PHYS 201     TEST #2         10/07/16         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 0.25 kg is thrown from the top of a building 4 meters high with an initial speed of 12 m/s at an angle of 34° 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 ball land?

18.09 m.

b) How long a time is the ball in the air?

1.818 sec

c) Draw a picture of the situation, and include on the picture all the given information in the problem:

 

2. A ride at the fair is designed so that it rotates at full speed at 6 revolutions per minute, and it has a radius of 9 meters.  For all the questions below, assume the ride is going at full speed.

a) What is the frequency in cps (cycles per second)?

0.10 cycles/sec.

b) What is the tangential speed (in m/s) of an object on the ride due to the spinning motion?

5.65 m/sec.

c)  What is the magnitude of the acceleration of the object due to the spinning?

3.55 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 ride have to spin (either in cps or rpm) if the resulting acceleration were to equal 10 times the acceleration due to gravity (acir = 98 m/s2)?

0.525 cps = 31.5 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 2 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.)

23.6o upstream.

b) How long will it take if the river is 140 meters wide?

30.55 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?

28.0 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 700 Nt. when the elevator is at rest?

71.43 kg

b) If the scale reads 630 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 630 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 630 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?

-0.98 m/s2 .

 

5) A 25 kg satellite is to be put into orbit around the Moon (radius of Moon = 1,740 km; mass of Moon = 7.34 x 1022kg) at a height of 360 km above Moon’s surface (for a radius of orbit = 2,100 km).   

a) What speed should this satellite have in order to orbit at this height?

1,527 m/s = 3,420 mph.

a) What period of orbit would this satellite have?

8,642 sec = 144 minutes plus 2 seconds.

c) What is the force of gravity on this satellite due to the Moon as it orbits at this height?

27.75 Nt.

 

6) Consider a weight hung from a combination of a rod attached to a wall and a rope attached to the ceiling.  The angle the rope makes with the ceiling is 77o.  The rod is free to swivel at the wall, and the angle the rod makes with the wall is 55o.  The rope is attached farther from the wall than the end of the rod.  The weight is 280 Nt.

a) Does the rod push up and to the right, or pull down and to the left?

Down and to the left.

b) What is the magnitude of the tension in the rod?

94.13 Nt.

c) What is the tension in the rope?

342.8 Nt.

 

7)  A person lifts a weight of 80 Nt located at the right end of a board 210 cm long (assume the board has negligible weight) by lifting up 30 cm from the left and pushing down on the left end. 

 

a)  Is the right force, Fright: [ less than;  the same as;  or greater than] the weight, W ?

 

Greater than.

 

b)  Is the right force, Fright : [ less than;  the same as;  or greater than]  the left force, Fleft ?

 

Greater than.

 

c)  What is the magnitude of the right force, Fright ?

 

560 Nt.

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