PHYS 201 TEST
#2 10/08/10 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 0.23 kg is thrown from the bottom of a pit 6 meters deep (below the ground) with an initial speed of 31 m/s at an angle of 78° above the horizontal. Assume the object does not hit the side of the pit. The object then hits the ground (assume a level surface and assume no air resistance).
a) How far away from the pit (where the person threw it, horizontal distance) does the object land? (If the object does not go high enough to reach ground level, answer NONE.)
38.6 m.
b) How long a time is the object in the air?
5.98 sec.
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 = 14 cm. For parts a, b, c and d, assume the frequency of rotation is 7,200 rpm (revolutions per minute).
a) What is the frequency in cps (cycles per second)?
120 cycles/sec.
b) What is the tangential speed (in m/s) of an object in the centrifuge due to the spinning motion?
105.6 m/s.
c) What is the magnitude of the acceleration of an object due to the spinning?
79,588 m/s2.
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)?
13.3 cps = 799 rpm.
3. A boat can travel at a speed of 5 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.)
53.1o upstream.
b) How long will it take if the river is 160 meters wide?
53.3 seconds.
c) What direction should the pilot head the boat to get across the river in the least time?
straight across.
d) How long will be the least time?
32.0 seconds.
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 780 Nt. when the elevator is at rest?
79.6 kg
a) If the scale reads 710 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 710 Nts (as in part b), is the direction of the acceleration: [up; down; none - zero acceleration; or can't be determined from information given] ?
Down.
d) If the scale reads 710 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?
-0.88 m/s2 .
5) A 50 kg satellite is to be put into orbit around Mars (radius of Mars = 3,400 km; mass of Mars = 6.0 x 1023kg) at a height of 100 km above the Martian surface (for a radius of orbit = 3,500 km).
a) What speed should this satellite have in order to orbit at this height?
3,381 m/s = 7,573 mph.
a) What will the period of orbit would this satellite have?
6,503 sec = 108 minutes plus 23 seconds.
c) What is the force of gravity on this satellite due to Mars as it orbits at this height?
163 Nt.
6) Consider a weight hung from a combination of a rod attached to the left wall and a rope attached to the ceiling. The angle the rope makes with the ceiling is 81o and it is attached to the left (near) side of the rod so the rope is angled to the left as it meets the rod, and the angle the rod makes with the left wall is 52o. The weight is 170 Nt.
a) Does the rod push up and to the right, or down and to the left?
Up and to the right.
b) What is the magnitude of the force of the rod?
30.4 Nt..
c) What is the tension in the rope?
153.2 Nt.
7) A person carries a weight at the right end of a rod by pushing down on the left end and up near the left end. The weight of the rod can be neglected. The weight of the object is 90 Nt. The rod is 260 cm long (with the weight at the end), and the upward force is 20 cm from the left end, and the downward force is at the left end.
a) Is the force up, Fup: [ less than; the same as; or greater than] the weight, W ?
greater than
b) Is the force down, Fdown : [ less than; the same as; or greater than] the force up, Fup ?
less than
c) What is the magnitude of the upward force, Fup ?
1,170 Nt.
d)
What is the magnitude of the downward force, Fdown ?
1,080 Nt.