Download Sample Exam Two B Solutions

Multiple Choice ( 6 Points Each ):
20 kg
F app = 40 N
Q = 60 O
ms,k= 0
1. A 20 kg box is pulled along a frictionless floor with an applied force of 40 N. The applied force
makes an angle of 60 degrees with the horizontal. If the box starts from rest, what is the
acceleration of the box and how fast is it moving after thirty seconds?
a. The acceleration is 3 m/s 2 and the velocity is 40 m/s.
b. The acceleration is 1 m/s 2 and the velocity is 30 m/s.
c. The acceleration is 2 m/s 2 and the velocity is 40 m/s.
d. The acceleration is 1 m/s 2 and the velocity is 60 m/s.
e. None of the above.
∑ F x=m a x
F app cos =ma x
40 N cos 60 o=20 kg a x
o
40 N cos 60
ax =
=1 m/ s 2
20 kg
40 kg
v x =v o a x t=0 m/s  1m /s 2  30 s =30 m/ s
x
v O = 30 m/s
ms,k= 0.2
2. A box with a mass of 40 kg moves along with a speed of 30 m/s when it encounters a rough
section of the floor where there is a 0.20 coefficient of friction. The box slows and comes to a
stop. What is the distance the box slides after it encounters the friction until it comes to rest?
a. 229.59 m
b. 114.80 m
c. 459.18 m
d. 0.0 m
e. None of the above.
∑ F y=m a y
F N −mg=0
F N =mg
∑ F x =ma x
− f =ma x
− F N =m a x
−m g=m a x
a x =− g=0.2  9.8 m/s 2 =−1.96 m/ s 2
v 2x =v 2o 2a  x
0=v 2o 2a  x
x
x
 x=
2
ox
2
−v
− 30 m/s 
=
=229.59 m
2a 2 −1.96 m/s 2 
3. An example of the “action-reaction” pair of forces described by Newton's third law are:
a. the normal force and the weight of a book sitting on the table.
b. the frictional force and applied force exerted on a box dragged across a floor.
c. the gravitational force of mass A on mass B and the gravitational force of mass B on mass A.
d. the frictional force and normal force on a box dragged across a floor.
e. None of the above.
4. A 60 kg jumps out of an airplane with a parachute. He decides not to pull the rip cord until he
reaches terminal velocity. If the drag force is equal to F D =−bv and b=2 kg / s , what is
the magnitude of the velocity when he decides to pull the cord?
a. 30.0 m/s
b. 294.0 m/s
c. 80.0 m/s
d. 9.8 m/s
e. None of the above.
∑ F y =m a y
bv−mg=m a y
bv T −mg=0
2
mg 60 kg  9.8 m/ s 
vT =
=
=294 m/ s
b
2 kg /s
m=
60
kg
h = 6m
60 O
5. A 60 kg box starts from rest and slides down a frictionless ramp with an incline of 60 degrees.
What is the acceleration of the box down the ramp?
a. 8.49 m/s2
b. 6.65 m/s2
c. 9.80 m/s2
d. 16.97 m/s2
e. None of the above.
∑ F x=m a x
mg sin =m a x
a x =g sin =9.8 m/ s2 sin 60o =8.49 m/ s 2
6. A 30 kg ball is dropped from rest from a height of 40 meters. What is the maximum velocity
reached by the ball before it hits the ground?
a. +28 m/s
b. -28 m/s
c. +20 m/s
d. -20 m/s
e. None of the above.
∑ F y=m a y
−mg=m a y
a y =−g =−9.8 m/s 2
v 2y =v 2o −2 g  y
or
PE i KE i =PE f KE f
1
mghi0=0 m v 2f
2
∣v f∣= 2 g hi
∣v f∣=  2  9.8 m/ s2  40 m=28 m / s
∣v f∣=−28 m /s
y
∣v y∣=−2 g  y− y o = 2  9.8 m /s 2  −40 m−0m  =28 m/s
v =−28 m /s
FT
20 kg
m1
FT
10 kg
m2
w = m2g
7. A 20 kg block sits on a frictionless table. A string is attached which hangs over a frictionless
pulley. A 10 kg block hangs over the end. What is the magnitude of the acceleration of the 20
kg mass?
a. 4.9 m/s2
b. 9.8 m/s2
c. 20 m/s2
d. 15 m/s2
e. None of the above.
m 1 a=F T
m 2 a=m2 g −F T
m1 a=F T
m2 a=m 2 g −m1 a
m2 g
10 kg  9.8 m/ s 2 
a=
=
=3.27 m/ s2
m1m2
20 kg10 kg
FN
r = 50 m
f
m
w = mg
m = 0.3
8. A 1000 kg car rounds a 50 meter radius curve at a constant speed. The coefficient of friction of
the road is 0.3 . What is the force which lets the car maintain its speed as it negotiates the
curve?
a. gravitational force
b. normal force
c. frictional force
d. weight
e. None of the above.
9. A 1000 kg car rounds a 50 meter radius curve at a constant speed. The coefficient of friction of
the road is 0.3 . What is the magnitude of maximum velocity which the car can safely negotiate
the curve?
a. 12.12 m/s
b. 24.24 m/s
c. 9.8 m/s
d. 6.06 m/s
e. None of the above.
∑ F x =m a x
∑ F y=m a y
F N −mg=0
F N =mg
f =m a x
mg=m
2
v
2
v=  r g= .3  9.8 m/s  50=12.12 m/ s
r
m2
+a
30 kg
60 kg m
1
10. Atwood's machine consists of a frictionless pulley and two masses connected by a cable over
the pulley. What is the magnitude of the acceleration of the masses?
a. 9.80 m/s2
b. 3.27 m/s2
c. 29.40 m/s2
d. 4.90 m/s2
e. None of the above.
m1 a=m1 g −F T
m2 a=F T −m2 g
F T =m1 g−m1 a
m2 a=  m1 g −m1 a −m2 g
a=
 m1−m 2  60 kg−30 kg  
g=
9.8 m/s 2 =3.27 m/s 2
 m1m 2  60 kg30 kg 
Problem One ( 20 Points ):
20
kg
10 m
ms,k= 0.1
Not drawn to scale.
60 O
A
ms,k= 0.3
B
A 20 kg block starts from rest at the top of a 60 degree incline and slides down the incline. There is a
0.1 coefficient of friction on the ramp. The block then continues to slide along the horizontal surface
where there is a 0.3 coefficient of friction. The block then slows, due to friction, until it comes to rest
at point B.
a. (2) What is the magnitude of the force due to gravity (i.e. the weight ) of the block on the incline?
b. (2) What is the magnitude of the Normal Force on the block on the incline?
c. (2) What is the magnitude of the frictional force on the block on the incline?
d. (2) What is the magnitude of the acceleration of the block down the incline?
e. (3) What is the velocity of the block at Point A?
f. (3) What is the magnitude of the force of friction on the block on the horizontal?
g. (3) What is the acceleration of the block along the horizontal?
h. (3) What is the distance between Point A and Point B?
a.) w=mg=20 kg  9.8 m/ s 2 =196 N
b.) ∑ F y =ma y
F N −mg cos =0
F N =mg cos =196 N cos 60 o=98 N
c.) f = F N =0.1  98 N =9.8 N
d.) mg sin − f =ma
196 N sin 60o−9.8 N =20 kg a
a=8.00 m/ s 2
e.)sin =
h
x
h
10 m
=
=11.55 m
sin  sin 60o
v 2 v 2o 2 a  x
 x=
∣v∣=  2 a  x = 2  8 m/s 2  11.55 m=13.59 m/s
f.) f = mg=0.3  20 kg  9.8 m/ s =58.8 N
2
−58.8 N
g.) a x =
=−2.94 m/s 2
20 kg
h.) v 2=v 2o2 a  x
2
v 2−v 2o 0− 13.59 m/ s 
 x=
=
=31.41 m
2
2a
2 −2.94 m/ s 
Problem Two ( 20 Points ):
m2
+a
m1
What is the acceleration and direction of the acceleration of the 40 kg mass?
m2 :
∑ F y=m2 a y
F N −m2 g cos =0
F N =m2 g cos 
m1 :
∑ F =m1 a
m1 g−F T =m1 a
F T =m1 g −m1 a
∑ F x=m2 a
F T − f −mg sin =m2 a
F T − F N −mg sin =m2 a
F T −m2 g cos −m2 g sin =m2 a
F T − m2 g cos −m 2 g sin =m 2 a
 m1 g−m1 a − m2 g cos −m2 g sin =m2 a
m1 g−m1 a− m2 g cos −m 2 g sin =m2 a
m1 g− m2 g cos −m2 g sin =m2 am1 a
m1 g− m2 g cos −m2 g sin = m 2m1  a
 m1− m2 cos −m2 sin  g =a
up the ramp.
 m2m1 
 30 kg −0.05  40 kg  cos 30 −40 kg sin 30 o  9.8 m/s 2
o
 40 kg30 kg 
=a=1.16 m /s 2
Extra Credit ( 10 Points ):
15 O
A car enters a curve in the road that has a radius of 50 m and an inclined bank of 15.0 degrees. The
road is snow covered and has a coefficient of friction of 0.0.
a.) What is the maximum speed the car can move and still navigate the curve safely?
b.) If the road crews sand the road and increases the coefficient of friction to 0.1 , what is the maximum
speed the car can move and still negotiate the curve safely?
c.) If the road crews sand the road and increases the coefficient of friction to 0.1 , what is the minimum
speed the car can move and still negotiate the curve safely?