PHYS 201 TEST
#3b 11/04/11 DR. HOLMES
NAME
Do all seven problems. The worth of each
part of each problem is marked beside the place for the answer. All answers
should be in MKS units unless otherwise indicated. Show your work for partial
credit. Work should be under the problem, or clearly labeled on an extra sheet
placed underneath the top page of the test.
INFORMATION: MASS OF EARTH = 6.0 x 1024kg;
RADIUS OF EARTH = 6,378 km.
1) Consider a car of mass 1,620 kg. It can accelerate
from zero to 35 m/sec (78 mph) in 12 seconds on a level road.
a) What is the final kinetic energy of the
car?
992,250 Joules
b) Assuming the engine was the source of
this final kinetic energy, what is the average power of the engine (neglecting
the power needed to overcome friction and air resistance) during the
acceleration
in
c) If the engine provided constant force,
did the power of the engine of the car: [increase with increasing speed, stay
constant with increasing speed, or decrease with increasing speed] ?
increase with increasing speed
d) If the engine provided a constant power,
did the acceleration of the car: [increase with increasing speed; stay constant
with increasing speed; or decrease with increasing speed] ?
decrease with increasing speed.
2) Consider a 70 kg object.
a) How much energy will it take to lift the
object from the earth's surface up to a height of 50 meters?
34,300 Joules
b) Will it take [significantly less than
twice, about twice, or significantly more than twice] the energy to lift the
object to twice the height (from the surface up to a height of 100 meters)?
[Here "about" means a difference of less than 10%; significantly more
or less means a difference of more than 10%.]
About twice
c) How much energy will it take to lift the
object from the earth's surface up to a height of 5,000 kilometers above the
earth's surface?
1.93 x 109
Joules.
d) Will it take [significantly less than
twice, about twice, or significantly more than twice] the energy to lift the
object to twice the height (from the surface up to a height of 10,000
kilometers)?
Significantly less than twice.
3) a) What is the
magnitude of the escape velocity for Callisto (one of Jupiter’s moons) [mass of
Callisto = 1.08 x 1023 kg or 1.8% that of earth's; radius = 2,400 km or about 37% that of earth's) ?
2,450 m/s = 5,488 mph.
b) Is this escape speed less than, the same
as, or more than the escape speed for the earth?
less than.
4) A person on a sled with combined mass 80
kg is at the top of a snow covered hill 22 meters in vertical height above the
base of the hill. The hill has a constant grade of 34° with the horizontal.
Assume there is no friction or air resistance.
a) Assuming the sled starts from rest (no initial
push), how fast will the sled be going at the base of the hill?
20.8 m/sec = 46.5 mph.
b) If the person had a running start so the
initial velocity was 5 m/s instead of zero, would the the answer to part-a be: (less
than 5 m/s more, 5 m/s more, or more
than 5 m/s more)?
Less than 5 m/s more.
c) If the sled started from rest but the
height of the hill were doubled (to 44 meters), would the final speed at the
base of the hill be: [less than twice as much, twice as much, more than twice
as much, can't determine with info given]
less than twice as much.
d) If the initial velocity were kept at zero
and the hill was at the original 22 meter height, but the angle of the hill was
decreased to 17o (made half as steep) from 34o, would the
final speed be: [half as fast; faster than half as fast; slower than half as
fast, the same speed] as the answer in part-a?
same.
e) If there WERE some friction, would the
sled be going [faster,
the same speed, or slower] down the steeper slope (34o) than the
more gentle slope (17o) assuming the height of the hills were the
same and both started from rest?
It would go faster down the steeper
slope.
5) Object #1 with mass1 =80 grams
moving North with a speed of 133 m/s crashes into object #2 with mass2 =
12,880 grams moving South with a speed of 7 m/s.
a) If the two objects stick together, what
will their speed be immediately after the crash?
6.14 m/s
b) Will the objects be moving North or South
after the crash?
South.
c) Was momentum conserved in the crash?
(If the answer was no, then tell where the
momentum went to or came from):
Yes.
d)
Was kinetic energy (total for
both balls) the same before and after the crash?
(If the answer was no, then tell where the
energy went to or came from):
No, some of the initial energy went into
deforming the two objects.
6) An astronaut with a massASTR =
80 kg and wearing a tool belt full of tools that have a mass of 5 kg (so
initial mass is 85 kg) is floating beside a space station 32 meters
away. The safety line has been cut by someone closing a door and catching the
line in the door.
a) Can the astronaut "swim" back
to the station?
No;
b) Explain your answer to part a above:
Assume the astronaut and tools are initially
stationary. To get back to the spaceship, the astronaut throws a small wrench
of masswrench = .470 kg away from the space station with a velocity
of 27 m/s.
c) What will the final velocity of the
astronaut be after the throw?
0.150 m/s .
d) How long will it take the astronaut to
float back to the station after the throw?
213 seconds
e) How fast would the astronaut have to
throw a hammer of mass 1.41 kg to obtain the same speed as when the wrench was
thrown in part c?
8.89 m/s.
f) Would the astronaut need [less, the
same, or more] energy to throw the wrench than the hammer to reach the speed of
part c?
More.
7) A brass ring of mass 12 grams and
radius 5.2 cm rolls (without slipping) down an incline. Neglect any air resistance.
a) If the vertical height of the incline was
58 cm and it made an angle of 34° with the horizontal, and if the initial
velocity of the cylinder were zero, what would be the final speed of the ring
at the base of the incline?
2.384 m/s.
b) What would its angular velocity, w , at the base of the
incline be?
45.85 rad/sec.
c) If air resistance were negligible, would
a wooden cylinder of mass 12 grams and radius 1.52 cm roll down the same
incline: [slower than; at the same speed as; or faster than] the brass ring?
faster.
d) Would a wooden ball (sphere) of the same
mass and radius as the wooden cylinder roll down the incline; [slower than; at
the same speed as; faster than] the original brass ring?
faster.
e) If the ring rolls without slipping, is
there friction acting on the ring?
yes
f) If the ring rolls without slipping, is
there energy lost to friction as the ring rolls down the incline?
no.