Download Physics 2010 Summer 2011 REVIEW FOR MIDTERM 5

Physics 2010
Summer 2011
REVIEW FOR MIDTERM 5
1.
A 58.0 kg skier is going down a 35.0° slope. The area of each ski which is in contact with the snow is
0.13 m 2. Determine the pressure that each ski exerts on the snow.
2.
A simple shelf is fastened to a wall by a hinge at one end and
supported by a cable on the free end (see drawing). The shelf is a
uniform long board (2.0 m length) with a mass of 4.20 kg. A
pewter trophy (mass = 20.0 kg) rests on the shelf. The cable can
withstand up to a maximum tension of 150.0 N. W hat is the
maximum distance from the wall that the trophy can be placed
without the cable breaking?
3.
A raft (6.0 m × 4.0 m in area) is floating on a river. A loaded car pulls onto the raft and the raft sinks 3.0
cm lower into the water. W hat is the weight of the car?
4.
In an aorta with a cross sectional area of 1.60 cm 2, the blood ( D = 1050 kg/m 3) flows with a speed of
30.0 cm/s.
A.
B.
W hat is the flow rate, in kilograms per second, of blood in the aorta?
The aorta branches to form a large number of fine capillaries with a combined cross sectional area
of 2.0 × 10 3 cm 2. W hat is the speed (in cm/s) of the blood flow in the capillaries?
5.
W ater is supplied to an office building 320m high through a pipe at ground level. Find the minimum
pressure in the supply pipe so that water can reach the top floor of the building. The density of water is
1000.0 kg/m 3.
6.
Only part of an iceberg is seen above the ocean. It turns out that all icebergs have the exact percentage of
their body above the water. W hat percentage is this? Dice = 917.0 kg/m 3; D seawater = 1025.0 kg/m 3
7.
A 0.20 kg cup made of copper is at 20.0°C. You pour 0.10 kg of aluminum at 50.0°C and 0.25 kg of water
at 85.0°C. W hat is the final temperature? Note: The final temperature is greater than 50.0°C.
Specific heat at atmospheric pressure:
CCO = 386 J/kg@°C; CAL = 900 J/kg@°C; CW = 4186 J/kg@°C
8.
An automobile weighing 1 × 10 4 N has weight equally distributed over its wheel. The weight of the car
causes each tire to be slightly flattened on the bottom so that there is a surface area in contact with the road.
The gauge pressure of the air in the tire is 2.00 × 10 5 PA (30 lb.in 2). Find the area of contact, assuming that
the only forces on the section of tire in contact with the road are the air pressure and the normal force
exerted by the surface of the road.
9.
A ferry boat is 4.00 m wide and 6.00 m long. W hen a large truck pulls on to it, it sinks 4.00 cm in the
water. W hat is the weight of the truck?
10.
A.
B.
W hat is the net upward force on an airplane wing of area 20 m 2 if the speed of flow is 300 m/s
across the top of the wing and 280 m/s across the bottom of the wing? [Dair = 1.29 kg/m 3]
1.
Calculate the flow rate (gm/sec) of blood ( D = 1.0 s/cm 3) in an aorta with a cross-sectional
area of 2.0 cm 2 if the flow speed is 40.0 cm/s.
2.
Assume that the aorta branches to form countless capillaries with a combined crosssectional area of 3.0 × 10 3 cm 2. W hat is the flow speed in the capillaries?
11.
A beaker of water sits in the sun until it reaches a temperature of 30°C. The beaker is made of 100 g of
aluminum and contains 180 g of water. In an attempt to cool the system down, 100 g of ice at 0°C is added
to the water. W hat is the final temperature?
12.
A spring (k = 830 N/m) is hanging from the ceiling of an elevator. An object (5.0 kg) is attached to the
lower end of the spring. By how much does the spring stretch (relative to its unstrained length) when the
elevator is accelerating upward at a = 0.60 m/s 2?
13.
The volume flow rate of blood through a 2.00 × 10 -6 m radius capillary is 3.8 × 10 -9 cm 3/s.
14.
(a)
(b)
W hat is the velocity of the blood in m/s?
Assuming all the blood in the body passes through capillaries, how many of them must there be to
carry a total flow of 90.0 cm 3/s?
A.
(a)
B.
15.
A spring is hanging from the ceiling. W hen a 5.00 kg steel mass is suspended from it, the spring stretches a
distance of 10.0cm relative to its unstretched length.
(a)
(b)
(c)
16.
W hat is the pressure drop as water goes into a 3.00 cm diameter nozzle from a 9.00 cm
diameter fire hose while carrying a flow of 40.0 cm 3/s?
(b)
After the water leaves the nozzle, what is the maximum height to which it can rise?
A 5,000 kg airplane is moving at a constant velocity and is climbing at an angle of 30° relative to
the horizontal. If the effective wing area is 25 m 2, and if air travels twice as fast over the top of the
wings as it does over the bottom, how fast is the airplane moving?
A.
B.
C.
W hat is the spring constant (k) of this spring?
If the steel mass is submerged in a beaker of water, what is the mass of
the water it displaces? (The density of steel is 7,860 kg/m 3.)
To what height, h, does the mass rise relative to its previous position?
(See diagram.)
A glucose solution being administered with an IV line has a flow rate of 4.00 cm 3/min. W hat will
the flow rate be if the glucose is replaced by whole blood having the same density but a viscosity
2.50 times that of glucose? (All other factors remain constant.)
A disk between vertebrae in a human spine is subjected to a shearing force of 600 N. Find the
shear deformation of the disk if its shear modulus is 1 × 10 9 N/m 2. The disk is equivalent to a solid
cylinder 0.700 cm high and 4.00 cm in diameter.
Suppose a 3.00 N force can rupture an eardrum having an area of 1.00 cm 2. At what depth in
water would a person's eardrum rupture, assuming the gauge pressure inside the eardrum (in the
middle ear) is zero?
17.
A school yard teeter-totter with a total length of 5.2 m and a mass
of 36.0 kg is pivoted at its center. An 18.0 kg child sits on one end
of the teeter-totter.
(a)
(b)
18.
A student on a piano stool rotates freely with an angular speed of 2.95 rev/s. The students with outstretched
arms holds a 1.25 kg mass in each hand at 0.759 m from the axis of rotation. The combined moment of
inertia of the student and the stool, ignoring the two masses, is 5.43 kg-m 2. As the student pulls his arms
inward, his angular speed increases to 3.54 rev/s.
(a)
(b)
19.
W here should a parent push with a force of 210 N in order
to hold the teeter-totter level?
W here should the parent push with a force of 310 N?
How far are the masses from the axis of rotation at this time?
Calculate the initial and final energy of the system.
A person with a mass of 81.0 kg and a volume of 0.089 m 3 floats quietly in water.
(a)
(b)
W hat is the volume of the person that is above the water?
If an upward force F is applied to the person, the volume above the water increases by 0.0018 m 3.
Find the force.
density of air = 1.29 kg/m 3 (1 atm pressure)
density of water = 1.000 × 10 3 kg/m 3
20.
You are sitting in an airplane looking out the window and begin wondering about the pressure outside.
Suppose the air outside the window moves with a speed of approximately 150 m/s shortly after take-off and
that the air inside the plane is atmospheric pressure.
(a)
(b)
Find the pressure difference between the inside and outside of the window.
If the window is 25.0 cm by 42.0 cm, find the force exerted on the window by the air pressure.
density of air = 1.29 kg/m 3 (1 atm pressure)
21.
A simple shelf is fastened to a wall by a hinge at one end and a cable on the
free end (see drawing to the right). The shelf is a uniform board 3.0 m long
with a weight of 50 N. A trophy (mass 20.0 kg) sits on the shelf. The cable
can withstand a maximum of 200 N. W hat is the maximum distance from the
wall that you can place the trophy without the cable breaking?
22.
A uniform thin rod (length = 0.50 m, mass = 0.2 kg) rotates about its center on a frictionless tabletop. The
rod has an initial angular velocity of 1.0 rad/s. Two bugs (each has a mass of 4.0 × 10 -3 kg) are initially
standing at the center. Each bug crawls to an opposite end of the rod.
(a)
(b)
W hen the bugs reach the ends of the rod, what is the angular velocity
of the rod?
W hat is the kinetic energy of the system when the bugs are at the
ends of the rod?
23.
A solid, square pinewood raft measures 4.0 m on each side and is 0.3 m thick.
(a)
(b)
(c)
(d)
24.
W hat percentage of the raft float above the surface of the water?
W hen Liz (mass 50.0 kg) sits on the raft, how high is the top of the raft above the surface of the
water?
Find the absolute pressure 3.0 m directly below the bottom of the raft when Liz is sitting on the
raft.
Liz has a group of friends, each with an average mass of 75.0 kg. How many friends can she have
on the raft with her before the raft starts to sink?
A trailer home is supported 1.0 m above the ground by sitting on stacks of cinder block at each of the four
corners. A decorative trim is placed around the edges of the trailer such that it creates an open space
underneath the trailer. The trim covers the bottom area in such a way that it is not air-tight, but reduces the
wind so that even in strong winds the airspeed beneath the trailer is essentially zero. The trailer measures
7.0 m wide × 14.0 m long × 3.0 m high and has a mass of 10,00 kg (10 metric tons).
(a)
(b)
Find the difference in atmospheric pressure above and below the trailer.
W hat is the greatest wind speed the trailer can withstand before it is lifted off the ground? Express
your answer in miles/hour. (In your calculations do not neglect the difference in atmospheric
pressure.)
Dair = 1.29 kg/m3 ; 1 mile = 1609 m
25.
A uniform boom (mass = 100 kg) is supporting a sign for a candy store (mass = 500 kg).
A cable is attached to the boom 3/4 the way up the boom and attached to the wall with a
hinge at point P.
(a)
(b)
26.
Find the tension in the cable.
Find the magnitude of the net force the wall exerts on the boom at point P.
Two cylinders of uniform density are placed in a tank containing both oil and
water. The tank is open to the air. Cylinder A is made of pine and is floating
such that 10 cm of the cylinder floats above the surface of the oil (r A = 2 cm,
Dpine = 550 kg/m 3). Cylinder B is made of iron and rests on the bottom of the
tank (r B = 2 cm, h B = 5 cm, Diron = 7860 kg/m 3).
(a)
(b)
(c)
(d)
W hat is the total height of cylinder A?
Find the gauge pressure 10 cm directly below the bottom surface of
cylinder A?
W hat is the magnitude of the normal force acting on cylinder B?
Determine the absolute pressure at the bottom of the tank.
1 atm = 1.01 × 105 Pa; Doil = 800 kg/m3; Dwater = 1000 kg/m3
27.
Three friends, Ryan, Tim and Nathan, each have a mass of 75 kg and are in the center of merry-go-round.
A fourth friend, Ben, is holding onto the outside edge while he runs providing a constant tangential force of
200 N. The merry-go-round is a solid cylinder that rotates about its center. Ben stops pushing and the
merry-go-round spins at a constant rate of 15 rpm while the three friends are in the middle.
(a)
(b)
Calculate the magnitude of the angular acceleration of the merry-go-round while Ben is pushing.
Find the total kinetic energy of the merry-go-round when they are all in the center.
Now, Ryan, Tim and Nathan each walk to the outside edge of the merry-go-round. Consequently, the
merry-go-round slows down.
(c)
(d)
W hat is the tangential speed of the outside edge of the merry-go around once everybody is
standing on the outside edge?
Find the total kinetic energy of the merry-go-round when they are standing on the outside edge.
Icylinder = ½ MR2 ; mass of merry-go-round = 200 kg; radius or merry-go-round = 2m
28.
A trailer home is supported at its corners by stacks of cinder blocks so
that it sits 1.0 m off the ground. A decorative trim is placed around the
bottom edges of the trailer creating an open space underneath. The trim
covers the area in a way that is not air tight, but reduces the wind so that
even in strong winds the airspeed beneath the trailer is essentially zero.
The rectangular shaped trailer is 2.5 m tall, 7.0 m wide and 15.0 m
long.
(a)
(b)
W hat is the difference in air pressure between the top and
bottom surfaces of the trailer when no wind is blowing?
A wind of 90 miles/hour just lifts the trailer off the ground.
Calculate the mass of the trailer. In your calculations, do not neglect the results found in part (a).
Dair = 1.29 kg/m3; 1 mile = 1609 m
29.
A.
A sign hangs by a rope attached at 30° to the middle of its upper edge. It rests against a
frictionless wall. If the weight of the sign were doubled, what would happen to the tension in the
string? sin 30° = 0.5; cos 30° = 0.87)
(a)
(b)
B.
It would increase by a factor of 2.
It would increase by a factor of 4.
1 kg
2 kg
(c)
(d)
3 kg
4 kg.
A child’s bathtub toy has a density of 0.45 g/cm 3 what fraction of the toy floats above the water?
(a)
(b)
D.
(c)
(d)
A 1.0 m board with uniform density, hangs in static equilibrium from a
rope with tension T. A weight hangs from the left end of the board as
shown. W hat is the mass of the board?
(a)
(b)
C.
It would remain the same
It would increase by a factor of 1.5.
5%
45%
(c)
(d)
55%
95%
The drawing to the right shows a hydraulic lift. A force is applied at
side 1 and an output force is generated at side 2. W hich of the following
is true?
(a)
(b)
(c)
(d)
The
The
The
The
force at side 1 is greater than the force at side 2.
force at side 1 is less than the force at side 2.
pressure at side 1 is greater than the force at side 2.
pressure at side 1 is less than the pressure at side 2.
E.
Three containers are filled with water to a depth of 1.0 m. In
which container is the pressure greatest?
(a)
(b)
(c)
(d)
F.
Container A.
Container B.
Container C.
The pressure is the same at the bottom of all the
containers.
A spigot is to be placed on a water tank below the surface of the water. W hich of the following
give the distance of the spigot below the surface h compared to the velocity with which the water
will run through the spigot
.
30.
A solid metal cylinder of uniform density D = 2700 kg/m 3 has a height of 10.0 cm and a
radius of 2.0 cm, and sits on the bottom of a 40.0 cm tall cylindrical tank of radius 25.0
cm. The tank is filled to the brim, half way up with water ( D = 1000 kg/m 3) and half
with oil ( D = 600 kg/m 3). The tank is open to the air. P atm = 1.01 × 10 5 Pa.
(a)
(b)
(c)
(d)
(e)
31.
W hat is the gauge pressure at the top surface of the metal cylinder?
W hat is the absolute pressure at the bottom surface of the metal cylinder?
W hat is the buoyant force the metal cylinder feels?
W hat is the normal force exerted on the metal cylinder?
A small hole is poked in the tank 10.0 cm up from the bottom. Right after the hole is made, with
what speed does the water leave the tank?
Three friends, Ashley, Cindy and Christine, each have a mass of 50 kg and are in the center of merry-goround. A fourth friend, Dawn, starts from rest and while holding onto the outside edge while she begins to
run providing a constant tangential force. The merry-go-round is a solid cylinder that rotates about its
center. Dawn stops pushing after 5.0 s and the merry-go-round spins at a constant rate of 4 rad/s while the
three friends are in the middle.
(a)
(b)
Calculate the magnitude of the tangential force Dawn exerted on the merry-go-round while she was
pushing.
Find the total kinetic energy of the merry-go-round after Dawn stops pushing.
Now, Ashley, Cindy and Christine each walk to the outside edge of the merry-go-round. Consequently, the
merry-go-round slows down.
(c)
(d)
W hat is the angular speed of the merry-go-round once everybody is standing on the outside edge?
Find the total kinetic energy of the merry-go-round when they are standing on the outside edge.
I cylinder = ½ MR 2; mass of merry-go-round = 200 kg; radius or merry-go-round = 2m
32.
A fireman climbs up a ladder to rescue a child in a burning building as
shown. The wall is smooth. There is static friction between the ladder and
the ground. The fireman rescues the boy and carries him safely down the
ladder without the ladder slipping, however if the boy were to weigh any
more the ladder would slip.
(a)
(b)
(c)
(d)
At the instant the fireman is at the top of the ladder with the boy in
his arms, what is the magnitude of the normal force exerted by the
wall on the ladder?
At the instant the fireman is at the top of the ladder with the boy in
his arms, what is the magnitude of the normal force exerted by the ground on the ladder?
At the instant the fireman is at the top of the ladder with the boy in his arms, what is the magnitude
and direction of the frictional force exerted by the ground on the ladder?
W hat is the value of the coefficient of static friction between the ground and the ladder?
Mass fireman = 85.0 kg, mass ladder = 30.0 kg, length ladder = 10.0 m, mass of child = 40.0 kg
33.
A
A trap door, of length and width 1.65 m, is held open at an angle of 65.0 degrees
with respect to the floor. A rope is attached to the middle of the raised edge of
the door and fastened to the wall behind the door in such a position that the rope
pulls perpendicularly to the trap door. If the mass of the trap door is 16.8 kg,
what is the torque exerted on the trap door by the rope?
B.
A 1.10 kg bucket is tied to a rope of negligible mass. The rope is wrapped around a
solid pole that is mounted horizontally on frictionless bearings. The cylindrical pole has
a diameter of 0.340 m and a mass of 2.60 kg. W hen the bucket is released from rest,
what is the acceleration of the bucket?
C.
The drawing to the right shows a hydraulic lift. A force of 12 N is applied at
disk A (radius 4 cm) and an output force is generated at disk B (radius 1.2 m).
W hat is the magnitude of the force applied to disk B?
D.
A block of birch wood floats in oil with 90.0% of its volume submerged. W hat is the density of
the oil? The density of the birch is 0.67 g/cm 3
34.
A.
A house with its own well has a pump in the basement with an output pipe of inner radius 6.3 mm.
Assume that the pump can maintain a gauge pressure of 410 kPa in the output pipe. A showerhead
on the second floor (6.7 m above the pump’s output pipe) has 36 holes, each with a radius of
0.33mm. The shower is on “full blast” and no other faucet in the house is open. Assume the speed
of the water in the tank is zero.
(a)
(b)
35.
Ignoring viscosity, with what speed does water leave the showerhead? Is this reasonable?
W hat is the speed of the water as it moves through the output pipe of the pump?
B.
A 60.0 kg woman is running at 8 m/s and jumps onto the edge of a large disk-shaped platform.
The platform rotates about its center on a frictionless axle and has a mass of 240 kg. The platform
is initially at rest and has a radius of 10 m. W hat is the angular speed of the platform after the
woman jumps on the platform?
C.
A ping-pong ball with an average density of 0.125 g/cm 3 is released from 1.3 m underwater. W hat
is its initial acceleration? [Acceleration is a vector.]
A.
Rich is standing at a height (h) of 8 m on the frictionless (falls without
slippins) ramp as shown and he is holding a thin spherical shell of radius 12
cm. Matt is also on the ramp and is holding a solid sphere of radius 23 cm.
Matt and Rich will release their objects from rest.
(a)
(b)
(c)
B.
From what height would Matt have to release his sphere so that it
has the same speed Rich’s object has at the bottom?
From what height would Matt have to release his sphere so that it
reaches the bottom at the same time as Rich’s object?
If Rich and Matt each started at a height of 1 m lower than the heights from b, whose
object would reach the bottom first? (You don’t need an answer to b to determine this)
The density of ice is 917 kg/m 3, and the density of sea water is 1025 kg/m 3. A swimming polar
bear climbs onto a piece of floating ice that has a volume of 5.2 m 3. W hat is the weight of the
heaviest bear that ice can support without sinking completely beneath the water?
36.
A.
A mountain climber is repelling down a vertical wall. The
rope is attached to a buckle (25°) and is strapped to the
climber’s waist 15 cm to the right of his center of gravity.
The climber weighs 770 N. The distance from foot to CG is
91 cm and the distance from foot to waist is 106 cm. He is
wearing a backpack (10 kg) with CG 36 cm to the right of his
waist.
(a)
(b)
37.
Find the tension in the rope.
Calculate both the magnitude and direction of the
contact force exerted by the wall on the climber’s
feet.
B.
Two identical containers are open at the top and are
connected at the bottom via a tube of negligible volume
and a valve which is closed. Both containers are filled
initially to the same height of 1.00 m, one with ethyl
alcohol in the left chamber and the other chamber with
mercury, as the drawing indicates. The valve is then
opened. Assume the two liquids, ethyl alcohol and mercury
are immiscible. The density of ethyl alcohol is 791 kg/m3
and the density of mercury is 1.36 × 104 kg/m3. Determine
the fluid level in the left container, meaning the full distance
from the bottom of the container to the top of the ethyl
alcohol, when equilibrium is re-established.
A.
The steering wheel of a car has a radius of 0.16 m, while the steering wheel of a truck has a radius
of 0.31 m. The same force is applied in the same direction to each. W hat is the ratio of the torque
produced by this force in the truck to the torque produced in the car?
B.
A person who weighs 602 N is riding a 92 N mountain bike. Suppose the entire weight of the rider
and bike is supported equally by the two tires. If the gauge pressure in each tire is 7.80 × 10 5 Pa,
what is the area of contact between each tire and the ground?
C.
Oil is flowing with a speed of 1.13 m/s through a pipeline with a radius of 0.320 m. How many
gallons of oil (1 gal = 3.79 × 10 -3 m 3) flow in one day?
D.
The main water line enters a house on the first floor. The line has an absolute pressure of
2.71 × 10 5 Pa. How high could a faucet be before no water would flow from it, even if the faucet
were open?
38.
39.
A.
A uniform solid disk with a mass of 24.3 kg and a radius of 0.313 m
is free to rotate about a frictionless axle. Forces of 120, 115 and 90.0
N are applied to the disk, as the drawing illustrates. W hat is the
magnitude of the angular acceleration of the disk?
B.
A meat baster consists of a squeeze bulb attached to a plastic tube. W hen the
bulb is squeezed and released, with the open end of the tube under the
surface of the basting sauce, the sauce rises in the tube to a distance h, as the
drawing shows. It can then be squirted over the meat. The atmospheric
pressure is 1.013 × 10 5 Pa outside the tube in the drawing. The density of the
basting sauce is 1200 kg/m 3. W hat is the absolute pressure P B in the bulb of
the basting tube if h = 0.10 m?
C.
A ping-pong ball with an average density of 0.225 g/cm 3 is released from 1.3
m underwater. W hat is its initial acceleration? (Acceleration is a vector.)
A.
A solid cylinder of length 4 m is floating in water so that 1 m of the cylinder is in the air and 3 m
of the cylinder is in the water.
1.
2.
40.
W hat is the density of the cylinder?
If oil ( Doil = 600 kg/m 3) is now poured into the container so that it goes
a height of 5 meters above the water (see picture), how many meters of
the cylinder is in the oil?
B.
Rich is standing at a height (h) of 8 m on the ramp as shown and he is holding
a thin spherical shell of radius 12 cm. Johnny is also on the ramp and is
holding a solid sphere of radius 12 cm. Rich and Johnny will release their
objects from rest. Assume each of the objects has the same mass and that
each rolls without slipping. From what height would Johnny have to release
his sphere so that it has the same rotational kinetic energy as Rich’s shell at
the bottom of the ramp?
A.
A wrecking ball (weight = 5200 N) is supported by a boom, which
may be assumed to be uniform and has a weight of 3600 N. As the
drawing shows, a support cable runs from the top of the boom to the
tractor. The angle between the support cable and the horizontal is
34°, and the angle between the boom and the horizontal is 46°. Find
the magnitude of the force exerted on the lower end of the boom by
the hinge at point P.
B.
A solid disk rotates at an angular velocity of 0.49 rad/s with respect to an axis perpendicular to the
disk at its center. The moment of inertia of the disk is 0.14 kg Am 2. From above, sand is dropped
straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of
0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place,
what is the angular velocity of the disk?
41.
42.
43.
A.
A CD has a mass of 17 g and a radius of 6.0 cm. When inserted into a player, the CD
starts from rest and accelerates to an angular velocity of 19 rad/s in 0.64 s. Assuming the
CD is a uniform solid disk, determine the net torque acting on it.
B.
Some researchers believe that the dinosaur Brachiosaurus held its head erect on a long
neck, much as a giraffe does. If so, fossil remains indicate that its heart would have been
about 14 m below its brain. Assume that the blood has the density of water, and calculate
the amount by which the blood pressure in the heart would have exceeded that in the
brain.
C.
A small crack occurs at the base of a 16.0 m high dam. The effective crack area through
which water leaves is 1.60 × 10-3 m2. Ignoring viscous losses, how many cubic meter of
water per second leave the dam?
D.
An airplane has an effective wing surface area of 20 m2 that is generating the lift force. In
level flight the air speed over the top of the wings is 61 m/s, while the air speed beneath
the wings is 52 m/s. What is the weight of the plane? (Note: The density of air is
1.29 kg/m3)
A.
A uniform plank of length 4.9 m and weight 203 N
rests horizontally on two supports, with 1.1 m of the
plank hanging over the right support (see the
drawing). What distance x can a person who weighs
455 N walk on the overhanging part of the plank
before it just begins to tip?
B.
A 0.80 m 0.90 m 0.50 m block is suspended from a wire and is completely under
water. The density of the block is 1200 kg/m3. What is the tension in the wire?
C.
A solid disk of radius R = 0.5 m rotates at an angular velocity of 0.37 rad/s with respect
to an axis perpendicular to the disk at its center. The moment of inertia of the disk is
0.12 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a
thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the
ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of
the disk?
A.
A bowling ball encounters a 0.76 m vertical rise
on the way back to the ball rack, as the drawing
illustrates. Ignore frictional losses and assume
that the mass of the ball is distributed uniformly.
If the translational speed of the ball is 5.80 m/s at
the bottom of the rise, find the translational speed
at the top.
B.
A rotating door is made from four rectangular glass panes, as shown
in the drawing. The mass of each pane is 70 kg. A person pushes on
the outer edge of one pane with a force of F = 74 N that is directed
perpendicular to the pane. Determine the magnitude of the door's
angular acceleration.
44.
A.
A mountain climber is repelling down a vertical wall. The rope
is attached to a buckle (25°) and is strapped to the climber’s
waist 15 cm to the right of his center of gravity. The climber
weighs 670 N. The distance from foot to CG is 91 cm and the
distance from foot to waist is 106 cm. He is wearing a
backpack (15.0 kg) with CG 36 cm to the right of his waist.
(a)
(b)
45.
B.
A meat baster consists of a squeeze bulb attached to a plastic tube.
When the bulb is squeezed and released, with the open end of the
tube under the surface of the basting sauce, the sauce rises in the
tube to a distance h, as the drawing shows. It can then be squirted
over the meat. The atmospheric pressure is 1.013 × 105 Pa outside
the tube in the drawing. The density of the basting sauce is 1200
kg/m3. What is the absolute pressure P in the bulb of the basting
tube if h = 0.20 m?
A.
A uniform solid CD has a mass of 15 g and a radius of 6.0 cm. When inserted into a
player, the CD starts from rest and accelerates to an angular velocity of 20 rad/s in 0.45 s.
1.
2.
46.
Find the tension in the rope.
Calculate both the magnitude and direction of the
contact force exerted by the wall on the climber’s feet.
What is the net torque acting on the CD?
How much rotational energy is stored in the CD when t = 0.45 s?
B.
A large dinosaur (Brachiosaurus) is drinking from a river with its neck fully extended.
While drinking, the head is 15 m from the heart at 36.9° below the horizon. Calculate the
amount by which the blood pressure in the brain exceeds that in the heart. Assume that
blood has the density of water.
C.
A small drainage valve sits at the base of a 18.0 m high dam. The effective valve
opening through which water leaves is 2.70 × 10-3 m2 when the valve is open. Ignoring
viscous losses, how many cubic meters of water per second can leave the dam?
D.
A block of birch wood floats in oil with 90% of its volume submerged. The density of
birch is 0.63g/cm3. Determine the density of the oil.
A.
On the crane shown the boom is 3.2 m long and weighs 1200 N. The cable can support a
tension of 10,000N. The cable is attached 0.5 m from the end of the boom.
1.
2.
What is the maximum weight that can be lifted?
What is the force at the base of the boom?
B.
A man holds a 150 N ball in his hand, with the forearm
horizontal (see the drawing). He can support the ball in
this position because of the flexor muscle force M, which
is applied perpendicular to the forearm. The forearm
weighs 22.5 N and has a center of gravity (cg) as
indicated.
1.
2.
47.
A.
The mobile shown here hangs in equilibrium. It consists of objects
held by vertical strings. Object 3 weighs 1.40 N, while each of the
identical uniform horizontal bars weighs 0.50 N
1.
2.
48.
Find the magnitude of M.
Find the magnitude and direction of the force
applied by the upper arm bone to the forearm at
the elbow joint.
Find the weight of object 1 and object 2.
Find the tension in the upper string.
B.
A block with dimensions 0.80 m × 0.90 m × 0.50 m and density
1200 kg/m3 is suspended from a wire and is completely under water.
What is the tension in the wire?
C.
A solid disk of radius R = 0.5 m rotates at an angular velocity of 0.37 rad/s with respect
to an axis perpendicular to the disk and at its center. The moment of inertia of the disk is
0.12 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a
thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the
ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of
the disk?
A.
A solid cylinder (radius = 15.0 cm, height = 12.0 cm) has a mass of 7.00 kg.
The cylinder is floating in water. Oil (ρ = 725 kg/m3) is poured on top of the
water until the situation shown in the drawing results.
1.
2.
3.
B.
How much of the height of the cylinder is in the oil?
When the oil was initially poured in, did the amount of the cylinder
in the water increase, decrease, or remains the same?
Now more oil is added. Does the cylinder rise, drop lower or remain in the same
location?
The moment of inertia for the pulley system shown is I = 1.70 kg·m2,
with r1 = 50 cm, and r2 = 20 cm. The system is initially at rest. What
is the speed of the 2.0 kg mass after it has fallen 1.5 m?
49.
50.
51.
A.
A 1.2 m thick raft (6.0 m × 4.0 m in area) is floating on a river. A loaded car pulls onto
the raft and the raft sinks 3.0 cm lower into the water. What is the weight of the car?
B.
A person who weighs 609 N is riding a 95N mountain bike. Suppose the entire weight of
the rider and bike is supported equally by the two tires. If the gauge pressure in each tire
is 7.10 × 105 Pa, what is the area of contact between each tire and the ground?
C.
An airplane has an effective wing surface area of 12 m2 that is generating the lift force.
In level flight the air speed over the top of the wings is 64 m/s, while the air speed
beneath the wings is 56 m/s. What is the weight of the plane? (Note: Density of air is
1.29 kg/m3.)
D.
A uniform thin rod (length = 0.50 m, mass = 0.2 kg) rotates about its center on a
frictionless tabletop. The rod has an initial angular velocity of 1.0 rad/s. Two bugs (each
has a mass of 4.0 × 10-3 kg) are initially standing at the center. Each bug crawls to an
opposite end of the rod. When the bugs reach the ends of the rod, what is the angular
velocity of the rod?
A.
A water line with an internal radius of 6.50 × 10-3 m is connected to a shower head that
has 22 holes. The speed of the water in the line is 1.2 m/s. At what speed does the water
leave one of the holes (effective radius = 4.6 × 10-4 m) in the head?
B.
Rich is standing at a height (h) of 9 m on the ramp as
shown and he is holding a hollow cylindrical shell of
radius 12 cm. Keyton is also on the ramp and is holding a
solid sphere of radius 12 cm. Rich and Keyton release
their objects from rest. Assume each of the objects has the
same mass and that each rolls without slipping. From
what height would Keyton have to release his sphere so
that both objects have the same angular momentum at the
bottom of the ramp?
A.
A uniform solid disk with a mass of 24.0 kg and a radius of
0.317 m is free to rotate about a frictionless axle. Forces of
90.0, 200.0 and 125 N are applied to the disk, as the
drawing illustrates. What is the magnitude of the angular
acceleration of the disk?
B.
One end of a thin rod is attached to a pivot, about which it can rotate without friction.
Air resistance is absent. The rod has a length of 0.62 m and is uniform. It is hanging
vertically straight downward. The end of the rod nearest the floor is given a linear speed
v0, so that the rod begins to rotate upward about the pivot. What must be the value of v0,
such that the rod comes to a momentary halt in a straight-up orientation, exactly opposite
to its initial orientation?
C.
A ping-pong ball with an average density of 0.325 g/cm3 is released from 1.3 m
underwater. What is its initial acceleration? (Acceleration is a vector.)
52.
53.
54.
A.
A 1340 N uniform beam is attached to a vertical wall at one end and is
supported by a cable at the other end. A W = 1840 N crate hangs from
the far end of the beam. Calculate the force that the wall exerts on the
left end of the beam. (Remember that force is a vector.)
B.
In an adjustable nozzle for a garden hose, a cylindrical plug is aligned along the axis of
the hose and can be inserted into the hose opening. The purpose of the plug is to change
the speed of the water leaving the hose. The speed of the water passing around the plug is
to be 3 times greater than the speed of the water before it encounters the plug. If the plug
has a radius of 1 cm, what is the inside hose radius?
A.
A swimming polar bear climbs onto a piece of floating ice that has a volume of 7.97 m3.
What is the weight of the heaviest bear that the ice can support without sinking
completely beneath the water? The density of ice is 917 kg/m3, and the density of sea
water is 1025 kg/m3.
B.
the human lungs can function satisfactorily up to a limit where the pressure difference
between the outside and inside of the lungs is one-twentieth of an atmosphere. If a diver
uses a snorkel for breathing, how far below the water can she swim? Assume the diver is
in salt water whose density is 1027 kg/m3.
C.
An airplane has an effective wing surface area of 14 m2 that is generating the lift force.
In level flight the air speed over the top of the wings is 64 m/s, while the air speed
beneath the wings is 56 m/s. What is the weight of the plane? The density of air is 1.29
kg/m3.
D.
Two disks are rotating about the same axis. Disk A has a moment of inertia of
.0 kg × m2 and an angular velocity of +7.1 rad/s. Disk B is rotating with an angular
velocity of -9.9 rad/s. The two disks are then linked together without the aid of any
external torques, so that they rotate as a single unit with an angular velocity of -2.5 rad/s.
The axis of rotation for this unit is the same as that for the separate disks. What is the
moment of inertia of disk B?
A.
Water flowing out of a horizontal pipe emerges through a nozzle. The radius of the pipe
is 2.0 cm, and the radius of the nozzle is 0.49 cm. The speed of the water in the pipe is
0.65 m/s. Treat the water as an ideal fluid, and determine the absolute pressure of the
water in the pipe. The atmosphere pressure is P = 1.01 × 105 Pa, and the density of water
is ρ = 1.00 × 103 kg/m3.
B.
Rich is standing at a height (h) of 10 m on the ramp as shown and
he is holding a thin cylindrical shell of radius 12 cm. Johnny is
also on the ramp and is holding a solid sphere of radius 12 cm.
Rich and Johnny will release their objects from rest. Assume each
of the objects has the same mass and that each rolls without
slipping. From what height would Johnny have to release his
sphere so that it has the same translational kinetic energy as
Rich’s shell at the bottom of the ramp?
55.
56.
A.
By means of a rope whose mass is negligible, two blocks are suspended
over a pulley, as shown in the drawing, with m1 = 10.9 kg and
m2 = 42.9 kg. The pulley can be treated as a uniform, solid, cylindrical
disk. The downward acceleration of the 42.9 kg block is observed to be
exactly one-half the acceleration due to gravity. Noting that the tension
in the rope is not the same on each side of the pulley, find the mass of
the pulley.
B.
A long, thin uniform rod is cut into two pieces, one being
twice as long as the other. To the midpoint of piece A (the
longer piece), piece B is attached perpendicularly, in order to
form the inverted "T" shown in the drawing. The application
of a net external torque causes this object to rotate about axis
1 with an angular acceleration of 4.97 rad/s2. When the
same net external torque is used to cause the object to rotate
about axis 2, what is the angular acceleration?
C.
A ball with an average density of 1.325 g/cm3 is released from 1.3 m underwater. What
is its initial acceleration? (Acceleration is a vector.)
A.
A 1340 N uniform beam of length L is attached to a vertical wall at one
end and is supported by a cable at the far end of the beam. A W =
1840 N crate hangs 1/4 L from the far end of the beam as shown.
Calculate the force that the wall exerts on the left end of the beam.
Remember that force is a vector.
B.
A small crack occurs at the base of a 16.0 m high dam. The effective crack area through
which water leaves is 1.30 × 10-3 m2. Ignore viscous losses. How many cubic meters of
water per second leave the dam?