PHYS 201 TEST #3 11/01/13 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 person riding a bike. The mass of the person plus the bike is 80 kg. Neglect air resistance and friction.
a) When the biker reaches a speed of 10 m/sec (22 mph) what is the final kinetic energy of the biker (plus bike) at this speed?
b) If the bike rider exerts a constant net power of 400 watts, how long a time will it take the rider to go from rest up to the speed of 10 m/s (again neglecting air resistance and friction)?
c) If the bike rider keeps up the 400 watts of net power output to go from rest to twice the speed (20 m/s), will it take: [less than twice as long, twice as long, more than twice as long] a time compared to the time to reach 10 m/s if we neglect air resistance and friction?
More than twice as long.
2) Consider a person riding a bike up a hill with a 5% grade. A 5% grade means that for every 100 m up the grade of the hill, the vertical height increases by 5 meters. If the person rides up the grade at a constant speed of 10 m/s (= 22 mph), the person climbs vertically up at a rate of 0.5 m/s. Assume the mass of the person plus the bike is 80 kg.
a) How much energy does it take to lift the person and bike up 0.5 meters (energy to life for each second)?
b) Assuming the bike rider was the source of this gravitational energy increase, what is the average power of the rider necessary to maintain the speed of 10 m/s during the climb (neglecting the power needed to overcome friction and air resistance):
in horsepower: 0.525 hp.
c) If the biker cliombed the hill at a 10% faster speed (11 m/s), would the power necessary to climb the hill at constant speed increase by: [less than 10%, 10%, greater than 10%]?
3) a) What is the escape velocity for an asteriod with mass of 5.1 x 1017 kg and a radius of 80 km ?
29.16 m/s = 46 mph.
b) Is this escape speed [less than, the same as, or more than] the escape speed for an asteriod with the same mass but a smaller radius?
4) A person on a sled with a combined mass of 80 kg is at the top of a snow covered hill 28 meters in vertical height above the base of the hill. The hill has a constant grade of 34° 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?
23.4 m/sec = 52.4 mph.
b) If the person had a running start so the initial velocity was 4 m/s instead of zero, would the 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 56 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 24 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?
e) If there WERE some friction, would the sled be going [faster, the same speed, or slower] down the more gentle slope (17o) than down the steeper slope (34o) 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 =50 grams moving North with a speed of 155 m/s crashes into object #2 with mass2 = 2,000 grams moving South with a speed of 8 m/s.
a) If the two objects stick together, what will their speed be immediately after the crash?
b) Will the objects be moving North or South after the crash?
c) Was momentum conserved in the crash?
(If the answer was no, then tell where the momentum went to or came from):
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 = 74 kg and wearing a tool belt full of tools that have a combined mass of 6 kg (so initial mass is 80 kg) is floating beside a space station 25 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?
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 = .20 kg away from the space station with a velocity of 30 m/s.
c) What will the final velocity of the astronaut be after the throw?
0.075 m/s .
d) How long a time will it take the astronaut to float back to the station after the throw?
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?
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?
7) An iron cylinder of mass 270 grams and radius 2.0 cm rolls (without slipping) down an incline. The vertical height of the incline is 30 cm and it made an angle of 34° with the horizontal. Neglect air resistance in all parts of this problem.
a) If the initial velocity of the cylinder were zero, what would be the final speed of the cylinder at the base of the incline?
b) What would its angular velocity, w , at the base of the incline be?
c) Would a wooden cylinder of mass 33 grams and radius 2.0 cm roll down the same incline: [slower than; at the same speed as; or faster than] the iron cylinder?
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 iron cylinder?
e) If the cylinder rolls without slipping, is there friction acting on the cylinder?
f) If the cylinder rolls without slipping, is there energy lost to friction as the cylinder rolls down the incline?