phys 221 test 2
A piece of clay with mass m = 0.01 kg collides with the floor at speed of 8 m/s and sticks. The collision takes 0.02 s. The magnitude of the average force the piece of clay experiences during the collision is
4 N.
An object is dropped from rest at t = 0 into a viscous fluid. Which of the following best describes the object's speed as a function of time?
(b)
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) 0.188 m2, (ii) 3.75*10^9
Two carts on an air track are pushed towards each other. Initially, cart 1 moves in the positive x direction and cart 2 moves in the negative x direction. They bounce off each other elastically. The graphs at the right describe some of the variables associated with the motion as a function of time. For the experiment described and for each item in the list below, identify which graph is a possible display of that variable as a function of time. If none apply, choose N (for none).(i) the momentum of cart 1(ii) the position of cart 1.(iii) the position of cart 2.
(i) D, (ii) B, (iii) N
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?
-226.2/s2
Blood and water have the same contact angle with glass. The density of blood is 5% higher than that of water. (ρblood= 1.05 ρwater)While you make your capillary action measurements you find that water rises in the same tube a factor 1.69 higher than a blood sample. The surface tension of water at the same temperature is 0.073 N/m. What is the surface tension of the blood sample?
0.045 N/m
A 40 kg child standing on a frozen pond throws a 0.5 kg stone to the east with a speed of 5 m/s. Neglecting friction between the child and the ice, what is the recoil velocity of the child?
0.0625 m/s west
A piece of clay with mass m = 0.01 kg collides with the floor at speed of 8 m/s and sticks. The collision takes 0.02 s. The magnitude of the impulse the piece of clay receives in this collision is
0.08 kgm/s2.
A 5.00 kg mass sliding along a horizontal frictionless surface at 2.00 m/s collides with a 1.00 kg stationary mass. After the collision the two masses stick together and contact a light Hooke's-law spring with spring constant k = 1000 N/m. What is the maximum compression (in m) of the spring?
0.13 m
A 65 kg physics student is at rest on a 5 kg sled that also holds a chunk of ice with a mass of 2 kg. The student throws the ice horizontally with a speed of 10 m/s relative to the ground. If the sled slides over a frozen pond without friction, how fast (in m/s) are the sled and student traveling with respect to the ground after throwing the chunk of ice?
0.286 m/s
An intravenous blood plasma drip enters a vein in the patient's arm from a bag raised a height h above the vein. If the diameter of the 5 cm long needle is 0.5 mm, use Poiseuille's law to find the height h that results in a 5 cm3/min flow rate.(Assume the blood pressure in the arm is 18 torr = 2392 Pa and the viscosity of the blood plasma is 1.5*10-3 Pa-s.)
0.66 m
Suppose the flow rate of blood in a coronary artery has been reduced to 0.64 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?
0.894
A certain pump can exert a negative gauge pressure of 12.6 kPa. It is used to suck a liquid out of a bucket up a thin pipe. A 7.6 m column of the liquid exerts a pressure of 100 kPa. To what maximum height ( in m) can the the liquid be sucked up the pipe by this pump?
0.96
A 90 kg man and a 10 kg girl are initially 10 m apart. They are connected by a massless rope, and are sitting on a frictionless horizontal surface. The man pulls on the rope until they meet. Where do they meet?
1 m away from the initial position of the man.
Angular speed is measured in units of s-1, which is rad/s. How many degrees correspond to 1 radian?
1 rad = 57.3 degrees
When the body requires an increased blood flow rate in a particular organ or muscle, it can accomplish this by increasing the diameter of arterioles on that area. By what factor must the diameter of an arteriole increase to double the volume flow rate of blood, all other factors remaining the same?
1.19
Two particles of masses 2 g and 8 g are separated by a distance of 6 cm. The distance of their center of mass from the heavier particle is
1.2 cm
Two fluids have the same contact angle with glass. The density of fluid 1 is larger than the density of fluid 2 . (ρ1 = 1.12 ρ2) The surface tension of fluid 1 is larger than that of fluid 2. (γ1 = 1.8 γ2) Find the ratio h1/h2 of the heights to which a liquid will rise through capillary action in the same capillary tube.
1.61
A hydraulic system is used to lift a 79 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 50 cm2, what is the minimum force that must be applied to lift the motor in units of N?
12.5
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?
15 m/s to the left
A wheel with moment of inertia 0.09 kgm2 rotates about a fixed axis. Its kinetic energy is 1,197 J. What is ts angular speed ω in s-1?
163
A 2 kg block of wood is floating in water. What is the magnitude of the buoyant force acting on the block?
19.6 N
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?
19.7 rad/s
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 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.
2.9
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?
20
A 10^4 N car is lifted by a manually operated hydraulic lift. The area of the shaft of the lift is 80 cm^2; the area of the piston that forces liquid into the system is 2 cm^2. What minimum force must be exerted on this piston to lift the car?
250 N
The angular acceleration of a object with moment of inertia 44 kg m2 about an axis is α = 0.7 s-2. A force is applied a distance 0.12 m from the axis, making an angle θ = 68 degree with the lever arm. What is the magnitude of this force in N?
277
The volume flow rate of water through a horizontal pipe is 1.6 m3/min. Determine the speed of flow (in m/s) at a point where the diameter of the pipe is 9.9 cm.
3.46
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.
465 Pa
Calculate the gauge pressure (in Pa) inside a soap bubble 2.9 cm in radius using the surface tension γ = 0.036 N/m for the solution. Enter a number with one digit behind the decimal point.
5
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?
5.65 rad/s2
You can chew through very tough objects with your incisors because they exert a large force on the small area of a pointed tooth. What pressure in MPa can you create by exerting a force of 500 N with your tooth on an area of 1.00 mm2? Enter an integer.
500
A beaker containing 5.0 kg of water is on a weighing scale. A 0.8 kg block of metal that has density 8*103 kg/m3 that is attached to a string is lowered completely into water without touching the bottom. Assume that the beaker is massless, and water has density 103 kg/m3, and g = 10 m/s2.What is the reading on the scale?
51 N
A CD spins at 5500 rpm (revolutions per minute). What is its angular speed in units of rad/s or s-1?
576
A wheel starts from rest with constant angular acceleration α. It requires 2.5 s to make 29 revolutions. What is its angular acceleration α in s-2?
58.3
A 9 kg object is placed on a 131 cm2 platform. What is the pressure the object exerts on the platform in N/m2?
6,733
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?
6.2 MPa
A horizontal pipe, 10 cm in diameter, has a smooth reduction to a pipe 5 cm in diameter. If the pressure of the water in the larger pipe is 8.00*104 Pa and the pressure in the smaller pipe is 6.00*104 Pa, what is the flow speed of the water (in m/s) in the smaller pipe?
6.53 m/s
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
A 50 g meter stick lies on the x-axis with its left edge (the 0 cm mark) at the origin. A 75 g mass is attached to the stick at x = 80 cm and a 12 g mass is attached at x = 10 cm. Find the x-coordinate of the center of mass of the system in cm.
62.9
A block of a plastic material floats in water with 79.6% of its volume under water. What is the density of the block in kg/m3?
796
A ball (mass 0.10 kg) is initially moving to the left at 40 m/s. After hitting the wall, the ball is moving to the right at 40 m/s. What is the impulse of the ball receives during its collision with the wall?
8 kg m/s to the right
A centrifuge starts from rest. Its angular acceleration α is constant for 15 s.Its final angular speed is ω = 233 revolutions per second.What is its angular acceleration α in units of s-2?
97.6
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
Consider two carts, of masses m and 2m, at rest on an air track.You push on each cart for 3 s, exerting equal force Fnet on each.
After the push, the momentum of mass m is the same as the momentum of mass 2m.
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 have heard the tried and true phrase "it is like running in to a brick wall". Now it is time to dig a little deeper and modify the phrase. Assume you are in a car driving and come in contact with this proverbial brick wall. Your car can do three things after the strike: it can go through, come to stop or bounce back. Select the option which will be the most dangerous to you assuming similar collision times.
Bouncing back.
A disk is spinning with angular velocity ω as shown. It begins to speed up. While it is speeding up, what are the (i) directions of its angular velocity ω (ii) and its angular acceleration α?
C, C
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. into the paper
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.
FB = 5 mg
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.
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
Suppose you are riding on a merry - go - round and you move out to the edge. What happens to the rotational rate of the system?
It decreases because angular momentum is conserved and the moment of inertia increases.
The fundamental dimensions of pressure are
M L-1 T-2
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 objects with masses m1 and m2, respectively, are initially at rest, and then are acted on by the same net force F for the same amount of time ∆t. If m2 = 4m1, which object will have the largest kinetic energy?
Object 1 with mass m1.
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.
Consider a rod of uniform density with an axis of rotation through its center and an identical rod with the axis of rotation through one end. Which has the larger moment of inertia about its axis of rotation?
Rod B with the axis through one end.
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.
Determine the character of the collision. The masses of the blocks, and the velocities before and after are given.
The collision is not possible because momentum is not conserved.
A bass has a gas-filled sac or air bladder that allows it to float motionless below the surface of the water. What is the bass's average density?
The density of water.
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.
Suppose that there is a partial blockage of the aorta, which normally pumps about 5 L of blood per minute. If the diameter of the aorta were reduced by 30%, what increase in blood pressure gradient would be needed to obtain the normal flow rate? (Assume that Poiseuille's law applies.)
The pressure gradient would have to increase by a factor of 4.2.
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.
During a July 4th firecracker party, a pop bottle rocket lying still on the ground explodes, sending fragments everywhere. If the momentum of the pop bottle rocket (ignore friction!) initially at rest is conserved during an explosion, what can be said about the kinetic energy of various fragments after the collision?
The total kinetic energy afterwards is greater than what it was initially.
Two carts collide on a nearly frictionless track. (See lab 6, experiment 3.)Cart 1 has mass m1 = 2 kg and cart 2 has mass m2 = 1 kg. For the velocities of the carts before and after the collision we obtain the following data. v1i = 8 cm/s and v2i = -3 cm/s. v1f = 4.334 cm/s and v2f = 4.334 cm/s. To within 1% uncertainty, which of the statements below are true?
The total momentum of the two carts is conserved.
Which of the following assumptions is not made in the derivation of Bernoulli's equation?
There is negligible gravity.
A pocket watch and Big Ben are both keeping perfect time. Which minute hand has the larger angular speed ω?
They both have the same ω.
A boat floating in a lake contains a block of volume V0. The density of the block is 5000 kg/m3. If the block is thrown overboard, the volume of the water displaced by the block is
V0
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 keeps on gaining speed.
Detergents or wetting agents
reduce the angle of contact.
A drum major is given two batons, one gold and one plastic. He is told that both batons have the same mass. He tries spinning each one and finds that the plastic one is much easier to start and stop spinning. He correctly concludes that the plastic baton, in comparison to the gold baton
has more of its mass distributed towards the center.
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
Two identical carts labeled A and B are initially resting on an air track. The coordinate system for describing the system is shown. The cart on the right, cart B is given a push to the left and is released. The clock is then started. At t = 0, cart B moves in the direction shown with a speed v0. They hit and stick to each other. The graphs below describe some of the variables associated with the motion as a function of time. For the experiment described and for each item in the list below, identify which graph is a possible display of that variable as a function of time assuming a proper scale. "The system" refers to carts A and B together. (i) the momentum of cart A(ii) the momentum of cart B(iii) the total momentum of the system(iv) the total kinetic energy of the system
i) #1, (ii) #3, (iii) #6, (iv) #2
When the kinetic energy of a moving object increases by a factor of 16, the magnitude of its momentum
increases by a factor of 4.
Dimples on a golf ball hit without spin
reduce drag.
Blood is called a complex fluid because
its viscosity depends on the velocity of the flow,
The SI units for viscosity are
kg/(m-s)
A radioactive nucleus of mass M moving along the positive x-direction with speed v emits an α-particle of mass m. If the α-particle proceeds along the negative x-direction, the centre of mass of the system (made of the daughter nucleus and the α-particle) will
move along the positive x-direction with speed equal to v.
A person sips a drink through a straw. At which of the following three positions is the pressure lowest?I. Inside the person's mouthII. At the surface of the drinkIII. At the bottom of the drink
only at position I
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
You can balance a broom on your hand if you're careful. To do this trick well, you must look at
the broom's center of gravity.
It is correct to say that impulse is equal to
the change in momentum.
A baseball bat with uniform density is cut at the location of its center of mass as shown in the figure. The piece with the smaller mass after the cut is
the piece on the left.
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.
Two objects with different masses collide and stick to each other. Compared to before the collision, the system of two objects after the collision has
the same total momentum but less total kinetic energy
When blood flows into an aneurysm
the speed decreases and the pressure increases.
A scuba diver descends to a depth of 20 m. At that depth, the pressure is approximately
three times atmospheric pressure.
The graph shows the acceleration of a cart with mass m = 0.555 kg, moving initially with constant speed, as a function of time, as a force F = ma stops the cart. Estimate the initial momentum of the cart in units of kgm/s.
~0.6
The four things that affect the amount of water flowing through a hose are
water viscosity, hose length, inlet and outlet pressure difference, and hose diameter.
A man jumps off of a bridge towards a river below. As he falls, he feels himself spinning forward (clockwise in diagram).To keep from hitting the water head-first, the man should
windmill his arms clockwise to keep upright.
Suppose you have a very long straw that can reach from a cup of water on the ground level to the top of a very tall building. When you use a pump to suck on the straw in order to bring water up,
you can bring the water up to only a maximum height in the straw, when the pressure of the water column is approximately equal to the atmospheric pressure.
A small wheel and a large wheel are connected by a belt. The small wheel is turned at a constant angular speed ωs. How does the angular speed of the large wheel ωL compare to that of the small wheel?
ωs > ωL