Chapter: Chapter 6 Learning Objectives: LO 6.1.0 Solve problems related to friction LO 6.1.1 Distinguish beteen friction in a static situation and a !inetic situation. LO 6.1." Determine direction and magnitude of a frictional force. LO 6.1.# $or objects on hori%ontal& vertical& or inclined planes in situations involving friction& dra free'bod( diagrams and appl( )eton*s second la. LO 6.".0 Solve problems related to drag force and terminal speed LO 6.".1 +ppl( the relationship beteen the drag force on an object moving through air and the speed of the object. LO 6."." Determine the terminal speed of an object falling through air. LO 6.#.0 Solve problems related to uniform circular motion LO 6.#.1 S!etch the p ath ta!en in uniform circular motion and e,plain the velocit(& acceleration& and force vectors -magnitudes and directions during the motion. LO 6.#." /dentif( that unless there is a radiall( inard net force -a centripetal force& an object cannot move in circular motion. LO 6.#.# +ppl( the relationship beteen the radius of the circular path& the particle*s speed speed and mass& and the net force acting on o n the particle. ultiple Choice 1. he coefficient coefficient of !inetic friction: + is in the direction of the frictional force force 2 is in the direction of the normal force C is the ratio ratio of force to area D can have units of netons 3 none of the above +ns: 3 Difficult(: 3 Section: 6'1 Learning Objective 6.1.0 ". 4hen the bra!es of an automobile automobile are applied& the road e,erts the greatest retarding force: force: + hile the heels are sliding 2 just before the the heels start to slide C hen the automobile automobile is going fastest D hen the acceleration is least 3 at the instant instant hen the speed begins to change +ns: 2 Difficult(: 3 Section: 6'1 Learning Objective 6.1.1
#. + bric! slides on a hori%ontal surface. 4hich of the folloing folloing ill increase the frictional force on it5 + utting a second bric! on top 2 Decreasing the surface surface area of contact C /ncreasing the surface area of contact D Decreasing the mass of the bric! 3 )one of the above +ns: + Difficult(: 3 Section: 6'1 Learning Objective 6.1." 7. + 70') crate rests on a rough hori%ontal floor. + 1"') hori%ontal force is then applied to it. /f the coefficients of friction are µ are µ s 8 0.9 and µ and µ k 8 8 0.7& the magnitude of the frictional force on the crate is: + ) 2 1" ) C 16 ) D "0 ) 3 70 ) +ns: 2 Difficult(: Section: 6'1 Learning Objective 6.1." 9. + "7') hori%ontal force is applied to a 70') bloc! initiall( at rest on a rough hori%ontal surface. /f the coefficients of friction are µ are µ s 8 0.9 and µ and µ k 8 8 0.7& the magnitude of the frictional force on the bloc! is: + 1" ) 2 16 ) C "0 ) D "7 ) 3 70 ) +ns: 2 Difficult(: Section: 6'1 Learning Objective 6.1." 6. + hori%ontal shove of at least "00') is re;uired to start moving moving an 00') crate initiall( at rest on a hori%ontal ho ri%ontal floor. he coefficient of static friction is: + 0.1"9 2 0."9
C 0.90 D 7.00 3 none of these +ns: 2 Difficult(: 3 Section: 6'1 Learning Objective 6.1." <. + force
F
-larger than the largest possible force of static friction is applied to the left to
an object moving to the right on a hori%ontal surface. hen: + the object must be moving at constant speed 2
F
and the friction force act in opposite directions
C the object must be sloing don D the object must be speeding up 3 the object ill come to rest and remain at rest +ns: C Difficult(: 3 Section: 6'1 Learning Objective 6.1." . + professor holds an eraser against a vertical chal!board b( pushing hori%ontall( on it. She pushes ith a force that is much greater than is re;uired to hold the eraser. he force of friction e,erted b( the board on the eraser increases if she: + pushes ith slightl( greater force 2 pushes ith slightl( less force C stops pushing D pushes so her force is slightl( donard but has the same magnitude 3 pushes so her force is slightl( upard but has the same magnitude +ns: D Difficult(: Section: 6'1 Learning Objective 6.1." =. + forard hori%ontal force of 1" ) is used to pull a "70') crate at constant velocit( across a hori%ontal floor. he coefficient of friction is: + 0.9 2 0.09 C " D 0." 3 "0 +ns: 2
Difficult(: 3 Section: 6'1 Learning Objective 6.1.# 10. he speed of a 7.0') hoc!e( puc!& sliding across a level ice surface& decreases at the rate of 0.61 m>s". he coefficient of !inetic friction beteen the puc! and ice is: + 0.06" 2 0."9 C 0.71 D 0.6" 3 1." +ns: + Difficult(: Section: 6'1 Learning Objective 6.1.# 11. + crate rests on a hori%ontal surface and a oman pulls on it ith a 10') force. )o matter hat the orientation of the force& the crate does not move. ?an! the situations shon belo according to the magnitude of the frictional force of the surface on the crate& least to greatest.
+ 2 C D 3
1& "& # "& 1& # "& #& 1 1& #& " #& "& 1
+ns: 3 Difficult(: 3 Section: 6'1 Learning Objective 6.1.# 1". + bo, ith a eight of 90 ) rests on a hori%ontal surface. + person pulls hori%ontall( on it ith a force of 19 ) and it does not move. o start it moving& a second person pulls verticall( upard on the bo,. /f the coefficient of static friction is 0.7& hat is the smallest vertical force for hich the bo, moves5
+ 9 )
2 C D 3
1" ) "0 ) "9 ) #9 )
+ns: 2 Difficult(: Section: 6'1 Learning Objective 6.1.# 1#. + bureau rests on a rough hori%ontal surface -µ s 8 0.90& µ k 8 0.70. + constant hori%ontal force& just sufficient to start the bureau in motion& is then applied. he acceleration of the bureau is: + 0 m>s" 2 0.= m>s" C #.= m>s" D 7.= m>s" 3 . m>s" +ns: 2 Difficult(: Section: 6'1 Learning Objective 6.1.# 17. + car is traveling at 19 m>s on a hori%ontal road. he bra!es are applied and the car s!ids to a stop in 7.0 s. he coefficient of !inetic friction beteen the tires and road is: + 0.# 2 0.6= C 0.<6 D 0.=" 3 #.<9 +ns: + Difficult(: Section: 6'1 Learning Objective 6.1.# 19. + bo( pulls a ooden bo, along a rough hori%ontal floor at constant speed b( means of a force
P
as shon. /n the diagram f is the magnitude of the force of friction& N is the
magnitude of the normal force& and F g is the magnitude of the force of gravit(. 4hich of the folloing must be true5
+ P 8 f and N 8 F g 2 P 8 f and N @ F g C P @ f and N A F g D P @ f and N 8 F g 3 none of these +ns: + Difficult(: Section: 6'1 Learning Objective 6.1.# 16. + bo( pulls a ooden bo, along a rough hori%ontal floor at constant speed b( means of a force
P
as shon. /n the diagram f is the magnitude of the force of friction& N is the
magnitude of the normal force& and F g is the magnitude of the force of gravit(. 4hich of the folloing must be true5
+ P 8 f and N 8 F g 2 P 8 f and N @ F g C P @ f and N A F g D P @ f and N 8 F g 3 none of these +ns: C Difficult(: Section: 6'1 Learning Objective 6.1.# 1<. + 700') bloc! is dragged along a hori%ontal surface b( an applied force
F
as shon. he
coefficient of !inetic friction is uk 8 0.7 and the bloc! moves at constant velocit(. he magnitude of
F
is:
+ 2 C D 3
100 ) 190 ) "00 ) "=0 ) 700 )
+ns: 2 Difficult(: B Section: 6'1 Learning Objective 6.1.# 1. + bloc! of mass m is pulled at constant velocit( along a rough hori%ontal floor b( an applied force
+ 2 C D 3
T
as shon. he magnitude of frictional force is:
T cos θ T sin θ 0 mg mg cos θ
+ns: + Difficult(: 3 Section: 6'1 Learning Objective 6.1.# 1=. + bloc! of mass m is pulled along a rough hori%ontal floor b( an applied force shon. he vertical component of the force e,erted on the bloc! b( the floor is:
+ mg 2 mg T cos θ C mg T cos θ
T
as
D mg T sin θ 3 mg T sin θ +ns: D Difficult(: 3 Section: 6'1 Learning Objective 6.1.# "0. + 1"'!g crate rests on a hori%ontal surface and a bo( pulls on it ith a force that is #0° belo the hori%ontal. /f the coefficient of static friction is 0.70& the minimum magnitude force he needs to start the crate moving is: + 77 ) 2 7< ) C 97 ) D 96 ) 3 <1 ) +ns: 3 Difficult(: B Section: 6'1 Learning Objective 6.1.# "1. + crate resting on a rough hori%ontal floor is to be moved hori%ontall(. he coefficient of static friction is 0.70. o start the crate moving ith the ea!est possible applied force& in hat direction should the force be applied5 + Bori%ontal 2 "7° belo the hori%ontal C ""° above the hori%ontal D "7° above the hori%ontal 3 66° belo the hori%ontal +ns: C Difficult(: B Section: 6'1 Learning Objective 6.1.# "". + 90') force is applied to a crate on a hori%ontal rough floor& causing it to move hori%ontall(. /f the coefficient of !inetic friction is 0.90& in hat direction should the force be applied to obtain the greatest acceleration5 + Bori%ontal 2 60° above the hori%ontal C #0° above the hori%ontal D "<° above the hori%ontal 3 #0° belo the hori%ontal
+ns: D Difficult(: Section: 6'1 Learning Objective 6.1.# "#. + hori%ontal force of 1" ) pushes a 0.90'!g boo! against a vertical all. he boo! is initiall( at rest. /f the coefficients of friction are µ s 8 0.60 and µ k 8 0.90 hich of the folloing is true5 + he frictional force is 7.= ) 2 he frictional force is <." ) C he normal force is 7.= ) D he bloc! ill start moving and accelerate 3 /f started moving donard& the bloc! ill accelerate +ns: + Difficult(: Section: 6'1 Learning Objective 6.1.# "7. + hori%ontal force of 9.0 ) pushes a 0.90'!g bloc! against a vertical all. he bloc! is initiall( at rest. /f µ s 8 0.60 and µ k 8 0.90& the frictional force after a period of time is: + 0 ) 2 ".9 ) C #.0 ) D 7.0 ) 3 7.= ) +ns: 2 Difficult(: Section: 6'1 Learning Objective 6.1.# "9. + hori%ontal force of 1" ) pushes a 0.90'!g boo! against a vertical all. he boo! is initiall( at rest. /f µ s 8 0.60 and µ k 8 0.90& the acceleration of the boo! is: + 0 m>s" 2 =.7 m>s" C =. m>s" D 17.7 m>s" 3 1=." m>s" +ns: + Difficult(: Section: 6'1 Learning Objective 6.1.# "6. + hori%ontal force of 9.0 ) pushes a 0.90'!g bloc! against a vertical all. he bloc! is
initiall( at rest. /f µ s 8 0.60 and µ k 8 0.90& the acceleration of the bloc! is: + 0 m>s" 2 #. m>s" C 7. m>s" D .0 m>s" 3 =. m>s" +ns: C Difficult(: Section: 6'1 Learning Objective 6.1.# "<. + bo, rests on a rough board 10 meters long. 4hen one end of the board is slol( raised to a height of 6 meters above the other end& the bo, begins to slide. he coefficient of static friction is: + 0. 2 0."9 C 0.7 D 0.6 3 0.<9 +ns: 3 Difficult(: Section: 6'1 Learning Objective 6.1.# ". he same heav( ooden bloc! is dragged b( a force
F
along a rough steel plate& as
shon belo for to possible situations. he magnitude of the acceleration is the same for the to situationsE do not assume that the magnitude of
F
is the same. he magnitude of the
frictional force in -ii& as compared ith that in -i is:
+ 2 C D 3
the same greater less less for some angles and greater for others can be less or greater& depending on the magnitude of the applied force.
+ns: C Difficult(: 3 Section: 6'1
Learning Objective 6.1.# "=. + bloc! is first placed on its long side and then on its short side on the same inclined plane. he bloc! slides don the plane on its short side but remains at rest on its long side. + possible e,planation is:
+ 2 C D 3
the short side is smoother the frictional force is less because the contact area is less the center of gravit( is higher in the second case the normal force is less in the second case the force of gravit( is more nearl( don the plane in the second case
+ns: + Difficult(: 3 Section: 6'1 Learning Objective 6.1.0 #0. + bloc! is placed on a rough ooden plane. /t is found that hen the plane is tilted #0° to the hori%ontal& the bloc! ill slide don at constant speed. he coefficient of !inetic friction of the bloc! ith the plane is: + 0.900 2 0.9<< C 1.<# D 0.66 3 7.=0 +ns: 2 Difficult(: Section: 6'1 Learning Objective 6.1.# #1. + crate is sliding don an incline that is #9° above the hori%ontal. /f the coefficient of !inetic friction is 0.70& the acceleration of the crate is: + 0 m>s" 2 ".7 m>s" C #.= m>s" D 9.6 m>s" 3 . m>s" +ns: 2 Difficult(:
Section: 6'1 Learning Objective 6.1.# #". + 9.0'!g crate is resting on a hori%ontal plan!. he coefficient of static friction is 0.90 and the coefficient of !inetic friction is 0.70. +fter one end of the plan! is raised so the p lan! ma!es an angle of "9° ith the hori%ontal& the force of friction is: + 0 ) 2 "0 ) C "1 ) D "" ) 3 77 ) +ns: C Difficult(: B Section: 6'1 Learning Objective 6.1.# ##. + 9.0'!g crate is resting on a hori%ontal plan!. he coefficient of static friction is 0.90 and the coefficient of !inetic friction is 0.70. +fter one end of the plan! is raised so the p lan! ma!es an angle of #0° ith the hori%ontal& the force of friction is: + 0 ) 2 1< ) C "0 ) D "9 ) 3 7= ) +ns: 2 Difficult(: B Section: 6'1 Learning Objective 6.1.# #7. + 9.0'!g crate is on an incline that ma!es an angle of #0° ith the hori%ontal. /f the coefficient of static friction is 0.90& the minimum force that can be applied parallel to the plane to hold the crate at rest is: + 0 ) 2 #.# ) C "1 ) D "9 ) 3 76 ) +ns: 2 Difficult(: Section: 6'1 Learning Objective 6.1.# #9. + 9.0'!g crate is on an incline that ma!es an angle #0° ith the hori%ontal. /f the coefficient
of static friction is 0.9& the ma,imum force that can be applied parallel to the plane ithout moving the crate is: + 0 ) 2 #.# ) C "1 ) D 76 ) 3 99 ) +ns: D Difficult(: Section: 6'1 Learning Objective 6.1.# #6. 2loc! +& ith mass m A& is initiall( at rest on a hori%ontal floor. 2loc! 2& ith mass m B& is initiall( at rest on the hori%ontal top surface of +. he coefficient of static friction beteen the to bloc!s is µ s. 2loc! + is pulled ith a hori%ontal force. /t begins to slide o ut from under 2 if the force is greater than: + m A g 2 m B g C µ sm A g D µ sm B g 3 µ s - m A m Bg +ns: 3 Difficult(: B Section: 6'1 Learning Objective 6.1.# #<. he s(stem shon remains at rest. he force of friction on the bloc! on the slope is:
+ 2 C D 3
7) ) 1" ) 16 ) "0 )
+ns: 2 Difficult(: Section: 6'1 Learning Objective 6.1.#
#. 2loc! +& ith a mass of 90 !g& rests on a hori%ontal table top. he coefficient of static friction is 0.70. + hori%ontal string is attached to + and passes over a massless& frictionless pulle( as shon. he smallest mass m B of bloc! 2& attached to the dangling end& that ill start + moving hen it is attached to the other end of the string is:
+ 2 C D 3
"0 !g #0 !g 70 !g 90 !g <0 !g
+ns: + Difficult(: Section: 6'1 Learning Objective 6.1.# #=. 2loc! +& ith a mass of 10 !g& rests on a #9° incline. he coefficient of static friction is 0.70. +n attached string is parallel to the incline and passes over a massless& frictionless pulle( at the top. he largest mass m B& of bloc! 2& attached to the dangling end& for hich + begins to slide don the incline& is:
+ 2 C D 3
".9 !g #.9 !g 9.= !g =.0 !g 10.9 !g
+ns: + Difficult(: Section: 6'1 Learning Objective 6.1.# 70. 2loc! +& ith a mass of 10 !g& rests on a #9° incline. he coefficient of static friction is 0.70. +n attached string is parallel to the incline and passes over a massless& frictionless pulle( at the top. he largest mass m B& attached to the dangling end& for hich + remains at rest is:
+ 2 C D 3
".9 !g #.9 !g 9.= !g =.0 !g 10.9 !g
+ns: D Difficult(: Section: 6'1 Learning Objective 6.1.# 71. 2loc! +& ith a mass of 10 !g& rests on a #0° incline. he coefficient of !inetic friction is 0."0. he attached string is parallel to the incline and passes over a massless& frictionless pulle( at the top. 2loc! 2& ith a mass of .0 !g& is attached to the dangling end of the string. he acceleration of 2 is:
+ 2 C D 3
0.6= m>s"& up 0.6= m>s"& don ".6 m>s"& up ".6 m>s"& don 0 m>s"
+ns: 2 Difficult(: B Section: 6'1 Learning Objective 6.1.# 7". 2loc! +& ith a mass of 10 !g& rests on a #0° incline. he coefficient of !inetic friction is 0."0. he attached string is parallel to the incline and passes over a massless& frictionless pulle( at the top. 2loc! 2& ith a mass of #.0 !g& is attached to the dangling end of the string. he acceleration of 2 is:
+ 2 C D 3
0."0 m>s"& up 0."0 m>s"& don ". m>s"& up ". m>s"& don 0 m>s"
+ns: + Difficult(: Section: 6'1 Learning Objective 6.1.# 7#. + 1000'!g airplane moves in straight flight at constant speed. he force of air friction is 100 ). he net force on the plane is: + 0 ) 2 11600 ) C 100 ) D =00 ) 3 none of these +ns: + Difficult(: 3 Section: 6'" Learning Objective 6.".0 77. 4h( do raindrops fall ith constant speed during the later stages of their descent5 + he gravitational force is the same for all drops 2 +ir resistance just balances the force of gravit( C he drops all fall from the same height D he force of gravit( is negligible for objects as small as raindrops 3 Fravit( cannot increase the speed of a falling object to more than =. m>s +ns: 2 Difficult(: 3 Section: 6'" Learning Objective 6.".1 79. + ball of mass m is thron donard from the edge of a cliff ith an initial speed that is three times the terminal speed. /nitiall( the drag force on it is + upard and greater than mg 2 upard and less than mg C donard and greater than mg D donard and less than mg
3 donard and e;ual to mg +ns: + Difficult(: 3 Section: 6'" Learning Objective 6.".1 76. + ball is thron upard into the air ith a speed that is greater than terminal speed. On the a( up it slos don and& after its speed e;uals the terminal speed but before it gets to the top of its trajector(: + its speed is constant 2 it continues to slo don C it speeds up D its motion becomes jer!( 3 none of the above +ns: 2 Difficult(: 3 Section: 6'" Learning Objective 6.".1 7<. + ball is thron upard into the air ith a speed that is greater than terminal speed. /t lands at the place here it as thron. During its flight the force of air resistance is the greatest: + just after it is thron 2 halfa( up C at the top of its trajector( D halfa( don 3 just before it lands +ns: + Difficult(: 3 Section: 6'" Learning Objective 6.".1 7. + cube has a drag coefficient of 0.. 4hat ould be the terminal velocit( of a sugar cube 1 cm on a side in air - ρ 8 1." !g>m#5 a!e the densit( of sugar to be 1.6 , 10# !g>m#. + 1.7 m>s 2 9 m>s C 1 m>s D 60 m>s 3 #"0 m>s +ns: C Difficult(: Section: 6'" Learning Objective 6."."
7=. + baseball has a terminal speed of 7" m>s in air - ρ 8 1." !g>m#. 4hat ould be its terminal speed in ater - ρ 8 1.0 , 10# !g>m#5 + 0.09 m>s 2 1.9 m>s C 1 m>s D 7" m>s 3 1"00 m>s +ns: 2 Difficult(: 3 Section: 6'" Learning Objective 6."." 90. /n uniform circular motion& + the acceleration ala(s points aa( from the center of the circle. 2 the velocit( ala(s points toards the center of the circle. C the acceleration and the velocit( are ala(s parallel. D the acceleration and the velocit( are ala(s perpendicular. 3 there is no fi,ed relationship beteen the direction of the acceleration and the direction of the velocit(. +ns: D Difficult(: 3 Section: 6'# Learning Objective 6.#.1 91. /n uniform circular motion& + the acceleration is ala(s constant in magnitude and direction. 2 the velocit( is ala(s constant in magnitude and direction. C both the acceleration and the velocit( are continuall( changing direction. D the velocit( is ala(s changing direction but the acceleration is ala(s in the same direction. 3 the net force is ala(s constant in magnitude and direction. +ns: C Difficult(: 3 Section: 6'# Learning Objective 6.#.1 9". Gniform circular motion is the direct conse;uence of: + )etonHs third la 2 a force that is ala(s tangent to the path C an acceleration tangent to the path D a force of constant magnitude that is ala(s directed aa( from the same fi,ed point 3 a force of constant magnitude that is ala(s directed toard the same fi,ed point
+ns: 3 Difficult(: 3 Section: 6'# Learning Objective 6.#." 9#. +n object moving in a circle at constant speed: + must have onl( one force acting on it 2 is not accelerating C is held to its path b( centrifugal force D has an acceleration of constant magnitude 3 has an acceleration that is tangent to the circle +ns: D Difficult(: 3 Section: 6'# Learning Objective 6.#." 97. /f a satellite moves above the 3arthHs atmosphere in a circular orbit ith constant speed& then: + its acceleration and velocit( are in the same direction 2 the net force on it is %ero C its velocit( is constant D it ill fall bac! to 3arth hen its fuel is used up 3 its acceleration is toard the 3arth +ns: 3 Difficult(: 3 Section: 6'# Learning Objective 6.#." 99. + coin is placed on a hori%ontal phonograph turntable. Let N be the normal force e,erted b( the turntable on the coin& f be the frictional force e,erted b( the turntable on the coin& and f s& ma, be the ma,imum force of the static friction. he speed of the turntable is increased in small steps. /f the coin does not slide& then + N increases& f increases& and f s& ma, sta(s the same 2 N increases& f increases& and f s& ma, increases C f increases and both N and f s& ma, sta( the same D N & f & and f s& ma, all sta( the same 3 N & f & and f s& ma, all increase +ns: C Difficult(: 3 Section: 6'# Learning Objective 6.#." 96. he driver of a 1000'!g car tries to turn through a circle of radius 100 m on an unban!ed
curve at a speed of 10 m>s. he actual frictional force beteen the tires and a slipper( road has a magnitude of =00 ). he car: + slides into the inside of the curve 2 ma!es the turn C slos don due to the frictional force D ill ma!e the turn onl( if it goes faster 3 slides off to the outside of the curve +ns: 3 Difficult(: 3 Section: 6'# Learning Objective 6.#." 9<. + car rounds a <9'm radius curve at a constant speed of 1 m>s. + ball is suspended b( a string from the ceiling the car and moves ith the car. he angle beteen the string and the vertical is: + 0I 2 1.7I C "7I D =0I 3 cannot be found ithout !noing the mass of the ball +ns: C Difficult(: Section: 6'# Learning Objective 6.#." 9. +n object of mass m and another object of mass "m are each forced to move along a circle of radius 1.0 m at a constant speed of 1.0 m>s. he magnitudes of their accelerations are: + e;ual 2 in the ratio of
√ 2 : 1
C in the ratio of " : 1 D in the ratio of 7 : 1 3 %ero +ns: + Difficult(: 3 Section: 6'# Learning Objective 6.#.0 9=. he magnitude of the force re;uired to cause an 0.07'!g object to move at 0.6 m>s in a circle of radius 1.0 m is: + ".7 × 10 " ) 2 1.7 × 10 " ) C 1.7π × 10 " )
D ".7π" × 10 " ) 3 #.1# ) +ns: 2 Difficult(: 3 Section: 6'# Learning Objective 6.#.# 60. + 0."'!g stone is attached to a string and sung in a circle of radius 0.6 m on a hori%ontal and frictionless surface. /f the stone ma!es 190 revolutions per minute& the tension force of the string on the stone is: + 0.0# ) 2 0." ) C 0.<9 ) D 1.=6 ) 3 #0 ) +ns: 3 Difficult(: 3 Section: 6'# Learning Objective 6.#.# 61. 4hich of the folloing five graphs is correct for a particle moving in a circle of radius r at a constant speed of 10 m>s5
+ 2 C D 3
/ // /// /J J
+ns: 3 Difficult(: 3 Section: 6'# Learning Objective 6.#.#
6". +n object moves around a circle. /f the radius is doubled !eeping the speed the same then the magnitude of the centripetal force must be: + tice as great 2 half as great C four times as great D one'fourth as great 3 the same +ns: 2 Difficult(: 3 Section: 6'# Learning Objective 6.#.# 6#. +n object moves in a circle. /f the mass is tripled& the speed halved and the radius unchanged then the magnitude of the centripetal force must be multiplied b( a factor of: + #>" 2 #>7 C =>7 D 6 3 1" +ns: 2 Difficult(: 3 Section: 6'# Learning Objective 6.#.# 67. +n 00') passenger in a car presses against the car door ith a "00 ) force hen the car ma!es a left turn at 1# m>s. he -fault( door ill pop open under a force of 00 ). Of the folloing& the least speed for hich the man is thron out of the car is: + 17 m>s 2 1= m>s C "0 m>s D "6 m>s 3 9" m>s +ns: D Difficult(: 3 Section: 6'# Learning Objective 6.#.# 69. /f a certain car& going ith speed v1& rounds a level curve ith a radius R1& it is just on the verge of s!idding. /f its speed is no doubled& the radius of the tightest curve on the same road that it can round ithout s!idding is: + " R1 2 7 R1
C R1>" D R1>7 3 R1 +ns: 2 Difficult(: 3 Section: 6'# Learning Objective 6.#.# 66. +n automobile moves on a level hori%ontal road in a circle of radius #0 m. he coefficient of friction beteen tires and road is 0.90. he ma,imum speed ith hich this car can round this curve is: + #.0 m>s 2 7.= m>s C =. m>s D 1" m>s 3 17< m>s +ns: D Difficult(: Section: 6'# Learning Objective 6.#.# 6<. + giant heel& having a diameter of 70 m& is fitted ith a cage and platform on hich a man of mass m stands. he heel is rotated in a vertical plane at such a speed that the force e,erted b( the man on the platform is e;ual to his eight hen the cage is at K& as shon. he net force on the man at point K is:
+ 2 C D 3
0 mg & don mg & up " mg & don " mg & up
+ns: D Difficult(: 3 Section: 6'# Learning Objective 6.#.# 6. + giant heel& 70 m in diameter& is fitted ith a cage and platform on hich a man can stand. he heel rotates at such a speed that hen the cage is at K -as shon the force e,erted
b( the man on the platform is e;ual to his eight. he speed of the man is:
+ 2 C D 3
17 m>s "0 m>s " m>s 0 m>s 1"0 m>s
+ns: 2 Difficult(: Section: 6'# Learning Objective 6.#.# 6=. + person riding a $erris heel is strapped into her seat b( a seat belt. he heel is spun so that the centripetal acceleration is g . Select the correct combination of forces that act on her hen she is at the top. Bere& F g 8 force of gravit(& donE F b 8 seat belt force& donE and F s 8 seat force& up. + F g 8 0& F b 8 mg& F s 8 0 2 F g 8 mg& F b 8 0& F s 8 0 C F g 8 0& F b 8 0& F s 8 mg D F g 8 mg& F b 8 mg& F s 8 0 3 F g 8 mg& F b 8 0& F s 8 mg +ns: 2 Difficult(: 3 Section: 6'# Learning Objective 6.#.# <0. One end of a 1.0'm long string is fi,edE the other end is attached to a ".0'!g stone. he stone sings in a vertical circle& passing the bottom point at 7.0 m>s. he tension force of the string at this point is about: + 0 ) 2 1" ) C "0 ) D #" ) 3 9" ) +ns: 3 Difficult(: 3 Section: 6'# Learning Objective 6.#.#
<1. One end of a 1.0'm string is fi,edE the other end is attached to a ".0'!g stone. he stone sings in a vertical circle& passing the top point at 7.0 m>s. he tension force of the string at this point is about: + 0 ) 2 1" ) C "0 ) D #" ) 3 9" ) +ns: 2 Difficult(: 3 Section: 6'# Learning Objective 6.#.# <". he iron ball shon is being sung in a vertical circle at the end of a 0.<'m string. Bo slol( can the ball go through its top position ithout having the string go slac!5
+ 2 C D 3
1.# m>s ".6 m>s #.= m>s 6.= m>s =. m>s
+ns: 2 Difficult(: Section: 6'# Learning Objective 6.#.# <#. Circular freea( entrance and e,it ramps are commonl( ban!ed to handle a car moving at 1# m>s. o design a similar ramp for "6 m>s one should: + increase the radius b( a factor of " 2 decrease the radius b( a factor of " C increase the radius b( a factor of 7 D decrease the radius b( a factor of 7 3 increase the radius b( a factor of √ 2 +ns: C Difficult(: 3 Section: 6'# Learning Objective 6.#.#
<7. +t hat angle should the roada( on a curve ith a 90m radius be ban!ed to allo cars to negotiate the curve at 1" m>s even if the roada( is ic( -and the frictional force is %ero5 + 0I 2 16I C 1
