Which iceboat crosses the finish line with more kinetic energy (KE)?

Transcription

1 Two iceboats (one of mass m, one of mass 2m) hold a race on a frictionless, horizontal, frozen lake. Both iceboats start at rest, and the wind exerts the same constant force on both iceboats. Which iceboat crosses the finish line with more kinetic energy (KE)? A. The iceboat of mass m: it has twice as much KE as the other. B. The iceboat of mass m: it has 4 times as much KE as the other. C. The iceboat of mass 2m: it has twice as much KE as the other. D. The iceboat of mass 2m: it has 4 times as much KE as the other. E. They both cross the finish line with the same kinetic energy.

2 More force was needed to stop the rock Review: Newton s Laws F 1 F F 3 2 F 4 Newton s First Law The velocity of an object does not change unless a force acts on the object Newton s Second Law: F net = m a The acceleration of an object is proportional to the net force on the object Newton s Third Law For every force an object exerts on a second object, there is an equal and opposite force exerted on the first object ALWAYS! These are equal and opposite forces even if you break the wall or your fist keeps going!

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4 A B C D E

5 Free-Body Diagrams (FBDs) F G weight n F pull If it doesn t have units of Newtons (kg m/s 2 ), then it doesn t belong on a FBD! (No velocity or acceleration) f k mg A FBD labels all of the forces acting on (not by) an object. Only forces acting on an object will affect its motion (acceleration).

6 Friction Static Friction: Force that keeps object from sliding against a surface when it is at rest f stat m s n Kinetic Friction: Force that slows you down when moving f k = m k n F fr =µ fr =µ s n s n F fr =µ k n Once it starts moving, kinetic friction takes over. Why it is easier to move something after it gets started moving.

7 Work Done by a Constant (or Average) Force x F Force F acting on an object causes the object to move a distance Δx does work W W F x magnitude of displacement of object component of force parallel to displacement of object Units: N m = Joule (J) Or equivalently: Only concerned with movement in the direction of the force

8 The Work-Energy Principle The work done on an object by a net force is W 1 mv 2 1 mv 2 net 2 2 o Translational kinetic energy (energy of motion) of an object: KE 1 mv 2 The net work done on an object is equal to the change in its kinetic energy 2 W net KE KE f KE o KE increases KE decreases

9 Gravitational Potential Energy y f PE grav mgy W G mgy mg( y yo) Δy PE PE f PE i mgy mgyo mgy y o W G PE Work done by gravity in going between two points is equal to the negative of the change in PE Note: 1. Origin to measure y is arbitrary, thus so is PE (PE is not) 2. Gravity does work only in the vertical direction, so work done by gravity in going from point 1 to point 2 only depends on y, independently of path taken

10 Mechanical Energy Last Time: Work-energy principle W net KE Separate net work done into work done by conservative and nonconservative forces: W net But W C = -PE W W NC NC W C KE W NC PE KE ( PE) KE If W NC = 0, PE KE (PE PE ) (KE KE ) 0 0 f i f i PE i + KE i = PE f + KE f Mechanical energy (PE + KE) of an object remains the same (is conserved) if only conservative forces act on the object

11 Last Time: Linear Momentum & Impulse p mv Units: kg m/s Linear momentum of an object is mass times velocity Linear momentum is a vector. Direction of linear momentum is the same as the velocity of the object F net p t I p Ft 1. A force must act on an object for impulse to occur 2. In a collision, an impulse occurs in the direction of the force acting on the object

12 Conservation of Linear Momentum in Isolated Systems. A system is a set of objects interacting with each other An isolated system has no unbalanced external forces, meaning no unbalanced forces outside the system (e.g., normal/gravity) p p f, system i, system m1v 1i m2v2i m1v 1 f m2v2 f

13 Elastic and Inelastic Collisions Inelastic collisions: mechanical energy (KE+PE) is not conserved Special case: Perfectly inelastic, objects stick Elastic collisions: mechanical energy is conserved For both elastic and inelastic collisions linear momentum is conserved

14 E, A, A Clicker answers

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