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Unformatted text preview: Physics 171.101 Exam 2 Nov. 14, 2000
Prof. Barnett You are allowed to use formulas written on one 3”x5” index card. You are allowed to use a
calculator. Write everything in INK. 1. A wooden plank with length 6 meters is held
horizontally with a hinge on the left end and a cable 4 m '
at the center. The cable has total length 5 meters /
and a square cross section. The side dimension of the /
square cable is 1 mm. The cable is attached to the wall /
4 meters above the hinge. The mass of the plank is /
12 kg. It’s cross section and density are constant. /
Take g = 10 m/sec2. / / A) (10 pts) What is the tension in the cable? B) (10 pts) What is the force, Fl,“ of the hinge on the plank?
C) (5 pts) If the cable stretched by 0.5 mm under this tension, what is its Young’s modulus? water 2. A spring is attached to the bottom of a swimming surface MW
pool and also to a wooden block. The wooden block is
submerged in the water of the pool, 2 meters above the wooden
swimming pool bottom. The density of the pool water block
is 1.0 g/cm3 and the density of wood is 0.5 g/cm3.
The wooden block is a cube with edge dimension 30 cm. 2 m
‘5 1' ’ B r“ l r (-0 L / / f / ( k A) (10 pts) What is the buoyant force on the wooden block? \ 10 cm
. H B) (10 pts) If the spring stretches by 1 cm what is its spring constant? / 3. A disc with uniform density p = 2 g/cm3, total mass M = 0.5 kg, and outer radius R = 10 cm.
starts from rest and rolls without slipping down an incline. The incline is at an angle of 37° to the /
horizontal. The length of the incline is 5 meters. /‘
sin(37") = 0.6, cos(37°) : 0.8, Idisc : 0.5 M R2
g : 11" W / 5:561 A) (15 pts) How much kinetic energy is associated with the motion of the disc’s center of mass, and how much with rotational motion about the disc’s center of mass, when it
arrives at the bottom of the incline? B) (10 pts) What is the minimum coefﬁcient of friction that must exist between the disc and
the incline to permit rolling without slippage? J, 4. Two bunches of bananas are attached to a bar
of total length 1.0 meter. Each bunch has a mass
of 2 kg. Each has a moment of inertia about its own
center of mass given by Icom : 0.25 kg m2. The E =
bar is attached to a massless, frictionless axle with
radius 10 cm. The axle has a massless rope wrapped
around it which extends downward toward the floor
2.5 m below. The total length of the rope is 5 meters. A
small spider monkey with mass 3 kg is on the floor, sees . . . W? the bananas and dec1des to climb the rope to get them.
He pulls on the rope to climb and gets just barely off the floor. The bananas start to spin
about the axle overhead. He ﬁnds he isn’t moving up so he pulls on the rope faster, but still
stays just barely off the ﬂoor, so he pulls the rope faster and faster and the bananas spin
faster and faster, but the monkey always stays just barely off the floor. Take g = 10 m/sec2. A) (10 pts) What is the tension in the rope?
B) (10 pts) What is the angular acceleration of the bananas about the axle? C) (10 pts) How much time passes from when the monkey starts to pull on the rope until
the other end of the rope comes off the axle, i.e. 2.5 meters of r0pe pass the monkey? ...
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