to a sprng = -k(s) s s dstance sprng s compressed or stretched rom ts relaxed length k s the sprng constant (how strong the sprng s) s = -k(-s) = +ks = -k(+s) = -ks Sprng orce Restorng orce: Always works to restore the orgnal poston. The k constant depends on many actors (materal, how many rngs, etc) Only good or a partcular sprng Measure o stness Large k real strong (shock absorber) Small k not strong (slnky) s Physcs 0: Lecture, Pg 9 Physcs 0: Lecture, Pg 0 Many objects can behae lke a sprng Restorng orce Example Bow and Arrow Pendulum Basketball Superball Tendons Deormng an object Many orces oer small dstances Molecules Knetc Energy and Gratatonal Potental Energy Dene knetc energy as an energy o moton: Dene gratatonal potental energy as an energy o poston: The sum K + U g s not changed when an object s n ree all. Its ntal and nal alues are equal: Physcs 0: Lecture, Pg Physcs 0: Lecture, Pg Potental energy due to a sprng A compressed sprng has potental energy. Energy o conguraton relaxed poston s 0 U S = ½k(s) s s dstance sprng s compressed or extended. s D k s constant that depends on sprng. New Conseraton o Mechancal Energy Good when only graty or a sprng-lke orce s actng E = E K + U =K + U ½kx + ½m + mgy = ½kx + ½m + mgy Physcs 0: Lecture, Pg 3 Physcs 0: Lecture, Pg 4 Page 4

5 Clcker Queston 6: A sprng s compressed by a ball an amount x = 0.5 m. The system s released and the ball s shot out down a rctonless table. At the end o the table the ball encounters a hump that brngs t up to a heght o 0.6 m. I the mass o the ball s 0 kg and the k or the sprng s 600 N/m what s the nal speed o the ball? a).33 m/s b) 4.56 m/s c) 3.45 m/s d).79 m/s e) 5 m/s Physcs 0: Lecture, Pg 5 Page 5