Exam 3 Questions
A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800. An 80.0-kg bucket of concrete is suspended from the top rung of the ladder, right next to the wall, as shown in the figure. What is the magnitude of the friction force that the floor exerts on the ladder? A) 538 N B) 706 N C) 1290 N D) 833 N E) 601 N
A
A 6.1-kg solid sphere, made of metal whose density is 2600 kg/ m3, is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid. A) 1500 kg/m3 B) 1400 kg/m3 C) 1300 kg/m3 D) 1200 kg/m3 E) 1100 kg/m3
A
A 7.8-kg solid sphere, made of metal whose density is 2500 kg/m3, is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m3), what is the tension in the cord? A) 46 N B) 61 N C) 76 N D) 92 N E) 110 N
A
A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm3 and that of water is 1000 kg/m3. A) 6.6 cm B) 37 cm C) 131 cm D) 79 cm
A
A horizontal tube consists of a 7.0-cm-diameter pipe that narrows to a 2.0-cm-diameter throat. In the pipe, the water pressure is twice atmospheric pressure and the water flows with a speed of 0.40 m/s. What is the pressure in the throat, assuming that the water behaves like an ideal fluid? The density of water is 1000 kg/m3, and atmospheric pressure is 1.01 × 105 Pa. A) 1.9 atm B) 0.12 atm C) 2.1 atm D) 2.0 atm
A
A paint sprayer pumps air through a constriction in a 2.50-cm diameter pipe, as shown in the figure. The flow causes the pressure in the constricted area to drop and paint rises up the feed tube and enters the air stream. The speed of the air stream in the 2.50-cm diameter sections is 5.00 m/s. The density of the air is 1.29 kg/m3, and the density of the paint is 1200 kg/m3. We can treat the air and paint as incompressible ideal fluids. What is the maximum diameter of the constriction that will allow the sprayer to operate? A) 8.07 mm B) 4.05 mm C) 12.2 mm D) 9.65 mm E) 14.3 mm
A
A steel rod 55 cm long has a diameter of 30 cm. The compressive strength (the maximum stress it can support without breaking) of this steel is 500 × 106 N/m2. What is the compression force that would break the rod? A) 3.5 × 107 N B) 2.4 × 107 N C) 1.4 × 108 N D) 4.7 × 108 N E) 8.9 × 108 N
A
A stepladder consists of two halves, hinged at the top, and connected by a tie rod that keeps the two halves from spreading apart. In this particular instance, the two halves are 2.50 m long, the tie rod is connected to the center of each half and is 70.0 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in the figure. Neglecting the weight of the ladder, and assuming that the ladder is resting on a smooth floor, what is the tension in the tie rod? Note: To solve this problem you must "cut" the ladder in half and consider the equilibrium of forces and torques acting on each half of the ladder. A) 140 N B) 240 N C) 280 N D) 360 N E) 560 N
A
A uniform sign is supported against a wall at point P as shown in the figure. If the sign is a square 0.40 m on a side and its mass is 4.0 kg, what is the magnitude of the horizontal force that the wall at P experiences? A) 20 N B) 0.00 N C) 7.8 N D) 98 N
A
As shown in the figure, a container has a vertical tube, whose inner radius is 32.00 mm, connected to it at its side. An unknown liquid reaches level A in the container and level B in the tubelevel A being 5.0 cm higher than level B. The liquid supports a 20.0-cm high column of oil, between levels B and C, whose density is 460 kg/m3. What is the density of the unknown liquid? A) 1800 kg/m3 B) 2000 kg/m3 C) 1400 kg/m3 D) 1600 kg/m3 E) 1700 kg/m3
A
Consider a very small hole in the bottom of a tank 20.0 cm in diameter filled with water to a height of 50.0 cm. Find the speed at which the water exits the tank through the hole. A) 3.13 m/s B) 9.80 m/s C) 31.8 m/s D) 34.9 m/s
A
In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m3? A) 4.00 kPa B) 7.50 kPa C) 5.82 kPa D) 6.42 kPa E) 4.61 kPa
A
One of the dangers of tornados and hurricanes is the rapid drop in air pressure that is associated with such storms. Assume that the air pressure inside of a sealed house is 1.02 atm when a hurricane hits. The hurricane rapidly decreases the external air pressure to 0.910 atm. A square window in an outside wall of the house measures 2.02 m on each side. What net force (directed outwards) is exerted on this window? (1 atm = 1.01 × 105 Pa.) A) 4.53 × 104 N B) 5.14 × 104 N C) 4.78 × 105 N D) 5.37 × 105 N
A
Tensile train is A) the ratio of the change in length to the original length. B) the stress per unit area. C) the same as force. D) the applied force per cross-sectional area. E) the ratio of stress to elastic modulus. Answer: A
A
The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 1010 Pa. What is the sheer stress on the block? A) 180 × 106 N/m2 B) 360 × 106 N/m2 C) 600 × 106 N/m2 D) 720 × 106 N/m2 E) 900 × 106 N/m2
A
The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m3. The manometer contains incompressible oil with a density of 820 kg/m3. What is the difference in elevation h if the manometer reading m is 25.0 cm? A) 0.045 m B) 0.025 m C) 0.065 m D) 0.115 m E) 0.205 m
A
Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was 36m/s, what is its speed in this smaller section? A) 49 m/s B) 42 m/s C) 31 m/s D) 27 m/s
A
What is the maximum length of a metal cable that can hang vertically supported from one end of the cable? The Young's modulus of this metal is 2.10 × 1011 N/m2, its tensile strength (the maximum tensile stress it can support without breaking) is 7.40 × 108 N/m2, and its density is 7.60 × 103 kg/m3. A) 9.94 km B) 4.22 km C) 456 km D) 1.75 km E) 24.8 km
A
A copper sphere has a radius of 2.50 m under normal room pressure of 1.0 × 105 N/m2. If we increase the pressure on this sphere to 10 times the normal room pressure, what is the change in its volume? The bulk modulus for copper is 1.4 × 1011 Pa.
-4.2 × 10-4 m3
An aluminum wire and a steel wire, each of length 2.0 m, are hung from the ceiling. A 5.0-kg mass is suspended from the lower end of each wire. The aluminum wire has a diameter of 2.2 mm. What must be the diameter of the steel wire if it is to stretch the same distance as the aluminum wire, so that the two wires maintain equal lengths after the masses are attached? Young's modulus for aluminum is 0.70 × 1011 N/m2 and for steel it is 2.0 × 1011 N/m2.
1.3 mm
A steel guitar string with a diameter of 0.300 mm and a length of 70.0 cm is stretched by 0.500 mm while being tuned. How much force is needed to stretch the string by this amount? Young's modulus for steel is 2.0 × 1011 N/m2.
10.1 N
A light board, 10 m long, is supported by two sawhorses, one at one edge of the board and a second at the midpoint. A small 40-N weight is placed between the two sawhorses, 3.0 m from the edge and 2.0 m from the center. What forces are exerted by the sawhorses on the board?
16 N at the end and 24 N at the midpoint
In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m3) that is 3.0 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be 5.0 × 104 Pa? The density of the oil is 510 kg/m3.
4.1 m
When the pressure applied to an unknown liquid is increased from 1.0 × 107 N/m2 to 5.5 × 107 N/m2, the volume of the liquid decreases by 0.70%. Calculate the bulk modulus of the liquid.
6.4 × 109 N/m2
In the figure, a 10.0-m long bar is attached by a frictionless hinge to a wall and held horizontal by a rope that makes an angle θ of 53° with the bar. The bar is uniform and weighs 39.9 N. How far from the hinge should a 10.0-kg mass be suspended for the tension T in the rope to be 125 N?
8.15 m from the hinge
A 1000-kg object hangs from the lower end of a steel rod 5.0 m long that is suspended vertically. The diameter of the rod is 0.80 cm and Young's modulus for the rod is 210,000 MN/m2. What is the elongation of the rod due to this object? A) 1.2 cm B) 0.46 cm C) 0.12 cm D) 1.8 cm E) 0.047 cm
B
A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? (For purposes of this problem, you can neglect the weight of the pistons.) A) 727 N B) 926 N C) 2900 N D) 3330 N E) 1.20 kN
B
A 30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0-kg child sits on the other end. The beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. How long is the beam? A) 2.12 m B) 1.98 m C) 1.93 m D) 2.07 m E) 2.20 m
B
A 50-cm3 block of wood is floating partially submerged in water, and a 50-cm3 block of iron is totally submerged in water. Which block has the greater buoyant force on it? A) the wood B) the iron C) Both have the same buoyant force. D) The answer cannot be determined without knowing the densities of the blocks.
B
A barge is 15.0 m wide and 75.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density 1000 kg/m3? A) 22.6 MN B) 13.2 MN C) 1.35 MN D) 1.13 MN E) 11.3 MN
B
A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m3. The board is floating partially submerged in water of density 1000 kg/m3. What fraction of the volume of the board is above the surface of the water? A) 0.350 B) 0.650 C) zero D) 0.200 E) The answer depends on which edge of the board is vertical.
B
A certain coin has a diameter of 21.21 mm, a thickness of 1.95 mm, and weighs 0.04905 N. What is its density? A) 29.1 × 103 kg/m3 B) 7.26 × 103 kg/m3 C) 9.25 × 103 kg/m3 D) 2.31 × 103 kg/m3 E) 71.2 × 103 kg/m3
B
A cubical box, 5.00 cm on each side, is immersed in a fluid. The gauge pressure at the top surface of the box is 594 Pa and the gauge pressure on the bottom surface is 1133 Pa. What is the density of the fluid? A) 1000 kg/m3 B) 1100 kg/m3 C) 1220 kg/m3 D) 2340 kg/m3 E) 12,000 kg/m3
B
A dump truck has a large cubical concrete block in its bed. The coefficients of friction between this block and the floor of the bed are µk = 0.450 and µs = 0.650. As the bed is slowly tilted above the horizontal, will the brick first begin to slide or will it first tip over? A) It will first tip over. B) It will first begin to slide. C) It will tip over just as it begins to slide. D) It is impossible to answer without knowing the mass of the block. E) It is impossible to answer without knowing the dimensions of the block.
B
A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m3) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density? A) 1050 kg/m3 B) 1040 kg/m3 C) 1030 kg/m3 D) 960 kg/m3 E) 56.1 kg/m3
B
A very light 1.00-m wire consists of two segments of equal length, one of steel (Young's modulus is 2.00 × 1011 N/m2) and one of brass (Young's modulus is 9.0 × 1010 N/m2). The steel segment is 1.50 mm in diameter, and the brass segment has twice this diameter. When a weight w is hung from the ceiling by this wire, the steel segment stretches by 1.10 mm. By what distance does the brass segment stretch? A) 0.50 mm B) 0.61 mm C) 1.2 mm D) 2.4 mm E) 9.8 mm
B
Air is flowing through a rocket nozzle. Inside the rocket the air has a density of 5.25 kg/m3 and a speed of 1.20 m/s. The interior diameter of the rocket is 15.0 cm. At the nozzle exit, the diameter is 2.50 cm and the density is 1.29 kg/m3. What is the speed of the air when it leaves the nozzle? A) 123 m/s B) 176 m/s C) 88.0 m/s D) 45.7 m/s E) 29.3 m/s
B
At a certain depth in the ocean, the absolute pressure is p. If you go to twice that depth (treating the water as incompressible) A) the absolute pressure will be 2p. B) the absolute pressure will be less than 2p. C) the absolute pressure will be greater than 2p. D) the gauge pressure will not change. E) the gauge pressure will increase but will not double.
B
Salt water is more dense than fresh water. A ship floats in both fresh water and salt water. Compared to the fresh water, the volume of salt water displaced by the ship is A) greater than the volume of fresh water. B) less than the volume of fresh water. C) the same as the volume of fresh water.
B
The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 1010 N/m2. What is the displacement of the upper face in the direction of the applied force? A) 3.0 mm B) 3.6 mm C) 4.2 mm D) 4.8 mm E) 5.4 mm
B
Water flows through a pipe having a varying width. More water flows per second through the wide section than through the narrow section because there is more room for it to flow. A) True B) False
B
When you blow some air above the upper face of a paper strip, the paper rises. This occurs because A) the air above the upper face of the paper moves faster, which makes the pressure higher than at the lower face. B) the air above the upper face of the paper moves faster, which makes the pressure lower than at the lower face. C) the air above the upper face of the paper moves faster but the pressure remains constant. D) the air above the upper face of the paper moves slower, which makes the pressure higher than at the lower face. E) the air above the upper face of the paper moves slower, which makes the pressure lower than at the lower face.
B
The weight of a car of mass 1.20 × 103 kg is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure in the tires is required so the area of contact of each tire with the road is 1.00 × 102 cm2? (1 atm = 1.01 × 105 Pa.) A) 11.6 × 105 Pa B) 11.6 × 104 Pa C) 2.94 × 105 Pa D) 2.94 × 104 Pa E) 2.94 × 103 Pa
C
Water flows in the horizontal pipe shown in the figure. At A the diameter is 5.00 cm and at B the diameter is 4.00 cm The fluid in the manometer is mercury, which has a density of 13,600 kg/m3. The manometer reading h is 4.40 cm. We can treat water as an ideal fluid having a density of 1000 kg/m3. What volume of water is flowing through the pipe per second? A) 0.0206 m3/s B) 0.0426 m3/s C) 0.00560 m3/s D) 0.372 m3/s E) 0.186 m3/s
C
Water, of density 1000 kg/m3, is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s. At what rate is water flowing in this channel? A) 2.0 × 105 kg/s B) 2.0 × 103 kg/s C) 3.0 × 105 kg/s D) 3.0 × 103 kg/s E) 3.0 × 102 kg/s
C
What is the radius of a sphere that has a density of 5000 kg/m3 and a mass of 6.00 kg? A) 4.98 cm B) 1.27 cm C) 6.59 cm D) 1.56 cm E) 7.22 cm
C
Which one of the following stresses would be most likely to cause a bone to fracture? A) tensile stress B) compressive stress C) sheer stress D) bulk stress
C
You are driving a late model convertible car at the 65 mph speed limit with its soft flexible roof closed up and the windows closed. You observe that the roof A) bows inward. B) is no different from when the car was at rest. C) bows outward. D) bows inward only when you are driving uphill. E) bows inward only when you are driving down
C
Two compressible solids are formed into spheres of the same size. The bulk modulus of sphere two is twice as large as the bulk modulus of sphere one. You now increase the pressure on both spheres by the same amount. As a result of the increased pressure, how is the change in volume of sphere two (△V2) related to the change in volume of sphere one (ΔV1)? A) ΔV2 = 2ΔV1 B) ΔV2 = 4ΔV1 C) vV2 = ΔV1 D) ΔV2 = 1/2ΔV1 E) ΔV2 = 1/4ΔV1
D
Water flows in the horizontal pipe shown in the figure. At point A the area is 25.0 cm2 and the speed of the water is 2.00 m/s. At B the area is 16.0 cm2. The fluid in the manometer is mercury, which has a density of 13,600 kg/m3. We can treat water as an ideal fluid having a density of 1000 kg/m3. What is the manometer reading h? A) 0.546 cm B) 1.31 cm C) 2.81 cm D) 2.16 cm E) 3.36 cm
D
Water is flowing in a horizontal pipe of diameter d. If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was, what should be the new diameter? A) d/4 B) d/2 C) d / D) d E) 2d
D
A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m3) is raised up so the rock is totally submerged in the water. The scale now reads 12.5 N. What is the density of the rock? A) 1.60 × 103 kg/m3 B) 2.50 × 103 kg/m3 C) 2.33 × 103 kg/m3 D) 3.00 × 103 kg/m3 E) 2.67 × 103 kg/m3
E
A solid steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m2. The bulk modulus for this steel is 1.6 × 1011 N/m2. What is the change in the radius of the sphere? A) -0.021 mm B) -4.2 mm C) -0.42 mm D) -0.19 mm E) -0.062 mm
E
A steel lift column in a service station is a solid cylinder 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is 20 × 1010 N/m2. By what distance does the column compress when a 5000-kg truck is on it? A) 4.7 × 10-7 m B) 8.0 × 10-7 m C) 3.2 × 10-6 m D) 7.8 × 10-6 m E) 3.1 × 10-5 m
E
An incompressible fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. What is the fluid speed at a location where the diameter has narrowed to 4.0 cm? A) 0.32 m/s B) 0.64 m/s C) 1.28 m/s D) 2.56 m/s E) 5.12 m/s
E
Fluid fills the container shown in the figure. At which of the indicated points is the pressure greatest? A) A B) B C) C D) D E) The pressure is the same at each of the labeled points.
E
If the torque on an object adds up to zero A) the forces on it also add up to zero. B) the object is at rest. C) the object cannot be turning. D) the object could be accelerating linearly but it could not be turning. E) the object could be both turning and accelerating linearly.
E
The tensile strength (the maximum tensile stress it can support without breaking) for a certain steel wire is 3000 MN/m2. What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this steel without breaking the wire? A) 64 kN B) 9.0 kN C) 42 kN D) 85 kN E) 21 kN
E
The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m3. The manometer contains incompressible mercury with a density of 13,600 kg/m3. What is the difference in elevation h if the manometer reading m is 25.0 cm? A) 1.58 m B) 4.20 m C) 3.75 m D) 3.40 m E) 3.15 m
E
Two identical ladders are 3.0 m long and weigh 600 N each. They are connected by a hinge at the top and are held together by a horizontal rope, 1.0 m above the smooth floor forming a symmetric "A" arrangement. The angle between the ladders is 60° and both ladders have their center of gravity at their midpoint. What is the tension in the rope? A) 240 N B) 300 N C) 220 N D) 260 N E) 280 N
E
A 20.0-kg uniform door has a width of 1.20 m and a height of 2.50 m. The door is mounted on a post by a pair of hinges, marked 1 and 2 in the figure, at the top and bottom of the door. An external force of 60.0 N, at an angle of 30.0° above the horizontal, is applied to the small doorknob, as shown in the figure. The doorknob is 1.00 m above the bottom of the door. (a) Find the x component of the force that hinge 1 exerts on the door at the top. (b) Find the SUM of the y components of the forces that hinges 1 and 2 together exert on the door.
(a) -53.4 N (b) 166 N
An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two narrow pillars 1.60 m apart, as shown in the figure. Find the magnitude and direction of the force exerted on the diving board (a) by pillar A. (b) by pillar B.
(a) 1.71 kN downwards (b) 2.51 kN upwards
A 3.00-kg ball rests in a frictionless groove as shown in the figure. (a) What is the magnitude of the force that the left side of the groove exerts on the ball? (b) What is the magnitude of the force that the right side of the groove exerts on the ball?
(a) 26.4 N (b) 21.5 N
A sphere is constructed of two concentric parts. The inner part is a solid sphere of radius 10.0 cm made of a material with density 4000 kg/m3. The outer part is a spherical shell with inner radius 10.0 cm and outer radius 20.0 cm. The material in the outer shell has a density 9000 kg/m3. (a) What is the mass of the sphere? (b) What is the average density of this sphere?
(a) 281 kg (b) 8.38 × 103 kg/m3
On planet X, the absolute pressure at a depth of 2.00 m below the surface of a liquid nitrogen lake is 5.00 × 105 N/m2. At a depth 5.00 m below the surface, the absolute pressure is 8.00 × 105 N/m2. The density of liquid nitrogen is 808 kg/m3. (a) What is the atmospheric pressure on planet X? (b) What is the acceleration due to gravity on planet X?
(a) 3.00 × 105 N/m2 (b) 124 m/s2
A large cylindrical water tank is mounted on a platform with its central axis vertical. The water level is 3.75 m above the base of the tank, and base is 6.50 m above the ground. A small hole 2.22 mm in diameter has formed in the base of the tank. Both the hole and the top of the tank are open to the air. We can ignore air resistance and treat water as an ideal fluid with a density of 1000 kg/m3. (a) How many cubic meters of water per second is this tank losing? (b) How fast is the water from the hole moving just as it reaches the ground?
(a) 3.26 × 10-5 m3/s (b) 14.2 m/s
A 20.0-kg uniform plank is supported by the floor at one end and by a vertical rope at the other as shown in the figure. A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor (a) What is the tension in the rope? (b) What is the magnitude of the force that the floor exerts on the plank?
(a) 466 N (b) 220 N
The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N. (a) Determine the force that must be applied to the small piston. (b) Determine the pressure applied to the fluid in the lift.
(a) 600 N (b) 1.2 × 105 Pa
In the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface. The crate weighs 930 N, and its center of gravity is at its geometric center. A horizontal force F is applied at a distance h above the floor. If h = 0.61 m, what minimum value of F is required to make the crate start to tip over? Static friction is large enough that the crate does not start to slide.
305 N
In the figure, a uniform ladder 12 meters long rests against a vertical frictionless wall. The ladder weighs 400 N and makes an angle θ of 79° with the floor. A man weighing 790 N climbs slowly up the ladder. When he has climbed to a point that is 7.8 m from the base of the ladder, the ladder starts to slip. What is the coefficient of static friction between the floor and the ladder?
0.12
A wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m3) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?
22 kg
A 0.600-mm diameter wire stretches 0.500% of its length when it is stretched with a tension of 20.0 N. What is the Young's modulus of this wire? A) 5.66 × 1010 N/m2 B) 3.54 × 109 N/m2 C) 1.41 × 1010 N/m2 D) 6.43 × 109 N/m2 E) 2.78 × 109 N/m2
C
A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil with a density of 800 kg/m3 and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? (For purposes of this problem, you can neglect the weight of the pistons.) A) 0.954 kN B) 1.88 kN C) 1.96 kN D) 3.67 kN E) 1.20 kN
C
A 5.0-m long, 12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall. The coefficient of static friction between the floor and the ladder is 0.28. What distance, measured along the ladder from the bottom, can a 60-kg person climb before the ladder starts to slip? A) 4.0 m B) 3.7 m C) 1.7 m D) 1.3 m E) 3.3 m
C
A baseball is located at the surface of the earth. Which statements about it are correct? (There may be more than one correct choice.) A) The earth exerts a much greater gravitational force on the ball than the ball exerts on the earth. B) The ball exerts a greater gravitational force on the earth than the earth exerts on the ball. C) The gravitational force on the ball due to the earth is exactly the same as the gravitational force on the earth due to the ball. D) The gravitational force on the ball is independent of the mass of the ball. E) The gravitational force on the ball is independent of the mass of the earth.
C
A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 103 kg/m3 with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 105 Pa. What is the weight of the cylinder? A) 2430 N B) 3550 N C) 4670 N D) 10,900 N E) 12,100 N
C
A cup of water containing an ice cube at 0°C is filled to the brim. The tip of the ice cube sticks out of the surface. As the ice melts, you observe that A) the cup overflows. B) the cup might overflow but it depends on the actual mass of the ice cube. C) the water level remains the same. D) the water level actually goes down. E) There is not enough information to answer this question.
C
A piece of wood is floating in a bathtub. A second piece of wood sits on top of the first piece, and does not touch the water. If the top piece is taken off and placed in the water, what happens to the water level in the tub? A) It goes up. B) It goes down. C) It does not change. D) This cannot be determined without knowing the volume of the top piece of wood.
C
A rock is under water in a shallow lake. As the rock sinks deeper and deeper into water, the buoyant force on it A) increases. B) decreases. C) remains constant.
C
A sample of tendon 3.00 cm long and 4.00 mm in diameter is found to break under a minimum force of 128 N. If instead the sample had been 1.50 cm long and of uniform composition and cross-sectional area, what minimum force would have been required to break it? A) 32 N B) 64 N C) 128 N D) 256 N E) 512 N
C
A very light 1.00-m wire consists of two segments of equal length, one of steel (Young's modulus is 2.00 × 1011 N/m2) and one of brass (Young's modulus is 9.0 × 1010 N/m2). The steel segment is 1.50 mm in diameter, and the brass segment has twice this diameter. When a weight w is hung from the ceiling by this wire, the steel segment stretches by 1.10 mm. Find the weight w. A) 190 N B) 390 N C) 780 N D) 1000 N E) 3100 N
C
As the speed of a moving fluid increases, the pressure in the fluid A) increases. B) remains constant. C) decreases. D) may increase or decrease, depending on the density of the fluid.
C
At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 107 N/m2). By how much has 1.0 m3 of water been compressed by this pressure? The bulk modulus of water is 2.3 × 109 N/m2. A) 2.3 × 10-3 m3 B) 3.3 × 10-3 m3 C) 4.3 × 10-3 m3 D) 5.3 × 10-3 m3 E) 6.3 × 10-3 m3
C
The graph in the figure shows the force on an object as a function of the elongation caused by that force. Which statement about this object is true? A) The object obeys Hooke's law at all points from A to C. B) The object obeys Hooke's law at all points from B to C. C) The object obeys Hooke's law at all points from A to B. D) The elastic limit occurs at point C. E) The region of elastic behavior occurs from B to C.
C
A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. What is the pressure change that produced the volume strain in the oil? A) 1.2 MN/m2 B) 1.4 MN/m2 C) 1.6 MN/m2 D) 1.8 MN/m2 E) 2.0 MN/m2
D
A 120-kg refrigerator, 2.00 m tall and 85.0 cm wide, has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.300. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it won't tip before it begins to slide? A) 0.710 m B) 1.00 m C) 1.21 m D) 1.42 m E) 1.63 m
D
A cable is 100 m long, has a cross-sectional area of 1.0 mm2, and is made of a material having a Young's modulus of 1.0 × 1011 N/m2. If a 1000-N force is applied to stretch the cable, how far does it stretch? A) 0.0010 m B) 0.010 m C) 0.10 m D) 1.0 m E) 10 m
D
A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 103 kg/m3 with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 105 Pa. What net force does the water exert on the lower face of the cylinder? A) 7.40 × 103 N B) 1.09 × 104 N C) 3.79 × 104 N D) 4.14 × 104 N E) 1.37 × 105 N
D
A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses. A) It is impossible to say without knowing the masses. B) It is impossible to say without knowing the distances. C) The side the boy is sitting on will tilt downward. D) Nothing will happen; the seesaw will still be balanced. E) The side the girl is sitting on will tilt downward.
D
A level pipe contains a nonviscous, incompressible fluid with a density 1200 kg/m3 that is flowing steadily. At one position within the pipe, the pressure is 300 kPa and the speed of the flow is 20.0 m/s. At another position, the pressure is 200 kPa. What is the speed of the flow at this second position? A) 567 m/s B) 16.2 m/s C) 32.9 m/s D) 23.8 m/s E) 186 m/s
D
A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm while the opposite face is held fixed in place. What is the resulting displacement of the face? (The shear modulus for aluminum is 2.5 × 1010 N/m2) A) 1.9 × 10-8 m B) 2.6 × 10-8 m C) 4.4 × 10-8 m D) 5.3 × 10-8 m E) 8.2 × 10-8 m
D
A solid uniform brick is placed on a sheet of wood. When one end of the sheet is raised (see figure), you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°. There is enough friction to prevent the brick from sliding. What is the width w of the brick? A) 5.18 cm B) 6.09 cm C) 6.81 cm D) 9.40 cm E) 10.5 cm
D
If you double the pressure on the surface of a can of water, the buoyant force on a stone placed in that water will A) increase, but not double. B) double. C) decrease, but not by one-half. D) not change.
D
In the figure, the horizontal lower arm has a mass of 2.8 kg and its center of gravity is 12 cm from the elbow joint pivot. How much force FM must the vertical extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put? A) 100 N B) 500 N C) 750 N D) 1000 N E) 1500 N
D
Incompressible water flows out of a large reservoir through a pipe that opens to the atmosphere 5.70 m below the level of the water in the reservoir. What is the speed of the water as it comes out of the pipe? A) 1.72 m/s B) 7.47 m/s C) 55.8 m/s D) 10.6 m/s E) 27.9 m/s
D
Tensile stress is A) the strain per unit length. B) the same as force. C) the ratio of the change in length to the original length. D) the applied force per cross-sectional area. E) the ratio of elastic modulus to strain.
D
A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil? A) 2.0 mL B) 2.4 mL C) 2.8 mL D) 3.2 mL E) 3.6 mL
E
A child is trying to stack two uniform wooden blocks, 12 cm in length, so they will protrude as much as possible over the edge of a table, without tipping over, as shown in the figure. What is the maximum possible overhang distance d? A) 5 cm B) 6 cm C) 7 cm D) 8 cm E) 9 cm
E
A nonuniform, 80.0-g, meter stick balances when the support is placed at the 51.0-cm mark. At what location on the meter stick should a 5.00-g tack be placed so that the stick will balance at the 50.0 cm mark? A) 16.0 cm B) 67.0 cm C) 66.0 cm D) 35.0 cm E) 34.0 cm
E