PHYS 201 TEST #3 11/04/16
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 10^{24}kg; RADIUS OF EARTH = 6,378 km.

1) Consider a car of mass
1,850 kg. It can accelerate from zero to
30 m/s (67 mph) in 6 seconds on a level road.

a) What is the final kinetic energy of the car?

**833,500 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 Watts:** 138,750 Watts**; in horsepower:** 186.0 hp.**

c) 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.**

d) If the engine provided a
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.**

2) Consider a 50 kg object.

a) How much energy will it
take to lift the object from the earth’s surface up a height of 45 meters?

**22,050 ^{ }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 90 meters)? [Here, “about”
means a difference of less than 10%; significantly 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 a height of 45,000
kilometers?

**2.75 x 10 ^{9 }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 90,000 kilometers)? [Here,
“about” means a difference of less than 10%; significantly means a difference
of more than 10%.]

**Significantly
less than twice.**

3) a) What is the escape velocity
for an asteroid with mass of 7.2 x 10^{18} kg and a radius of 85 km ?

**106.3 m/s**

b) Is this escape speed [less
than, the same as, or more than] the escape speed for an asteroid with the same
mass but a smaller radius?

**Less than.**

4) A person on a sled with a
combined mass of 70 kg is at the top of a snow covered hill 38 meters in
vertical height above the base of the hill. The hill has a constant grade of
44° with the horizontal. Assume in parts a-d that 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?

**27.3 m/s.**

b) If the person had a
running start so the initial velocity was 4 m/s instead of zero, would the answer
to part-a be: (less than 4 m/s more, 4
m/s more, or more than 4 m/s more)?

**Less than 4 m/s more.**

c) If the sled started from
rest but the height of the hill were doubled (to 76 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 38 meter height, but the
angle of the hill was decreased to 22^{o} (made half as steep) from 44^{o},
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 more gentle slope (22^{o})
than down the steeper slope (44^{o}) assuming the height of the hills
were the same and both started from rest?

**It would go slower down
the more gentle slope.**

5) Object #1 with mass_{1 }=
40 grams moving East with a speed of 185 m/s crashes into the back of object #2
with mass_{2 }= 3,800 grams also moving East with a speed of 2 m/s.

a) If the two objects stick
together, what will their speed be immediately after the crash?

**3.91 m/s**

b) Will the objects be moving
East or West after the crash?

**East.**

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 mass_{astr}_{ }= 60 kg and wearing a tool
belt full of tools that have a combined mass of 5 kg (so initial mass is 65 kg)
is floating beside a space station 22_{ }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 mass_{wrench}_{ }=
.12 kg away from the space station with a velocity of 32 m/s.

c) What will the final
velocity of the astronaut be after the throw?

**0.059 m/s .**

d) How long a time will it
take the astronaut to float back to the station after the throw?

**371.7 seconds**

e) How fast would the
astronaut have to throw a hammer of mass 1.2 kg to obtain the same speed as
when the wrench was thrown in part c?

**3.15 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) An iron ring of mass 270
grams and radius 3.0 cm rolls (without slipping) down an incline. The vertical height of the incline is 38 cm
and it makes an angle of 34° with the horizontal. Neglect air resistance in all parts of this
problem.

a) If the initial velocity of
the ring were zero, what would be the final speed of the ring at the base of
the incline?

**1.93 m/s.**

b) What would its angular
velocity, w , at the base of the incline be?

**64.3 rad/sec.**

c) Would a wooden ring of
mass 37 grams and radius 3.0 cm roll down the same incline: [slower than; at
the same speed as; or faster than] the iron ring?

**Same speed.**

d) Would a wooden ball
(sphere) of the same mass and radius as the wooden ring roll down the incline;
[slower than; at the same speed as; faster than] the original iron 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.**