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college physics reasoning
Questions and Answers of
College Physics Reasoning
Water is flowing through a pipe (area 4.0 cm2) that connects to a faucet adjusted to have an opening of 0.50 cm2. If the water is flowing at a speed of 5.0 m/s in the pipe, what is its speed as it
A piece of aluminum is attached to a string and suspended in a pool of oil with density 750 kg/m3. If the apparent weight of the aluminum is 540 N, what is the volume of the aluminum?
A piece of balsa wood is placed into a tub full of ethanol. What fraction of the balsa wood is above the surface of the ethanol?
A solid object is made by gluing together two pieces of equal mass. If one of the pieces is made from a material with density 500 kg/m3, while the other has a density 1400 kg/m3, will the object
A chest of volume 1.2 m3 filled with gold sits at the bottom of a lake of depth 12 m. How much force is required to lift the chest to the surface?
For the blocks in Problem 50, assume they are barely submerged in water so that block 1 is just below the surface. If block 2 has a density twice that of block 1, what is the density of block
For the blocks in Figure P10.50, suppose instead of being near the surface of the lake they are just above the bottom of the lake. Find the buoyant force in this case. Figure P10.50 ? V1 V2
A submarine uses tanks that can be filled with either water or air so that the submarine can have “neutral buoyancy.” That means its average density is equal to the density of water where it is
Consider a glass tube that has the shape shown in Figure Q10.13. It is filled with a fluid and is closed at the end on the left. If PAis the pressure at point A, PBthe pressure at point B, and so
Two metal blocks are attached by a cable as shown in Figure P10.50 and are submerged at rest near the surface of a lake. If the volumes are V1= 2.0 m3and V2= 1.2 m3, what is the total buoyant force
You want to design a helium-filled balloon that will lift a total payload of 1500 kg. What volume of helium is needed to just barely lift this payload? Assume the balloon itself has negligible mass.
You want to build a raft that can hold you (80 kg) plus some supplies (40 kg) for a long trip. You decide to make the raft out of logs that are each 20 cm in diameter and 3.0 m long. If the density
Consider a wooden block of density 700 kg/m3 and volume 2.0 m3. What force is required to hold it completely under water?
An object has a weight of 20 N in air and an apparent weight of 5.0 N when submerged in water. What is its density? Will it float?
Estimate your apparent weight when you are under water.
A rectangular block of wood (density 750 kg/m3) of height 25 cm floats in a lake. What is the height of the wood above the water level?
Under normal conditions in the air, you are just barely able to lift a mass of 90 kg. Your friend drops a box of volume 2.5 m3 into a lake. If you are just able to lift it to the surface, what is the
A wooden log is found to float in a freshwater lake. If 35% of the log’s volume is above the surface, what is the log’s density?
A large suitcase full of gold sits at the bottom of a lake. A team of treasure hunters uses a crane to recover the suitcase and finds that a force of 3.0 × 105 N is required to lift the suitcase to
A car of mass 1400 kg rests on a hydraulic lift with a piston of radius 0.25 m that is connected to a second piston of radius 0.030 m. If the car is just barely lifted off the ground, what is the
A block of mass 20 g sits at rest on a plate that is at the top of the fluid on one side of a U-tube as shown in Figure P10.38. The U-tube contains two different fluids with densities ρ1= 1000
Cars use a hydraulic system to transmit the force from the brake pedal to the actual brakes. If this system amplifies the force of your foot by a factor of 10, what is the ratio of the area of the
A syringe has an area of 1.0 cm2 in the barrel and then narrows down to an area of 0.10 mm2 at the needle end. If a force of 5.0 N is applied to the syringe, what is the force produced at the tip of
The water system in a town is designed by a careless engineer. He places the new water tower at the top of an extremely tall hill, overlooking the mayor’s house. The mayor then finds that some of
A swimming pool of depth 2.5 m is filled with ordinary (pure) water (ρ = 1000 kg/m3). (a) What is the pressure at the bottom of the pool? (b) When the pool is filled with very salty water,
The water pressure in the pipes in the basement of a tall house is 5.0 × 105 Pa. Estimate the water pressure on the second floor.
When a person is given intravenous fluid, the bag containing the fluid is typically held about 1.0 m above the person’s body. If the pressure in this fluid is just barely able to push the fluid
The blood pressure in a person’s feet when he is standing is greater than the pressure in his head. Estimate this pressure difference and compare it with normal blood pressure, which is typically
A bucket is filled with a combination of water (density 1000 kg/m3) and oil (density 700 kg/m3). These fluids do not mix. (The oil will float on top of the water.) If the layer of oil is 20 cm tall,
An engineer is given the job of designing the water system for a tall building. He decides to locate the pumps at ground level and feed the entire building from there. If the top floor of the
Figure 10.12 shows a device that can be used to measure atmospheric pressure. If h = 6.5 m, what is the density of the liquid? Figure 10.12 ? Ptop = 0 (vacuum) h Patm
A U-tube contains two fluids with densities?µ1= 1000 kg/m3and ρ2= 600 kg/m3as sketched in Figure P10.27. What is the difference d in the heights of the top surfaces of the two fluids? Figure
Consider a fish of average size swimming near the bottom of a lake of depth 20 m. (a) What is the water pressure next to the fish? (b) Estimate the total force exerted by the water on the
Estimate the force exerted by the water on Hoover Dam.
A diver is swimming at a depth of 10 m. What is the pressure in the water around him?
Consider again the swimming pool in Problem 22. What is the force exerted by the water on one of the sidewalls of the pool?Data from problem 22Consider a rectangular swimming pool of depth 2.5 m with
Consider a rectangular swimming pool of depth 2.5 m with a width and length of 15 m. What is the total force on the bottom of the pool due to the water pressure?
The author once had a small car with a ???hatchback,??? a rear door that opens upward. One day, he forgot to latch it before driving on the highway, and he found that at high speeds the rear door
Find the pressure at the bottom of a swimming pool that is 2.5 m deep.
The region near the South Pole in Antarctica has an altitude of about 3000 m, making the air pressure lower than at sea level. Explain why it is more difficult for an airplane to take off from the
Add a new column to Table 10.1, listing the specific gravity of each substance. TABLE 10.1 Densities of Some Common Solids, Liquids, and Gases Density (kg/m) Substance SOLIDS Ice (at 0°C) 917
Explain how the specific gravity of a substance is connected with the buoyant force when an object is immersed in water.
Each tire of a car contacts the road over an area of approximately 150 cm2. Estimate the mass of the car.
In preparation for a bike tour of several countries, you ship your bicycle by air freight to Europe. When you arrive, you find that the tires of your bicycle have both blown out. Explain why that
The water in the pipes of a typical house is at a gauge pressure of 3.0 times atmospheric pressure. What is the absolute pressure in pascals and in units of pounds per square inch?
An altimeter is a device used to measure altitude. Most altimeters are based on measurements of air pressure. Explain how they work and estimate how much the pressure changes for a 100-m change in
Express a pressure of 5.0 × 106 Pa in units of pounds per square inch.
Explain how there can be dust on a moving fan blade.
The recommended pressure in your car’s tires is usually specified as a gauge pressure. If a tire has a gauge pressure of 15 lb/in.2, what is the absolute pressure in pascals?
Figure Q10.16 shows a popular demonstration involving a moving fluid. Here an air jet is aimed upward and levitates a small object such as a table-tennis ball. The ball is
When a typical 1200-page textbook is sitting on a table, it exerts a force on the table. Estimate the associated pressure.
When traveling in a commercial airplane, you are sometimes given snacks, such as peanuts, in a sealed bag. The bag is often “bulging” much more than when you purchase a bag of peanuts in a store.
Estimate the pressure exerted by your feet when you stand upright on the floor. Compare it to the pressure when you are wearing “stiletto” heels (use the value at the heel).
The four tires on the author’s car are inflated to an absolute pressure of 2.5 × 105 Pa. If the car has a mass of 1800 kg, what is the contact area between each tire and the ground?
Two blocks with the same volume but different densities are in a lake as shown in Figure Q10.14. Block m1floats at the surface with a portion above the water level, and block m2floats
A suction cup works by virtue of a vacuum that is created within the cup. When the cup is pressed against a flat surface, most of the air is forced out, leaving a region of very low pressure. If a
Why are dams thicker at the bottom than at the top?
A block sits on a plate that in turn rests on the surface of a fluid as shown in Figure P10.11. The plate is partially submerged in the fluid, its area is 0.30 m2, and there is air at atmospheric
Consider a swimming pool and a tall graduated cylinder (like the one in Fig. Q10.4), both containing water and filled to the same height. (a) Is the pressure at the bottom of the pool greater
The pressure in the atmosphere is not constant, but fluctuates as the weather changes. If the pressure outside a window drops by 5% while the pressure inside does not change, what is the force on the
Why does the lava in a Lavalamp (Fig. Q10.10) rise and then fall?Figure Q10.10
Consider a box with a lid 1.5 m wide and 0.70 m long. If the inside of the box is evacuated (i.e., its pressure is zero), how much force is required to open the lid? Could you open the lid?
Three containers are filled with water to the same height (Fig. Q10.9). For which container is the pressure at the bottom the greatest? Or, are the pressures the same? Explain.Figure Q10.9 Container
Consider an airplane window (area 0.30 m2). If the pressure inside the plane is atmospheric pressure and the pressure outside is 20% of Patm, what is the force on the window? Ignore the velocity of
A cargo ship travels from the Mississippi River into the Gulf of Mexico. Will the ship sink or rise with respect to the waterline as it moves from the river to ocean water? Why?
Knowing the density of water, estimate the volume of your body.
Explain why some people are able to float in ocean water but not in a freshwater lake (see Fig. Q10.7). (A freshwater lake contains rainwater.)Figure Q10.7
Consider a steel sphere of mass 20 kg. Find its radius.
When water flows slowly from a faucet or pipette, the stream narrows and then eventually breaks into droplets (Fig. Q10.6). Explain why. Consider the effect of surface tension. Figure Q10.6
Estimate the mass of water in a typical bathtub. Assume the tub contains just enough water that you could be completely submerged.
Explain why an ice cube floats in water. For ordinary water (i.e., not salt water) at room temperature, what fraction of an ice cube is above the water?
Consider a highway composed of concrete. If the road is 2.0 km long, 10 m wide, and 0.50 m thick, what is its mass?
Figure Q10.4 is a photograph of a graduated cylinder filled with four fluids. Starting with mercury on the bottom and going up, we have salt water, water, and vegetable oil. In addition, a solid
A piece of gold has a mass of 20 g. If this gold were formed into a very thin sheet of thickness 0.50 mm, find the area of the sheet. Assume it has the same density as listed in Table 10.1.
In a neutron star, all the mass has “collapsed” into a relatively small volume. (a) If a particular neutron star has a radius of 1000 m and a mass of 2.0 × 1028 kg, what is its
The specific gravity of a substance is the ratio of its density to the density of water. Among other applications, measurements of the specific gravity are used by mineralogists to determine the
Explain how Archimedes’s principle can be used to measure a person’s percentage body fat. Fat has a different density than other body tissue.
Design a hydraulic lift that could be used to move a car. Assume the input piston the person would push on has an area of 0.10 m2. If you want a force of 300 N applied by the person to lift a car,
A solid wood ball is rotating about an axis that passes through its center. If its angular speed is doubled, (a) by what factor does its rotational kinetic energy change? (b) By what factor
Consider again the problem of a tipping car in Example 8.6. This time, instead of applying a force F to the car, assume the car is traveling around a curve on a level road. Let the radius of
A long, non-uniform board of length 8.0 m and mass m = 12 kg is suspended by two ropes as shown in Figure P8.83. If the tensions in the ropes are mg/3 (on the left) and 2mg/3 (on the right), what is
The end of a pencil of mass m and length L rests in a corner as the pencil makes an angle θ with the horizontal (x) direction (Fig. P8.82). If the pencil is released, it will rotate about point O
A wheel of mass 11 kg is pulled up a step by a horizontal rope as depicted in Figure P8.81. If the height of the step is equal to one-third the radius of the wheel, h = 1/3 R, what minimum tension is
Runner???s gait. The amount of torque required by an external applied force (other than gravity) to move a leg forward is less than that required to move it backward if the leg is bent as shown in
A bodybuilder is in training and performs curls with a 10-kg barbell to strengthen her biceps muscle. At the top of the stroke, her arm is configured as in Figure P8.79, with her forearm at 35° with
Bicycles like the one shown in the photo in Figure P8.78 typically have 24 possible gear ratios (three gears on the front and eight on the back). Suppose the diameters of the largest and smallest
A chain drive (Fig. P8.77) transfers the rotational motion of a tractor transmission to a grain elevator. The drive shaft places a counterclockwise torque on the small sprocket of radius 2.2 cm so
Three gears of a mechanism are meshed as shown in Figure P8.76 and are rotating with constant angular velocities. The ratio of the diameters of gears 1 through 3 is 3.5/1.0/2.0. A torque of 20 N · m
Consider again the problem of overhanging bricks in Figure P8.74. Find the maximum overhang distance d for systems of (a) three bricks and (b) four bricks. (c) How many bricks are needed for the top
Two bricks of uniform density are stacked as shown in Figure P8.74. What is the maximum overhang distance d that can be achieved? Consider how the torque on each brick???s center of mass must be in
The wheels on a special bicycle have different radii Rfand Rb(Fig. P8.73). The bicycle starts from rest at t = 0 and accelerates uniformly, reaching a linear speed of 10 m/s at t = 9.0 s.? (a) What
A car has a top speed of 70 m/s (about 150 mi/h) and has wheels of radius 30 cm. If the car starts from rest and reaches its operating speed after 9.0 s, what is the angular acceleration of the
The wheel of an adult’s bicycle rolls a distance of 3.0 km. Approximately how many revolutions does the wheel make during this journey?
A truck accelerates from rest to a speed of 12 m/s in 5.0 s. If the tires have a radius of 40 cm, how many revolutions do the tires make during this time?
A string is rolled around a cylinder (m = 4.0 kg) as shown in Figure P8.69. A person pulls on the string, causing the cylinder to roll without slipping along the table. If there is a tension of 30 N
A cylinder rolls without slipping down an incline that makes a 30° angle with the horizontal. What is the acceleration of the cylinder?
Consider a tennis ball that is hit by a player at the baseline with a horizontal velocity of 45 m/s (about 100 mi/h). The ball travels as a projectile to the player’s opponent on the opposite
A car is traveling with a speed of 20 m/s. If the tires have an angular speed of 62 rad/s, what is the radius of the tires?
A car starts from rest and then accelerates uniformly to a linear speed of 15 m/s in 40 s. If the tires have a radius of 25 cm, what are the magnitudes of (a) The average linear acceleration of
A board of length 1.5 m is attached to a floor with a hinge at one end as shown in Figure P8.64. The board is initially at rest and makes an angle of 40° with the floor. If the board is then
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