PHYS 150 , TEST #2 , 10/12/07 , DR. HOLMES , NAME
Do all seven problems. The worth of each part of each problem is marked beside the place for the answer. Show your work for partial credit. All answers should be in MKS units unless otherwise specified. Work should be under the problem, or clearly labeled on an extra sheet placed underneath the top page of the test.
MASS of EARTH = 6.0 x 1024 kg; RADIUS of EARTH = 6,380 km.
1. An object at the bottom of a hole 8 meters below the ground is thrown up and out with an initial speed of 37 m/s and an initial angle of 71o above the horizontal. Assume the ground is level (except for the hole) and neglect air resistance, and assume the ball does not hit the side of the hole on the way up,
a) How far from the building will the ball land?
b) How long a time was the ball in flight?
c) What was the maximum height of the ball during its flight?
2. A jet plane is to make a high speed turn. The speed of the jet is 300 m/s. The circular acceleration should be 50 m/s2 (about 5 gees) since any more may cause the pilot to black out.
a) What is the radius of the turn if the velocity is 300 m/s and the acceleration is 50 m/s2
b) How long (a time) will it take to make a complete circle under the above conditions (that is, what is the period)?
c) What is the angular velocity (in rad/sec) in this circular orbit?
3. A boat can travel at a speed of 6 m/sec on a calm lake. This boat is now put in an "ideal" river that flows Southward at a uniform and constant rate of 5 m/sec.
a) If the boat starts from the West bank, which direction should you point the boat to cross the river to a point directly opposite (East of) your starting position? [Answer in angles from standard directions, such as 45o East of North or 22o South of West.].
56.4o North of East.
b) How long will it take if the river is 150 meters wide?
c) What direction should you head your boat if you want to just get across the river in the least time?
due East (straight across).
d) How long will be the least time?
4) A weight is held up by two ropes attached to a ceiling. The weight is 100 Nt, qleft = 70° and qright = 10°. (Neglect the weight of the ropes).
a) Which rope will have the bigger tension?
b) Will the sum of the magnitudes of the two tensions be equal to, greater than, or less than the weight?
c) What is the tension in the LEFT rope?
5) A car with driver of total mass 2100 kg can accelerate at a rate of 3.40 m/s2.
a) What is the net force (resultant) exerted on the car to make it accelerate at that rate?
b) What is the weight of the car?
c) How long a time does the car take in accelerating from zero to 30 m/s (67 mph)?
6) Consider an object on a scale in an elevator. At one particular instant the elevator has an acceleration of -1.5 m/s2 and a speed of -3 m/s. (Plus means up and minus means down.)
a) Is the elevator speeding up (going faster whether positive or negative), slowing down (approaching zero), or maintaining its speed?
b) If the scale reads 600 Nts at this instant, is the actual weight of the object more than, equal to, or less than 600 Nts ?
c) If the motion of the elevator changes so that the scale now reads 800 Nts, is the new acceleration of the elevator [less than +1.5 m/s2 (even bigger negative value), still the same as, or more than +1.5 m/s2 (less negative or positive value)] ?
d) When the elevator has an acceleration of -1.5 m/s2 and the scale reads 600 Nts, what is the mass of the object on the scale?
7) A satellite of mass 100 kg is orbiting the moon (the moon has a mass of 7.4 x 1022 kg or 1.23% of that of earth and a radius of 1,700 km or 27% that of earth) at a height of 300 km (185 miles).
a) What should be the period of the circular orbit for the satellite to have at this height?
8,000 seconds = 133 minutes and 20 seconds.
b) What speed will the satellite need to have to orbit in a circle at this height?
1,571 m/s = 3,520 mph.
c) What is the force of gravity on this satellite while it orbits at this radius?
d) What is the acceleration due to gravity (gMars) on the surface of Mars?