Name:_______________________

Test 3

12/18/2008

Ch. 9-11

Directions: All questions have the value indicated. Do not spend too much time on any one problem. Do everything that you can do easily, and then return to parts that are harder for you. If you cannot answer one part of a question that you need for a later part then assume an answer or use a symbol to represent the part that you do not know.

Useful number(s): Gravitational
Constant: G=6.6726x10^{-11} N×m^{2}/kg^{2}

1)
(30 points) You are designing a compact disc (CD) player. The diameter of a CD is 120mm and has a mass
of 15 grams. (Assume the CD is a solid
cylinder I=M R^{2}/2, and the
axle on which it rotates is frictionless and massless.)

a) What is the moment of inertia of the CD?

b) If the CD spins at an angular speed of 28,000 rpm, find the angular momentum of the CD.

c) Find the constant angular acceleration needed to stop the CD in one revolution.

d) How long does it take to stop the CD?

e) How much torque is needed to stop the CD?

f) How much work is done stopping the CD?

g) (Extra Credit 5 points) The torque to stop the CD is applied by a frictional brake (μ=0.77) near the hub of the CD at radius of 8mm. What is the magnitude of the normal force needed to stop the CD?

Name:_______________________

Test 3

12/18/2008

Ch. 9-11

2)
(10 points) Your 70 kg
friend is standing on the outer edge of a merry-go-round (a large rotating
solid cylinder mounted on a frictionless shaft) with moment of inertia of I=695
kg·m^{2} and radius 2.6m initially rotating at 12.8 rpm. If the friend moves to a radius of 0.5m what
will be the new angular velocity? (Assume the person is a point mass.)

Name:_______________________

Test 3

12/18/2008

Ch. 9-11

3) (30 points) A 90 kg man is standing on a rung 8m up a uniform 40 kg, 12 m ladder that makes a 75-degree angle with the ground and is resting on a frictionless vertical wall (hint: A frictionless wall can only produce a normal force.).

a) Assuming the ladder does not slip, what is total force on the ladder?

b) Assuming the ladder does not slip, what is total torque on the ladder?

c) Assuming the ladder does not slip, what is the normal force on the ladder from the ground?

d) Assuming the ladder does not slip, what is the normal force on the ladder from the wall?

e) What is the minimum friction coefficient needed between the ladder and the ground such that the ladder will not slip?

f) Using the friction found in part a, how high could the man climb if the ladder were at a 60-degree angle?

Name:_______________________

Test 3

12/18/2008

Ch. 9-11

4) (15 points.) You drop a 5kg mass from rest at a height of 2m above the top of an unstretched mass-less spring, which obeys Hooke’s Law.

a) If the maximum compression of the spring is 4cm, what is the spring constant of the spring?

b) What is the speed of the mass when the spring is compressed 4cm?

c) What is the speed of the mass when the spring is compressed 1cm?

d) Ignoring air friction how high will the mass go as it returns from the spring? (Note: the mass leaves the spring when the spring is uncompressed.)

Name:_______________________

Test 3

12/18/2008

Ch. 9-11

5)
(15 points) A normal section of an artery has a radius of 3mm
and a blood speed of 0.14m/s. Due to
plaque build up a section of the same artery has a radius of 1mm. The density of blood is 1050 kg/m^{3}.

a)
When lying down the artery is **horizontal**. What is the speed of the blood in the
constricted section (thinner 1mm section)?

b)
When lying down the artery is **horizontal**. What is the difference in pressure between
the normal and constricted sections?

c)
When standing up the constricted section is 0.5 meters **below**
the normal section. Assuming the speed in the normal section is the same, what
is the speed of the blood in the constricted section?

d)
When standing up the constricted section is 0.5 meters **below**
the normal section. Assuming the speed in the normal section is the same, what
is the difference in pressure between the normal and constricted sections?

e)
Recalculate parts c) and d) assuming the constricted section
were 0.5 m **above** the normal section?