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Home , Circular motion

L-9 Conservation of , and Circular • If something moves in • Kinetic energy, and any way, it has conservation of energy kinetic energy • kinetic energy (KE) • What is friction and what determines how is energy of motion m v big it is? • If I drive my car into a • Friction is what keeps our cars moving tree, the kinetic energy of the car can • What keeps us moving in a circular path? do on the tree – KE = ½ m v2 • centripetal vs. centrifugal it can knock it over KE does not depend on which direction the object moves

Potential energy conservation of energy

• If I raise an object to some height (h) it also has • if something has energy W stored as energy – potential energy it doesn’t loose it GPE = mgh • If I let the object fall it can do work • It may change from one • We call this Gravitational Potential Energy form to another (potential to kinetic and F GPE= m x g x h = m g h back) h • KE + PE = constant mg mg m in kg, g= 10m/s2, h in m, GPE in (J) • example – • when we do work in W=mgh PE regained • the higher I lift the object the more potential lifting the object, the as KE energy it gas work is stored as • example: pile driver, spring launcher potential energy.

Amusement park Up and down the track • the roller coaster is an excellent example of the conversion of energy from one form into another • work must first be done in lifting the cars to the top of the first hill. PE PE

• the work is stored as Total energy Kinetic Energy gravitational potential energy If friction is not too big the ball will get • you are then on your way! PE KE up to the same height on the right side.

1 Loop-the-loop What is friction?

• Friction is a force that acts between h two surfaces that are in contact R • It always acts to oppose motion • It is different depending on whether or Here friction works to our advantage. Without it the ball slides rather than rolls. there is motion or not. A ball won’t roll without friction! • It is actually a force that occurs at the The ball must start at a height h, at least microscopic level. 2 ½ R to make it through the loop

A closer look at friction Static friction

If we push on a block and it doesn’t move then 25 microns the force we exert is less than the friction force.

push, P friction, f Magnified view of a smooth surface This is the static friction force at work

If I push a little harder, the block may still not At the microscopic level even two smooth surfaces move Æ the friction force can have any value up look bumpy Æ this is what produces friction to some maximum value.

Homer discovers that kinetic friction Kinetic friction is less than static friction! • If I keep increasing the pushing force, at some point the block moves Æ this occurs when the push P exceeds the maximum static friction force. • When the block is moving it experiences a smaller friction force called the kinetic DUFF friction force BEER • It is a common experience that it takes more force to get something moving than to keep it moving.

2 Measuring friction Going in friction “Normal” Force of incline on block

Force of block Fg, incline on incline

mg

At some point as the if the plane is increased Bart swings the tennis ball around his head in a the block will start slipping. . The ball is accelerating, what force makes At this point, the friction force and are equal. it accelerate? The tension in the string!

Uniform circular motion Centripetal , aC • means both the and direction • Uniform here means that aC the speed is constant as v R the objects goes around R • The direction of v is changing constantly, so v there is an acceleration a The acceleration • For this type of motion points toward the we call this acceleration centripetal acceleration center of the circle

Centripetal force and acceleration Ball on a string • centripetal acceleration • 2 v v The tension in the string magnitude a=C R provides the necessary a • in the direction toward the C to keep center of the circle R the ball going in a circle. • since F = ma , some force is necessary to produce this centripetal acceleration, path of ball if the string • we call this a centripetal force breaks Î we must identify this in each situation

3 Magnitude of centripetal acceleration Carnival Ride

• The centripetal acceleration depends on two factors Æ the speed with which you • There are 2 forces on take the and how tight the turn is the tennis ball- , • More acceleration is required with a higher mg and the tension, T • The vertical part of the speed turn T TV tension force T • more acceleration is required with a tighter V TH R supports the weight turnÆ smaller of curvature mg • The centripetal force is provided by the horizontal part, 2 TH = mv /R

Centripetal acceleration v Wide turns and tight turns R ac, Fc v2 • centripetal acceleration: a=C little R R • for some turns, the “safe” speed is posted • a force is needed to produce this big R centripetal accelerationÆ for the same • CENTRIPETAL FORCE speed, the tighter • where does this force come from? turn requires more acceleration

Example Negotiating a flat (level) turn • What is the tension in a string used to twirl a 0.3 kg ball at a speed of 2 m/s in a circle of 1 • The centripetal force is meter radius? provided by the friction force between the road • Force = x acceleration [ m × aC ] 2 2 and tires. • acceleration aC = v / R = (2 m/s) / 1 m = 4 m/s2 • this force is reduced if the road is wet or icy • force = m aC = 0.3 × 4 = 1.2 N • If the string is not strong enough to handle this tension it will break and the ball goes off in a straight line.

4 Banked Turns Banked turns • Since the road is banked (not horizontal) the force of the road on the box is N not vertical • Part of the force on the R box from the road points

FCENT toward the center of the circle 31 degree bank • This provides the centripetal force • No friction is necessary to Velodrome keep the box in the circle

What’s this ? ?

• The red object will make the turn only if there is enough friction between it and the dash, otherwise it moves in a straight line • The car actually slides out from under the object object on • the apparent outward force (as seen the dashboard by someone in the car) is called the centrifugal force •it isNOT A REAL force! It is a straight line object naturally follows • an object will not move in a circle until something makes it!

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