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CU-Boulder PHYS 1010 - More Acceleration

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1Physics 1010:The Physics of Everyday LifeTODAY• More Acceleration• Newton’s Second Law• Gravity2Help, Office and Tutorial HoursTUTORIALS (G1B75/77/79)Isidoros: 12:30-2:30 Thursday (same as office hours)Shaun: 10:00-12:50 MondayJoseph: 4:00-5:00 Monday, 2:00-4:00 FridayHELP (G1B90)Mark (exams + overall): ???Ye (Clickers): 3:00-5:00 FridayYin (Homework): 2:00-3:00 Monday and FridayTimes may still change, depending on demand3Review• Acceleration is to velocity as velocity is toposition• Acceleration is– Change in velocity divided by elapsed time– Slope on velocity versus time graph• Acceleration is proportional to force (F = ma)4Newton’s second law:Force = mass x accelerationF=ma• Force and acceleration are both VECTORS• Acceleration and force are always IN THE SAME DIRECTION (velocity and force do not have to be)• The mass tells us the ratio5ACCEL E RATIONThe car is subjected to a constant force in the direction away fromthe motion detector. Sketch your predictions for the velocity andacceleration of the cart moving toward the motion detector, slowingdown at a steady rate, and then reversing direction and speeding up.(Start your graph after the push that gets the cart moving.)+0-VelocitytimeAcceleration+0-timev start0feet5-56ACCEL E RATION+0-VelocitytimeAcceleration+0-time#1#1+0-VelocitytimeAcceleration+0-time#1#1+0-Velocitytime+0-time+0-VelocitytimeAcceleration+0-timeADCBAccelerationSketch yourpredictions for thevelocity andacceleration of thecart moving towardthe motion detector,slowing down at asteady rate, andthen reversingdirection andspeeding up.E none of the above7ACCEL E RATIONThe car accelerates always away from the motion detector, eventhough it initially moves towards the motion detector.v startANSWER IS DA constant force is pointing down the slope (away from the detector) so a constant acceleration is also pointing down the slope (away from detector)0feet5-5+0-VelocitytimeAcceleration+0-#1#1D8Newton’s second law:Force = mass x accelerationF=ma• Force and acceleration are both VECTORS• Acceleration and force are always IN THE SAME DIRECTION (velocity and force do not have to be)• The mass tells us the ratio9From acceleration and velocity we canfind the positionAcceleration (a) = change in velocity time elapsedVelocity = Starting velocity + change in velocityVelocity = Starting velocity + acceleration x time V(t) = vinitial + atPosition = initial position + (average velocity) x timevaverage = (vinitial + vfinal)/2 = (vinitial + vinitial + at)/2 = vinitial + (1/2) atx = xinitial + vaverage t = xinitial + (vinitial + (1/2) at) t x(t) = xinitial + vinitial t + (1/2) at2To succeed in this course you have to be able to do this algebra.10ACCEL E RATIONFor a = 1.0 m/s2, plot the distance against time for the first two seconds.Assume the body starts from rest at x=0.0x(t) = xinitial + vinitial t + (1/2) at2We often leave out the (t), so we write x = xinitial + vinitial t + (1/2) at2We also often write xinitial as x0, meaning x(t=0)11ACCEL E RATIONdistancetimedistancedistancedistancetimetimetimeABCDFor a = 1.0 m/s2, plot the distance against time for the first two seconds.Assume the body starts from rest at x=0.0x = x0 + v0 t + (1/2) at2A12We can plot the formula to see what themotion looks likex = xinitial + vinitial t + (1/2) at2xinitial =0, a=1;“from rest” means vinitial = 0x = (1/2) t2Table t xtx00.51.02.00 001 21 0.52 213We can plot the formula to see what themotion looks liketx00.51.02.00 001 21 0.52 2Answer is Ax = xinitial + vinitial t + (1/2) at2xinitial =0, a=1;“from rest” means vinitial = 0x = (1/2) t2Table t x14The Formula, Graph, and Physical Motionare all interconnected• Graph: shows picture of physical motion in one instant• Formula: Relates– Position to average velocity– Velocity to acceleration– Position to acceleration• Plotting the formula gives instant visualization of themotion!15ACCEL E RATIONSketch Position vs. time graph for the car moving towards the motiondetector and slowing down at a steady rate. (Velocity and accelerationgraphs shown.)+0-VelocitytimeAcceleration+0-time+0-Positiontime?0feet5-5160feet5-5ACCEL E RATIONSketch Position vs. time graph for the car moving towards the motiondetector and slowing down at a steady rate. (Velocity and accelerationgraphs shown.)+0-Positiontime+0-Positiontime+0-Positiontime+0-Positiontimea)b)c)d)17ACCEL E RATIONSketch Position vs. time graph for the car moving towards the motiondetector and slowing down at a steady rate. (Velocity and accelerationgraphs shown.)+0-VelocitytimeAcceleration+0-timeThe correct answer is d0feet5-5+0-Positiontimed)18GRAVITY• GALILEODroped balls of different weight from tower ofPisa; balls reach the ground at the same time• NEWTONSaw apple falling, deduced Universal Law ofGravitation19F ON CARThere is a net force on the car. SOMETHING is exerting a force on the car -- Gravity Car accelerates in same direction as net force:Fnet = mass x accelerationFnet = Fon car = massof car x accelerationof carWhat causes the acceleration?GRAVITY20I drop heavy metal ball and light wooden ball whenstanding on top of desk.a. the light ball will hit the ground first.b. they will hit the ground together.c. the heavy ball will hit the ground first.d. neither will fall, they will stay suspended in mid aire. they will both fall up and hit the ceiling.We figure out the force of gravity by dropping stuff21I drop heavy metal ball and light foam ball whenstanding on top of desk.a. the light ball will hit the ground firstb. they will hit the ground togetherc. the heavy ball will hit the ground first.d. neither will fall, they will stay suspended in mid aire. they will both fall up and hit the ceiling.Dropping stuff22I drop heavy metal ball and light foam ball whenstanding on top of desk.a. the light ball will hit the ground firstb. they will hit the ground togetherc. the heavy ball will hit the ground first.d. neither will fall, they will stay suspended in mid aire. they will both fall up and hit the ceiling.Dropping stuffMetalFoam rubberFgravityFgravity on foam rubber ballGravity must pull harder on larger mass.agravity23Since acceleration is the same, forcemust be proportional to massFmetal ball = Mmetal ball x ametal ballFfoam ball = Mfoam ball x afoam ballafoam ball = ametal ball = univeral constantFor metal ball,


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