Concept explainers
A cubical block is observed to float in a beaker of water. The block is then held near the center of the beaker as shown and released.
- Describe the motion of the block after it is released.
- In the space provided, draw, a free−body diagram for the block at the instant that it is released. Show the forces that the water exerts on each of the surfaces of the block separately.
Make sure the label for each force indicates:
- the type of force,
- the object exerting the force is exerted, and
- the object exerting the force.
Did you use the relationship between pressure and depth to compare the magnitudes ofany of the vertical forces? If so, how?
Did you use information about the motion of the block to compare the magnitudes of any of the vertical forces? If so, how?
Is this vector sum the net force on the block? (Recall that the net force is defined as the vector sum of all forces acting on an object.)
Is the magnitude of the sum of the forces exerted on the block by the water greater than, less than, or equal to the weight of the block? Explain.
(1)
To Explain: The motion of the block after it is released in the center of the block.
Explanation of Solution
Introduction:
According to Newton’s second law of motion, anybody under influence of a net force accelerates along the direction of the net force. For an object inside a fluid, the forces along the vertical direction are the upward buoyant force and the downward force of gravity. The object moves along the direction of the dominating force. If the two forces are equal, the object stays at rest.
It is given that the block floats in water, which means when the block is released in the center of the beaker, the upward buoyant force dominates and the block moves in the upward direction. So, after release, the block accelerates towards the surface of the water. After reaching the surface, the block comes to rest at the equilibrium position.
Conclusion:
After releasing, the block accelerates towards the surface of the water.
(2)
To Draw: A free body diagram of the fully submersed block.
Explanation of Solution
Introduction:
By Archimedes’ principle, the buoyant force (acts upwards) on an object in a fluid is equal to the weight of the water which is displaced by the object. The other forces that act on the object are the downward force due to gravity and the pressure force exerted by the surrounding fluid on the surface of the object. The pressure force exists due to the weight of the water column that lies above the object and acts equally from all directions due to the properties of an incompressible fluid.
The free-body diagram for the block at the instant it is released is given below.
(3)
To rank: The magnitudes of the vertical forces in the free body diagram.
If the relationship between pressure and depth is used to compare the magnitudes of vertical forces.
If the information about the motion of the block is used to compare the magnitudes of forces.
Explanation of Solution
Introduction:
If an object is in water, the water above the object exerts pressure on the surface of the object. Due to the properties of the fluid, this pressure is exerted on the object from all directions. The magnitude of this pressure is given by
According to Newton’s second law of motion, anybody under influence of a net force accelerates along the direction of the net force. For an object inside a fluid, the forces along the vertical direction are the upward buoyant force and the downward force of gravity. The object moves along the direction of the dominating force. If the two forces are equal, the object stays at rest.
The different vertical forces that act on the block in the free body diagram are the upward buoyant force (
Since the block floats on the water, following Newton’s second law, it can be said that the upward buoyant force is larger than the downward force of gravity.
So,
But since the pressure force acts equally from all the directions, it does not initiate any motion and cannot be compared with the other forces on the basis of Newton’s second law.
As the block is in a beaker, the depth of the block inside the water is quite negligible. But the atmospheric pressure term is very large as compared to any other vertical force
Conclusion:
The relationship between pressure and depth is used.
The information about the motion of the block is used.
(4)
To draw: The vector sum of all the forces on the block and explain it.
Explanation of Solution
Introduction:
According to Newton’s second law of motion, anybody under influence of a net force accelerates along the direction of the net force. For an object in a fluid, the forces along the vertical direction are the upward buoyant force and the downward force of gravity. The object moves along the direction of the dominating force. If the two forces are equal, the object stays at rest. One other force that acts on the object is the pressure force due to the weight of the water column above the object. But this force acts equally from all directions. So, the resultant of this force on the object is zero.
The arrow in the box below represents the vector sum of all the forces exerted by the surrounding water on the block.
The direction of this force can be determined by the fact that the vector sum of the pressure forces exerted by the surrounding water is zero. So, the only force exerted by the surrounding water that remains is the upward buoyant force.
This force is not the vector sum of the net forces on the block. Because this force is only the vector sum of the forces exerted by the fluid on the block. The one other force that acts on the block is the force due to gravity (weight of the block). The vector sum of these two forces is the net force on the block.
As the block tends to move in the upward direction after release, the net force on the block must be in the upward direction. i.e. the magnitude of all the forces exerted on the block by the water is greater than the weight of the block.
Conclusion:
The net force exerted by the water on the block is in the upward direction.
This force is not equal to the vector sum of all the forces on the block.
The buoyant force on the block is greater than the weight of the block.
Want to see more full solutions like this?
Chapter 12 Solutions
Tutorials in Introductory Physics
Additional Science Textbook Solutions
Conceptual Physics (12th Edition)
Modern Physics
Life in the Universe (4th Edition)
Introduction to Electrodynamics
College Physics
University Physics with Modern Physics (14th Edition)
- Use the worked example above to help you solve this problem. An airplane has wings, each with area 4.15 m2, designed so that air flows over the top of the wing at 246 m/s and underneath the wing at 221 m/s. Find the mass of the airplane such that the lift on the plane will support its weight, assuming the force from the pressure difference across the wings is directed straight upwards. Approximately what size wings would an aircraft need on Mars if its engine generates the same differences in speed as in the "Practice It" and the total mass of the craft is 350 kg? The density of air on the surface of Mars is approximately one percent Earth's density at sea level, and the acceleration of gravity on the surface of Mars is about 3.8 m/s2.arrow_forwardA diving bell is to be designed to withstand the pressure of sea water at a depth of 900 m. The density of seawater is 1,030 kg/m3. Solve this on the space provided in the answer sheet.a. What is the total pressure at this depth?b. What is the force due to this depth of the seawater on a circular glass 15 cm in diametarrow_forwardShow the complete solution. 1.) Water runs into a fountain, filling all the pipes, at a steady rate of 0.750 m^3/s. (a) How fast will it shoot out of a hole 4.50 cm in diameter? (b) At what speed will it shoot out if the diameter of the hole is three times as large?arrow_forward
- In (Figure 1), how much force does the fluid exert on the end of the cylinder at A? How much force does the fluid exert on the end of the cylinder at B?arrow_forwardA tie of uniform width is laid out on a table, with a fraction of its length hanging over the edge. Initially, the tie is at rest. (a) If the fraction hanging from the table is increased, the tie eventually slides to the ground. Explain. (b) What is the coefficient of static friction between the tie and the table if the tie begins to slide when one-fourth of its length hangs over the edge? Show your work and explain.arrow_forwardCOMPLETE SOLUTION with given and required ASAP Refer to the diagram and consider that the pressure in each chamber is equal. Determine the direction ofmovement of the piston, is it going to the left or the right? Prove and justify your answer using equations.arrow_forward
- The old rubber boot shown has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of leak 1? Explain your responses in terms of energy.arrow_forwardI need more detail about my answer, so watch the professor's comment and write your solution more detail. 2. A cylindrical object—with radius R, length L, and density ??—sits on a scale at the bottom of vat of fluid with density??.a. Draw and label a free body diagram for the object. (Don’t forget to set up a coordinate system and to label the acceleration info. Also, be sure to use the gridlines to help you draw arrows that show the correct directions and relative magnitudes of the forces. Finally, be sure to label your forces clearly to indicate the types of forces.)b. Use Newton’s 2nd Law to derive an expression for the reading on the scale.arrow_forwardSketch how water curls down a sink, say, in clock-wise rotation. Draw the resulting vector of the curl-operator applied on this water flow.arrow_forward
- A scuba driver and her gear displace a volume of 69.6 L and have a total mass of 72.8 kg. a What is the bouyant force on the diver in seawater? b. Will the driver sink or float? Show your free body diagram, compuraion and your answer.arrow_forwardFluid A flows three times as fast as fluid B through the same pipe. Which has a greater density, and how many times greater it is? Show your equation and solution.arrow_forwardFor numbers 1-3, only choose one correct answer. No need for explanation. 1. If water is filled in a glass of water, which part of thebottle experiences the greatest pressure? A. at the bottom B. at the top C. on its sides D. all are correct 2. WHich location should the water tnak be constructed in orderto supply household consumers? A. at the ground level B. below the gorund level C. highly elevated from the ground D. all are correct 3. What is the speed of sound when the temperature is 39 degree celsius in aluminum? A. 5119.2 m/s B. 5122.2m/s C. 5123.4 m/s D. 5127.4 m/sarrow_forward
- Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill