PHYS 201 TEST #2 10/07/11a 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. SET EACH PROBLEM UP FIRST. Do the algebra only if you have time. All numerical answers should be in MKS units unless otherwise indicated. 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 = 6,380 km.
1. A ball of mass 0.4 kg is thrown from the top of a building 9 meters high (above the ground) with an initial speed of 25 m/s at an angle of 35° above the horizontal. The object then hits the ground (assume a level surface and assume no air resistance).
a) How far away from the building (where the person threw it, horizontal distance) does the object land?
b) How long a time is the object in the air?
c) Draw a picture of the situation, and include on the picture all the given information in the problem:
2. A centrifuge spins objects around in a circle of radius = 18 cm. For parts a, b, c and d, assume the frequency of rotation is 5,400 rpm (revolutions per minute).
a) What is the frequency in cps (cycles per second)?
b) What is the tangential speed (in m/s) of an object in the centrifuge due to the spinning motion?
c) What is the magnitude of the acceleration of an object due to the spinning?
d) What is the direction of that acceleration [toward the center, toward the outside, along the direction of motion, opposite the direction of motion, or other]?
Toward the center.
e) At what frequency would the centrifuge have to spin (either in cps or rpm) if the resulting acceleration were to equal 100 times the acceleration due to gravity (a = 980 m/s2)?
11.7 cps = 705 rpm.
3. A boat can travel at a speed of 7 m/sec on a calm lake. This boat is now put in a river that flows downstream at a rate of 4 m/sec.
a) What direction should a pilot point the boat to go directly across this river? [Indicate an angle measured from straight across, and indicate whether the angle is directed upstream or downstream.)
b) How long will it take if the river is 120 meters wide?
c) What direction should the pilot head the boat to get across the river in the least time?
d) How long will be the least time?
4) An object rests on a scale inside an elevator.
a) What is the mass of an object on the scale if the scale reads 680 Nt. when the elevator is at rest?
a) If the scale reads 760 Nts with the object of part a on the scale at a later time (some time later - not just after it was at rest), is the elevator moving: [up; down; none - zero speed; can't be determined from information given]?
Can't be determined from information given.
c) If the elevator (sometime later, not just after it was at rest) has the scale reading 760 Nts (as in part b), is the direction of the acceleration: [up; down; none - zero acceleration; or can't be determined from information given] ?
d) If the scale reads 760 Nts. (with the same object on the scale in the elevator as in part a above), what is the value of the acceleration of the elevator?
+1.15 m/s2 .
5) A 40 kg satellite is to be put into orbit around Mercury (radius of Mercury = 2,440 km; mass of Mercury = 3.3 x 1023kg) at a height of 100 km above the surface (for a radius of orbit = 2,540 km).
a) What speed should this satellite have in order to orbit at this height?
2,940 m/s = 6,580 mph.
a) What will the period of orbit would this satellite have?
5,421 sec = 90 minutes plus 21 seconds.
c) What is the force of gravity on this satellite due to Mercury as it orbits at this height?
6) Consider a weight hung from two ropes attached to the ceiling. The angle the left rope makes with the ceiling is 74o and the angle the right rope makes with the ceiling is 33o. The weight is 500 Nt.
a) Is the magnitude of the tension in the left rope plus the magnitude of the tension in the right rope: [the same as, more than, or less than] the magnitude of the tension in the right rope?
b) Is the magnitude of the tension in the left rope: [less than, the same as, or more than] the magnitude of the tension in the right rope?
c) What is the tension in the left rope?
7) Two people carry a weight of 650 Nt on a board of length 250 cm, one person lifting on the left and one lifting on the right. The weight of the object is located 180 cm from the left end of the board.. The weight of the board can be neglected.
a) Is the left force, Fleft: [ less than; the same as; or greater than] the weight, W ?
b) Is the left force down, Fleft : [ less than; the same as; or greater than] the right force, Fright ?
c) What is the magnitude of the left force, Fleft ?