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 1024kg; 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 109 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 1018 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 22o (made half as steep) from 44o, 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 (22o) than down the steeper slope (44o) 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 mass1 = 40 grams moving East with a speed of 185 m/s crashes into the back of object #2 with mass2 = 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 massastr = 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 masswrench = .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.

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