1Physics 1010:The Physics of Everyday LifeTODAY• Rolling Friction• Hook’s Law, Springs2Today• Rolling Friction• Units• Springs Hooke’s law, F =-kx. Experiments tocheck when and if it holds Scales Springs in your life3What do Most People Around You ThinkAbout The Homework?A They look like they’re easy to overthinkB Too many questionsC We have homework?D All of the above4What do Most People Around You ThinkAbout Their Groups?a. My group is great. I learn a lot by discussingwith them.b.My group is no help. They are not payingattention.c. My group is a drag. I do all the work.d.I’m in a group?5Wheels- no sliding surfaces across each other! So no work,no heating, no wasted energy.tireroad61. Why you stop faster in car on snow if don’t skid?2. How to keep from getting stuck in snow. Friction allows cars to speed up or slow down.Car tires exert force on road … road exerts force on tires.When tires “glued to the road”, have control Drive … engine rotates tire. Tire pushes backwards on road.Friction Force of tire on roadFriction Force of road on tire (car)ROLLING FRICTIONFriction always opposes motion7If no sliding takes place, what causes theresistance when pulling a heavy load onwheels (at constant speed)?ABCD8If no sliding takes place, what causes theresistance when pulling a heavy load onwheels?Surfaces deform. Deformations generate forces against the motion,transform energy to heat.9Rolling is better than sliding• Rolling: static friction (larger) iscontrolling. Static friction larger:Turn betterStop faster(also keep control)• Antilock breaks keep wheels at thresholdof sliding --> greater breaking force.10Does rolling always produce less opposingforce than sliding? YESA the surface doesn’t matterB NOC depends on the surfaceD11RelaxedSpringPull down on spring with2N (0.45 lbs) of forceSpring stretchesX meters.Hook’s Law, Springs12RelaxedSpringPull down on spring with2N (0.45 lbs) of forceSpring stretchesX meters.How much would it stretch if pull down on spring with force of 6 N?a. same distance as for 2 N force b. 2 times as farc. Between 2 and 3 times as far d. 3 times as fare. More than 3 times as farAnswer is d. 3 times as far13RelaxedSpringPull down on spring with2N (0.45 lbs) of forceSpring stretches1 meter.How much would it stretch if pull down on spring with force of 6,000,000 N (about as much as a steam engine)?A 3,000,000 m B it will breakC it will contractApplying Hooks law gives 3,000,000 m, but Hook’s law is only valid for small deformations.14Data says the largerthe mass (or forcedown), the further thespring DEFORMS, andthese are proportional… 2 times the force, 2times the stretch … 3times, 3 times, … etc.Fgravity pulls down on massFgravity = weight = mg = 0.2 kg x 9.8 m/s2MassRelaxedSpringPull down on spring with2N (0.45 lbs) of force …Fspring pulls up on massFspring, balances weightStretch distance = XMeans that Fspring = constant x distance stretched.HOOK’s LAW: Fspring = -kxMinus says that force is in opposite direction to DEFORMATION. The larger the stretch (x), the larger the force of the spring pulling up!Constant = k Is the “Spring Constant”15Scales0LBS510MasskxmgIn equilibrium, Fnet = 0 Fnet = mg – kx = 0So, mg = kx When these spring forcebalances gravity force so thatthe net force is 0 and the massis stationary, we say the massis in equilibrium.So if you have a spring and measure the value of k,then you can hang any weight on it, and from x can calculatethe weight = kx.Scale relatesx to weight16What about if squashing the spring?How much would it compress if weplaced 0.2 kg mass on top of itspring?a. x squash smaller than x hangb. they are about the samec. x squash bigger than x hangd. I still haven’t figured out thebuttons on my clicker.RelaxedSpringMassX?Answer is b. Compression distance aboutthe same as the stretch distance.Fspring must still balance same weight, mg.Fspring = -kxk is same for compression or stretchMassXkxmg17Trucks, cars, mountain bikes are held upby springs to reduce feeling of bumpsA truck weighs 2000 kg. The weight isequally distributed: 500 kg on eachof the four wheels.The truck’s suspension springs are0.3 m inside the truck.When fully loaded (with 250 kg on eachof the back wheels), the back of thetruck drops 0.1 mHow long are the springs when outsidethe truck?a) 0.2 mb) 0.3 mc) 0.4 md) 0.5 me) 0.6 mRelaxed springSpring in truckAdding 250 kg makes springs 0.1 m shorter, soRemoving 500 kg makes springs 0.2 m longer.Relaxed length = 0.3 m + 0.2 m = 0.5 m18Motion in 2 DimensionsWe can separate motion in two (arbitrary) PERPENDICULAR axes.We can consider motion independently for EACH axis.Vx = v0x + atx = x0 + v0x t + (1/2) axt2X-axisVY = v0Y + aty = y0 + v0Y t + (1/2) aYt2Y-axis19Circular MotionIn circular motion, acceleration is always perpendicular to the velocity.ac=v2/RFc=mv2/RθRsS=Rθv=Rωω = angular velocity (eg.