Physics 221 Exam 2 Homework Questions
Suppose the flow rate of blood in a coronary artery has been reduced to 0.645 times its normal value by plaque deposits, and that the pressure difference across the artery has not changes. By what factor has the radius of the artery been reduced, assuming no turbulence occurs?
(0.645)^1/4 0.896
The diameter of a pipe is tripled while the pressure difference across the pipe remains the same. The volume flow rate of the pipe increases by a factor of
(3)^4 81
Modeling a meter stick as a forearm, compare the force FB that the biceps has to exert to keep the forearm horizontal to the weight of the forearm FW = mg. Let d = 10 cm and the distance from where the biceps muscle attached to the center of mass be d' = 40 cm
(40+10)/10 FB = 5 mg
A CD spins at 5500 rpm (revolutions per minute). What is its angular speed in units of rad/s or s-1?
(5500rev/min)(2*pi rad/1 rev)(1 min/60s) =576
The radius of the aorta is ~ 10 mm = 10-2 m and the blood flowing through it has a speed ~ 300 mm/s = 0.3 m/s. A capillary has a radius ~ 4×10-3 mm = 4×10-6 m, but there are literally billions of them. The average speed of blood through the capillaries is ~ 5×10-4 m/s. (i) Calculate the effective cross sectional area of the capillaries and(ii) the approximate number of capillaries.
(i) A1V1=A2V2 A1=(3.14*10^-2)^2*(0.3)/(5*10^-4) =*0.188m2* (ii)N=A1/pir2 (0.188)/(3.14)(4*10-6)^2 =*3.75*10^9*
A fan rotating with an initial angular velocity of 1000 rev/min is switched off. In 2 seconds, the angular velocity decreases to 200 rev/min. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time?
*need angular acceleration to find revolutions* w=wo+at 200=1000+a(2/60) a=-24000rev/min^2 revolutions=wot+1/2at^2 =1000(2/60)-(0.5)(-24000)(2/60)^2 *=20*
An object rotates initially with a period of 1.0 s. It accelerates with constant angular acceleration for 10 s. Its final rotation period is 0.1 s.What was the magnitude of its angular acceleration?
1.0 period= 2*3.14/1.0= 6.28 rad/s 0.1 period=2*3.14/0.1= 62.8 rad/s a=Wf-Wi/t a=62.8-6.28/10s =*5.65 rad/s2*
You live in an apartment directly above an open-air tavern and you possess a really, really long and sturdy straw. You plan to steal beer by leaning out of your apartment window and, when the beer-drinkers are not looking, sticking your straw into beer glasses and sucking on the straw. Assuming you can create a perfect vacuum when you suck on the straw, for this plan to have a chance of working, the height difference between you and the beer must be less than approximately what distance? (Assume the density of beer is equal to the density of water and the pressure is 1 atm = 101 kPa.)
10 m
You are bored during the summertime when school is not in session and you decide to do an experiment where you compare the properties of water and air. If the density of air is 1.25 kg/m3 and the density of water is 1000 kg/m3, what volume of air weighs the same as 1 liter (10-3 m3) of water?
1000/1.25=800 liters
A 1 kg rock is suspended by a massless string from one end of a meter stick at the 0 cm mark. What is the mass m suspended from the meter stick at the 75 cm mark if the system is balanced?
2 kg
A 2 kg block of wood is floating in water. What is the magnitude of the buoyant force acting on the block?
2kg*9.8 m/s^2 19.6 N
Substance A has a density of 3.0 g/cm3 and substance B has a density of 4.0 g/cm3. In order to obtain equal masses of these two substances, the ratio VA/VB of the volume of A to the volume of B has to be equal to
4:3
A 2 kg mass is at x = 0 m, y = 2 m, and a 3 kg mass is at x = 2 m, y = 0 m. The x- and y-coordinates, respectively, of the center of mass of this system are
6/5 m, 4/5 m
Fluid is flowing from left to right through the pipe. Points A and B are at the same height, but the cross-sectional areas of the pipe differ. Points B and C are at different heights, but the cross-sectional areas are the same. Rank the pressures at the three points, from highest to lowest.
A,B,C
A nozzle with a radius of 0.17 cm is attached to a garden hose with a radius of 1.03 cm. If the speed of the water in the hose is 1.62 m/s, what is the speed of the water in the nozzle in m/s?
A1V1=A2V2 A=3.14r^2 V1=A2V2/A1 V1=(1.03)^2(1.62)/(0.17)^2 (10-2 cancels out when converting radius) V1=59.47 59.47
A 50 kg woman balances on one heel of a high-heel shoe. If the heel is circular with radius 0.5 cm, what pressure does she exert on the floor?
A=PiR^2 F=mg P=F/A F=(50)(9.8)=490 A=(3.14)(0.005)^2=0.0000785 P=(490)/(0.0000785)=6242038 Pa=6.24 Mpa
The picture below shows 5 blocks. The blocks have equal volumes but different masses. The blocks are placed in an aquarium tank filled with water and blocks 2 and 5 come to rest as shown in the figure. Which answer is correct
Block 3 will come to rest in the same position as block 5.
You need to loosen a very tight bolt. You have one wrench and you exert maximum force. Which configuration shown below gives you maximum chance of success?
C(has no angle written in description)
An object moves with constant speed in the clockwise direction along the circular path shown below.At the point indicated by the black dot, in which direction is the angular velocity vector ω pointing?
D
A 500 N weight sits on the small piston of a hydraulic machine in equilibrium. The small piston has area 2.0 cm2. If the large piston has area 40 cm2, how much weight does the large piston support?
F1/A1=F2/A2 solve for F2 (500)/(0.02m)=F2(0.4m) 0.4*500/0.02=F2 F2=10000 N
A 26 kg object is placed on a 114 cm2 platform. What is the pressure the object exerts on the platform in N/m2? Let g = 9.8 m/s2
F=MG, Pressure= F/Area F=(26)(9.8)= 254.8 Area=114 cm^2=0.0114 m^2 Pressure=254.8/0.0114 =22,350
Let g = 9.8 m/s2. A hydraulic system is used to lift a 70 kg motor in a garage. If the motor sits on a piston of area 0.31 m2, and a force is applied to a piston of area 86 cm2, what is the minimum force that must be applied to lift the motor in units of N?
F=mg; P=F/A F=(70)(9.8)=686 F1/A1=F2/A2 solve for F2 (686/0.31)=(F2/0.0086) F2=(686*0.0086)/0.31 F2=19.03N
A 26 kg object is placed on a 187 cm2 platform. What is the pressure the object exerts on the platform in N/m2? Let g = 9.8 m/s2.
F=mg; P=F/A F=(26)(9.8)=254.8 P=(254.8)/(0.0187m^2) =13,625
In soap box car races, the cars are boxes with wheels. They begin at rest at the top of a hill, and at the start of the race they all begin rolling down the hill. The soap box car that reaches the bottom of the hill first is the winner. You have entered a soap box car race where the rule is that all the wheels and cars must have equal mass. Since you have taken Physics, you know that it is worse to have wheels with spokes (where the mass is mostly on the rim) rather than solid wheels because
Given the same torque, the wheels with spokes have a higher rotational mass or moment of inertia and therefore will have a smaller angular acceleration.
Two masses are located on the x-axis. Mass m1 = 4 kg is located at x = -50 cm and mass m2 = 6 kg is located at x = 20 cm. What is the moment of inertia of the system about the z-axis in units of kgm2.
I=MR^2 I=M1R1^2+M2R2^2 I=(4kg)(-0.5m)^2+(6kg)(0.2)^2 *I=1.24*
Consider two masses, each of size 2m at the ends of a light rod of length L with the axis of rotation through the center of the rod. The rod is doubled in length and the masses are halved. Compare IA and IB.
IA < IB
A wheel with moment of inertia 0.07 kgm2 rotates about a fixed axis. Its kinetic energy is 779 J. What is ts angular speed ω in s-1?
KE=1/2Iw^2 I=0.07 kgm^2 KE=779J W=? w=squareroot[(2*779)/0.07)] *w=47.5 rad/s*
A 3.5 kg object has kinetic enery 9,254 J. What is the magnitude of its momentum (in kg m/s)?
KE=P^2/2m P^2=KE(2m) P^2=(9254J)(2*3.5) P^2=64778 *P=254.5*
Consider a 100 kg father and his 20 kg girl. They decide to enjoy balancing on a seesaw, which is a uniform board 4 m long and pivoted exactly at its center. If girl sits at the seesaw's end (2m from the center), how far from the center on the other side should the father sit?
Mf*Rf=Md+Rd Rf=MdRd/Mf Rf=(20kg*2m)/100 kg *0.4 m*
Consider the earth spinning from west to east on its axis. It is slowing down in its rotation due to friction with the air. Using the right hand rule, in what direction is the frictional torque?
N pole to S pole
Two moving objects have masses m1 and m2, respectively. If m2 = 4m1, and both have the same kinetic energy, which has more momentum?
Object 2 with mass m2.
Which of the following statements is false?
Plaque deposit on an artery or arteriole wall causes an increase in local blood pressure and can lead to bursting of that vessel.
A DVD is rotating with an ever increasing speed. How do the angular velocity, angular acceleration, tangential velocity, and tangential acceleration compare at points P and Q?
Points P and Q have the same angular velocity and the same angular acceleration.
In a stationary homogeneous liquid near the surface of Earth, which of the following is true?
Pressure is the same at all points at the same height.
Blood is pumped from the heart at a volume flow rate of 5.0 liter/min into the aorta (of radius 1.0 cm). Determine the speed of blood through the aorta.
Q=AV V=Q/A Q=5L/min--> (1min/60sec)(1000cm3/1L)=83.3 cm3/sec V=83.3/(3.14)(1)^2 =26.5 cm/s
The volume flow rate of water through a horizontal pipe is 2.5 m3/min. Determine the speed of flow (in m/s) at a point where the diameter of the pipe is 10.6 cm.
Q=VA V=Q/A A=(3.14)(0.053)^2=0.00882 Q=2.5m3/min*(1min/60sec)=0.0416 m3/sec V=0.0416/0.00882 =4.72
Suppose you are changing a car tire and loosening a lug nut. You weigh 800 N and stand on the end of a horizontal 2 m long wrench. How much torque do you exert on the lug nut?
T=FR T=(800N)(2m) 1600 Nm
A block and a rod are joined together. Each object is of uniform density. The center of mass of the combined object is at the position shown by the "X."Which has the greater mass, the block or the rod?
The block has the greater mass.
An ideal, non-compressible fluid is used in the system of pipes shown below. The cross sectional area of pipe 1 is 4 m2, that of pipe 2 is 3 m2, and that of pipe 3 is 2 m2. The fluid enters pipe 1 at 2 m/s, and leaves pipe 2 at 3 m/s. What is the speed of the fluid in pipe 3 and in which direction does it flow?
The fluid leaves pipe 3 (downward) with speed 0.5 m/s.
Which of the following assumptions is not made in the derivation of Bernoulli's equation?
There is negligible gravity.
Why do elastic balls bounce so well?
They store energy through compression, like a spring.
Suppose you are on a cart, initially at rest on a frictionless, horizontal track. You throw a series of identical balls against a wall that is rigidly mounted to the cart. If the balls are thrown at a steady rate and bounce straight back, is the cart put into motion?
Yes, it starts to move to the left and steadily gains speed.
Suppose you work in the E.R. and a choking patient comes in with their trachea half obstructed. (The diameter is half of what it was before the obstruction.) You manage to correct the problem and send them on their way safely, explaining that such obstructions are particularly dangerous because
a half - blocked airway passes only 1/16 the regular amount of air.
The shape of a droplet of liquid on a surface is due to a combination of
adhesion and cohesion
The vessels shown below all contain water to the same height.Rank them according to the pressure exerted by the water on the vessel bottoms, least to greatest.
all pressures are the same
The left tip of a wind turbine blade accelerates upward, as you view it. By the right-hand rule, the torque on the wind turbine is pointing
away from you
In SI units, what is the change in the magnitude of the momentum of a 1,713 kg car that accelerates uniformly along a straight line from a speed of 3 m/s to a speed of 18 m/s in 7 s?
change in momentum= m(change in v) so time does not matter in this situation =1713kg(18-3) =25,695 kg(m/s)
Suppose the circumference of a bicycle wheel is 2 m. If it rotates at 1 revolution per second when you are riding the bicycle, then your speed will be
circumference=2piR 2=2*3.14*R R=1/3.14=0.318 m speed=distance/time speed=(2*3.14)*(R/3.14) pi cancels out speed=2m/s
A boat is floating in a lake. Since it is floating the buoyant force acting on the boat must be
equal to its weight
The volume flow rate of water through a horizontal pipe is 3.8 m3/min. Determine the speed of flow (in m/s) at a point where the diameter of the pipe is 10.7 cm.
flow rate=A1V1 3.8m3/min*( 1 min/60s)=0.0633 m3/sec radius=10.7/2= 5.35 cm=0.0535 m V1=flow rate/A A=3.14(0.0535m)^2 V1=0.0633/0.00898 =7.04
Suppose you have two containers with liquid in them. One has a density of 760 kg/m3 and the other has a density of 910 kg /m3. If an object floats in one container and sinks in the other, the density of the object
has a value between 760 kg/m3 and 910 kg/m3.
During a football game the ball is kicked and it travels across the field. If the ball is kicked away from its center of mass it will
have translational and rotational motion
A man, with his arms at his sides, is spinning on a light frictionless turntable.When he extends his arms
his angular momentum remains the same.
Flowing honey is less likely to become turbulent than flowing water because
honey's large viscosity favors laminar flow
If a viscous fluid flows steadily in a pipe, the fluid speed
is least near the pipe wall but increases toward the center.
The SI units for viscosity are
kg/(ms)
Water pours gently from an open hose because it
lost energy throughout its trip to the hose end.
A 1.3 kg toy car moving in the positive x direction with speed 5.4 m/s hits a toy car of equal mass moving in the positive y-direction with speed of 2.2 m/s. If the collision is perfectly inelastic, calculate the speed of the cars (in m/s) right after the collision.
m1=1.3 v1=5.4 m2=1.3 v2=2.2 M1v1+m2v2=(M1+M2)Vf; solve for Vf v= (1.3)(5.4)+(1.3)(2.2)/(1.3+1.3) Vx=7.02/2.6 Vy=2.86/2.6 v= squareroot(2.7)^2+(1.1)^2 *v=2.92*
Two blocks of mass M and 3 M are placed on a horizontal frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them. A cord holding them together is burned, after which the block of mass 3 M moves to the right with a speed of 5 m/s. What is the speed of the block of mass M?
m1v1=m2v2 v1=(m2v2)/m1 v1=(3)(5)/1 15 m/s to the left(goes to side that is least)
The quantities remain constant in an inelastic collision are
momentum, but neither kinetic energy nor temperature.
In SI units, what is the magnitude the net force acting on a 1,003 kg car that accelerates uniformly along a straight line from a speed of 4 m/s to a speed of 17 m/s in 6 s?
net force=(change in momentum)(change in velocity)/ time net force=(1003 kg)(13 m/s)/ 6 s =2,173
Mercury has an unusually large surface tension γ = 0.465 N/m. Calculate the excess pressure inside a drop of mercury 4 mm in diameter
pressure= 2(Surface tension/radius) diameter=4 mm=0.004 m radius=0.004/2=0.002 m Pressure =2(0.465/0.002) =465 Pa
Rockets receive their forward propulsion through
pushing against the exhaust
A bicycle's wheels have a radius of 33 cm. The bicycle is traveling at a speed of 6.5 m/s. What is the angular speed of the front tire?
r=33 cm=0.33 m v=6.5 m/s w=v/r w=6.5/0.33 *19.7 rad/s*
A skater who is spinning and throws her arms out slows down because
she makes her rotational mass or moment of inertia bigger.
Two cars move towards each other on a frictionless road as shown in the sketch below.The two cars collide and immediately come to a standstill.During the collision, the total momentum of the two vehicles will
stays constant
One kilogram of iron (density ~7.8 gm/cm3) and 1 kilogram of aluminum (density ~2.7 gm/cm3) are dropped into a pool. Which is acted on by the largest buoyant force?
the aluminum
It is correct to say that impulse is equal to
the change in momentum
After clearing the bar on a high jump, you land softly on a giant mattress. Landing on a mattress is more comfortable than landing on a sand heap of equal size because
the force the mattress exerts on you to stop your descend is much less than the force the sand heap would exert on you.
It is possible for two objects of equal mass to have different moments of inertia about the same axis because
the moment of inertia depends on the total mass and the mass distribution.
If you dangle two pieces of paper vertically a few inches apart and blow air between them
the papers will move together because the increased velocity reduces the pressure between the papers.
Blood flows through a section of a horizontal artery that is partially blocked by a deposit along the artery wall. A hemoglobin molecule moves from the narrow region into the wider region. What happens to the pressure acting on the molecule as it moves from the narrow to the wider region?
the pressure increases
A beaker is filled with water to the rim. Gently you place a toy duck in the beaker and some of the water spills out. The duck floats. The weight of the beaker with the duck floating in it is
the same as its weight before adding the duck.
Suppose you have an aquarium. You have a solid plastic decoration and a rock of about the same volume but the rock has twice the mass. Both are totally submerged in the water. The buoyant force on the plastic object is about
the same as that on the rock.
Compared to a gear tooth on the rear sprocket (on the left, of small radius) of a bicycle, a gear tooth on the front sprocket (on the right, of large radius) has
the same linear speed and a slower angular speed.
When blood flows into an aneurysm
the speed decreases and the pressure increases.
A centrifuge starts from rest. Its angular acceleration α is constant for 20 s.Its final angular speed is ω = 160 revolutions per second.What is its angular acceleration α in units of s-2?
w0= 0 wf=160 rev/s(2)(3.14)=1004.8rad/s t=20 s wf=w0+at a=wf-w0/t a=1004.8rad/s-0/20s a=50.24rad/s^2
A centrifuge in a medical laboratory rotates at an angular speed of 3600 rev/min. When switched off, it rotates 50 times before coming to rest. What is the constant angular acceleration of the centrifuge?
w^2=w0^2+2a(theta or angle) w=(3600 rev/min)(2pi*rad/1rev)(1min/60s)=376.8rad/s theta=50 rev(2pi*rad)=314 rad a=w^2-w0^2/2(theta) a=(0)^2-(376.8)^2/(2*314) *-226.3rad/s^2*
Two carts A and B are moving towards each other as shown in the diagram. They collide and come to rest at the point of impact. From this observation we can conclude that the carts
were moving with momenta equal in magnitude and opposite in direction.