AP Physics 105: Final Exam Samples, Parts B&C, Set 2
Topics
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Friction
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Atwoods
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Incline Planes
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Springs
Projectiles: Horizontal
Projectiles: at Angles
1. A 77 g mouse pushes a 1.35 kg wooden box across a level wooden shelf.
a. How much force was required to start the box moving?
b. How much force is required to keep the box moving once it has begun to move?
c. If the mouse continues to push with the force that got the box moving, at what rate will the box
accelerate?
2. A 45 g spider slings its silken thread over a glass rod in the corner of the Biology Lab. (Note: silk on glass is
virtually friction free.) This smart spider then proceeds to attach the end of the thread to a 65 g scoopula
and tips the scoopula off the end of the table.
a. What net force causes the spider to rise?
b. At what rate will the spider accelerate?
3. A 45 kg diver runs straight off a 6 m high diving platform at 1.25 m/s.
a. How long is the diver in the air?
b. How far out in the pool will the diver land?
4. Rowdy launches a tee shirt from his air powered bazooka into the stands in section 104 while standing at the
very edge of the rink. The tee shirt leaves the bazooka at 4 m/s while Rowdy is holding it at a 50o angle. A
girl in row K (8.5 m above the ice) catches the shirt.
a. What was the shirt’s initial vertical velocity?
b. What was the shirt’s initial horizontal velocity?
c. How long was the shirt in the air?
d. How far is row K set back from the ice?
5. Kira is standing on her Viper King skateboard which has experimental frictionless magnetic bearings (a
combined mass of 60.0 kg) on a launch ramp which is made from a 5.50 m long metal plank resting on a 1.25
m high loading dock.
a. What is the ramp’s angle of inclination?
b. How much force is going to cause Kira to roll down the ramp when she lets go of the grab bars?
c. At what rate will Kira accelerate down the ramp?
d. If she were to use her Cobra skateboard instead (muK = 0.27), how much friction would be in the
system?
e. What net force would now cause Kira to accelerate down the incline?
6. A rubber floor mat (m = 0.75 kg) is pulled across a dry concrete garage floor.
a. How much force was required to start the mat moving?
b. How much force is required to keep the mat moving once it has begun to move?
c. At what rate will the mat accelerate if 10.0 N of force is applied to it while moving?
7. BettieLou (m = 45.0 kg) and BettyJo (m = 40.0 kg) are using a pulley on their mother’s construction sight as a
thrill ride. The pulley has two platforms connected by a rope which is slung over a frictionless pulley.
BettyJo is standing on her platform on the ground when BettieLou steps off of a 4th floor ledge onto her
platform.
a. What net force causes the girls to move?
b. At what rate will the girls accelerate?
8. A 3.75 kg cat runs straight off of a counter 1.15 m high.
a. How long is the cat in the air?
b. How far away from the cabinet will the cat land if he was running at 1.50 m/s?
Note: Be comfortable with and able to make a graph so the slope is significant.
e.g. Ff vs FN Y :; F vs x Y k;
1. A 77 g mouse pushes a 1.35 kg wooden box across a level wooden shelf.
a. How much force was required to start the box moving?
m = 1.35kg
µ S = 0.42
Ff = ?
F f = µF N = µmg = ( 0 .42)(1.35kg )(9 .81m / s 2 ) = 5.6 N
b. How much force is required to keep the box moving once it has begun
to move?
m = 1.35kg
µ S = 0 .30
Ff = ?
F f = µF N = µmg = ( 0 .30)(1.35kg )(9 .81m / s 2 ) = 4 .0 N
c. If the mouse continues to push with the force that got the box moving,
at what rate will the box accelerate?
F a = 5.6 N
F f = −4 .0 N
m = 1.35kg
a =?
F net F a + F f
5.6 N − 4 .0 N
a=
=
=
= 1.19m / s 2
m
m
1.35kg
2. A 45 g spider slings its silken thread over a glass rod in the corner of the
Biology Lab. (Note: silk on glass is virtually friction free.) This smart spider
then proceeds to attach the end of the thread to a 65 g scoopula and tips
the scoopula off the end of the table.
a. What net force causes the spider to rise?
m sp = 0 .045kg
m sc = 0 .065kg
F net = ?
F net = ( m sc − m sp ) g = ( 0 .065kg − 0 .045kg )(9 .81m / s 2 )
F net = 0 .20 N
b. At what rate will the spider accelerate?
m sp = 0 .045kg
m sc = 0.065kg
a =?
F net ( m sc − m sp ) g ( 0 .065kg − 0.045kg )(9 .81m / s 2 )
a=
=
=
m tot
m tot
( 0.065kg + 0.045kg )
a = 1.78m / s 2
3. A 45 kg diver runs straight off a 6 m high diving platform at 1.25 m/s.
a. How long is the diver in the air?
work vertical...
d = 6m
a=g
v i = 0m / s
t =?
d = v i t + 1 2 at2 =
t=
2d
=
a
1
2
at2
2 (6m )
2 = 1.1 s
9 .81m / s
b. How far out in the pool will the diver land?
v = 1.25m / s
t = 1.1 s
d =?
d = vt = (1.25m / s )(1.1 s ) = 1.38m
4. Rowdy launches a tee shirt from his air powered bazooka into the stands
in section 104 while standing at the very edge of the rink. The tee shirt
leaves the bazooka at 4 m/s while Rowdy is holding it at a 50o angle. A girl
in row K (8.5 m above the ice) catches the shirt.
a. What was the shirt’s initial vertical velocity?
v iv = v sin Θ = ( 4 m / s )(sin 50) = 3.0642m / s
b. What was the shirt’s initial horizontal velocity?
v ih = v cosΘ = ( 4 m / s )(cos 50) = 2 .5712m / s
c. How long was the shirt in the air?
work vertical
v i = 3.0642m / s
a = −g
d = 8 .5 m
t =?
d = v i t + 1 2 at2
1 at2 + v t − d = 0
2
i
2
Ax + Bx + C = 0 form yields
A = 4 .905, B = −3.0642, C = 8 .5
− b ± b 2 − 4 ac 3.0642 ± 3.0642 2 − 4 ( 4 .905)(8 .5 )
t=
=
2a
9 .81
3.0642 ± −157.3807 3.0642 m 157.3807
=
t=
9 .81
9 .81
t = 1.5911 or t = −0 .9664
d. How far is row K set back from the ice?
work horizontal
t = 1.5911s
v i = 2 .5712m / s
d =?
d = vt
d = ( 2 .5712m / s )(1.5911s )
d = 4 .0910m
1.25m
.o
sin α =
= 131
5.50m
1.25 m
5. Kira is standing on her Viper King skateboard which has experimental
frictionless magnetic bearings (a combined mass of 60.0 kg) on a launch
ramp which is made from a 5.50 m long metal plank resting on a 1.25 m
high loading dock.
a. What is the ramp’s angle of inclination?
5.50
m
a
b. How much force is going to cause Kira to roll down the ramp when she
lets go of the grab bars?
F / / = mgsin α = ( 60.0 kg )(9 .81m / s 2 ) sin(131
. ) = 133 N
c. At what rate will Kira accelerate down the ramp?
F
133 N
F = ma ⇒ a = =
= 2 .2 m / s 2
m 60.0 kg
d. If she were to use her Cobra skateboard instead (muK = 0.27), how
much friction would be in the system?
F fK = µF N = µF ⊥ = µmgcosα
F fK = ( 0.27)(60.0 kg )(9 .81m / s 2 ) cos(131
. ) = 155 N
e. What net force would now cause Kira to accelerate down the incline?
Since Ff > F// the net force causing motion = 0
6.
A rubber floor mat (m = 0.75 kg) is pulled across a dry concrete garage
floor.
a.
How much force was required to start the mat moving?
F fS = µF N = µmg = ( 0 .90)(0 .75kg )(9 .81m / s 2 ) = 6 .6 N
b.
How much force is required to keep the mat moving once it has
begun to move?
F fK = µF N = µmg = ( 0 .68)( 0 .75kg )(9 .81m / s 2 ) = 5.0 N
c.
At what rate will the mat accelerate if 10.0 N of force is applied to
it while moving?
F net = F a + F fK = 10 N + ( −5.0 N ) = 5.0 N
F
5.0 N
a= =
= 6 .7 m / s 2
m 0 .75kg
7.
BettieLou (m = 45.0 kg) and BettyJo (m = 40.0 kg) are using a pulley on
their mother’s construction sight as a thrill ride. The pulley has two
platforms connected by a rope which is slung over a frictionless pulley.
BettyJo is standing on her platform on the ground
when BettieLou steps off of a 4th floor ledge onto her
platform.
a.
What net force causes the girls to move?
F net = ( m Lou − m Jo ) g
F net = ( 45.0 kg − 40.0 kg )(9 .81m / s 2 ) = 49 N
b.
At what rate will the girls accelerate?
a=
F
49 N
=
= 0 .58m / s 2
m ( 45kg + 40kg )
8.
A 3.75 kg cat runs straight off of a counter 1.15 m high.
a.
How long is the cat in the air?
work vertical
d =
b.
1
at ⇒ t =
2
2
2d
=
a
2 (1.15m )
= 0.48s
9 .81m / s 2
How far away from the cabinet will the cat land if he was running
at 1.50 m/s?
work horizontal
d = vt = (1.50m / s )(0.48s ) = 0.72m