Get the frictional force from the normal force. Use dynamics to get the normal force.

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Kory Burns
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1 . L F n µ k L =00 t µ k = 0.60 = 0 o = 050 lb F n +y +x x = sin y = cos = µf n Is the initial elocity o the car reater than 30 mph? Approach: Use conseration o enery. System: car Initial time: beore you apply brakes. Final time: ater you stop. Enery output rom car by rictional orce and component o raitational orce (weiht) alon direction o motion. Nelect the air resistance. Use dynamics to et rictional orce. Enery diaram L = 0 0 Initial State Enery Transer Final State E i = m E = 0 L L E output = dx dx sin L L 0 x + = + 0 Conseration o Enery: E - E i = E input - E output. 0 m = ( sin L + L ) and =m ( sin L L ) o = + Get the rictional orce rom the normal orce. Use dynamics to et the normal orce. Fy = ( Fn cos) = 0

2 Plan Find unknowns ( sin L L ) = + [] Find = µf n [] F n Find F n ( F n cos) = 0 [3] 3 unknown, 3 equations ( F n cos) = 0 F n = cos into [] = µ k cos into [] = = ( sin L + µ cosl) ( sin L + µ k cos L) ( sin + µ ) = L k cos check units k m m = [ m] = correct or elocity s s t + 0 s o o ( 00t )( sin cos ) = 3 = 70 t/s t mi 60s 60 min 70 = 48mph s 580t min hr were speedin. This is reater than the 30 mph speed limit. You The elocity has the correct units o t/s. I were 90 o, the car would be allin straiht down. The answer becomes = L which does not depend on the coeicient o riction. This is reasonable i the car is in ree all. I the skid lenth increases, the initial elocity would be reater. This is reasonable since it would take a loner distance to stop the car i it were oin at a hiher speed.

3 3. m a x m h Find the distance the ruit hits the round as a unction o the initial speed and anle o the arrow, the heiht o the ruit on the tree, the mass o the ruit and the mass o the arrow. + y + x Approach: Use kinematics to calculate rom and h. Ater the arrow enters the ruit and it lies throuh the air with a constant ertical acceleration and constant horizontal elocity. Since the arrow sticks in the ruit, there is a lare internal enery chane in the arrow-ruit system. Use conseration o momentum to relate the arrow s elocity just beore it hits the ruit to the elocity o the ruit just ater the arrow enters it. Since the arrow hits the ruit at the hihest part o its path, its elocity is horizontal and equal to the horizontal component o the arrow s initial momentum. The horizontal component o the elocity o the arrow is constant. x = cos Conseration o momentum p x - p ix = p input x - p output x System: arrow + ruit Initial time: just beore arrow enters ruit pix = m a x = m a cos Final time: just ater arrow enters ruit p x = ( m a + m ) No momentum transer in x direction since no orces in x direction. ( m a + m ) ma cos = 0 Fliht o arrow and ruit ater leain the tree Constant horizontal elocity: aerae x component o elocity = instantaneous x component o elocity. x = a = = Constant ertical acceleration: aerae y component o acceleration = instantaneous y component o acceleration. x = a = and y = a y ( ) + y( ) + yo

4 Plan unknowns Find = [], Find [] Find ( m a + m ) ma cos = 0 [3] 3 unknowns, 3 equations ( m + m ) m cos 0 a a o = ma cos = into [] ( ma + m ) h t = into [] ma cos ( m + m ) a = h ma cos h = ( m a + m ) Ealuate: Check units: m [ k] s k [ ] [ m] m = [ s ] = [ m] m s s correct or a distance I the initial speed ( ) o the arrow is reater, the ruit oes a reater distance (). This is reasonable. I the anle the arrow is shot is 90 o, the distance the ruit oes is zero. That is reasonable because i the arrow is shot straiht up, the ruit must be directly oer the hero to hit it. The ruit will then all straiht down ater it is hit.

5 I the mass o the ruit is larer, then it does not o as ar rom the tree. That is reasonable. The hiher the ruit is o the round, the arther it alls rom the tree. That is reasonable since its horizontal component o elocity is the same but it has a loner time to trael. Conceptual Questions:. b. a 3. a 4. a 5. c 6. e 7. d 8. c 9. b 0. b

P6.5 (a) static friction. v r. = r ( 30.0 cm )( 980 cm s ) P6.15 Let the tension at the lowest point be T.

P6.5 (a) static friction. v r. = r ( 30.0 cm )( 980 cm s ) P6.15 Let the tension at the lowest point be T. Q65 The speed chanes The tanential orce component causes tanential acceleration Q69 I would not accept that statement or two reasons First, to be beyond the pull o raity, one would hae to be ininitely