As a submerged body moves through a fluid, the particles of the fluid flow around the body and thus acquire kinetic energy. In the case of a sphere moving in an ideal fluid, the total kinetic energy acquired by the fluid is
Fig. P19.98
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- An object of mass m=2kg is part of a system and it is subject only to conservative forces and constrained to move along a horizontal line such that the potential energy of the system is given by the function U(x)=(−10)/(x2+1), where x is in meters and U is in joules. The graph of the function is shown in the image. (e) Another object is subject only to a different set of conservative forces and constrained to move along a horizontal line such that its potential energy is given by a different function U(x). Explain how the new function U(x) could be used to locate a point of stable equilibrium.arrow_forward2 Kinetic energy of a rigid body can be found by integrating the square of the velocity of differential mass elements over the entire mass of the body. True Falsearrow_forwardQuestion 2. A fluid of density p is contained in a cylinder of radius R as shown in the Figure below. The cylinder and the fluid are both spinning at an angular velocity w. Due to the spin, the difference in elevation of the fluid's free surface between the rim of the cylinder and its centre is h. Taking the acceleration due to gravity as g, answer the following, while showing all your work: (a) If h is thought to be a function of the other parameters in the problem (R, p, g, and w), generate all the non-dimensional parameters in the problem without choosing the acceleration due to gravity as a repeating variable. (b) Show that at least one of the non-dimensional parameters can be recast as the Froude number for the problem. Additionally, show the functional relationship between the independent and dependent non-dimensional parameters. (c) Through an experimental design of your choice, explain how and with how many experiments, you would determine the functional form of the…arrow_forward
- es Channel AB is fixed in space, and its centerline lies in the xy plane. The plane containing edges AC and AD of the channel is parallel to the xz plane. The surfaces of the channel are frictionless and the sphere E has 1.8 kg mass. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 4.552 N D 30° T 4.552 N A 30° E X 20° B 30° Determine the force supported by cord EF, and the reactions RC and Rp between the sphere and sides C and D, respectively, of the channel. (Round the final answers to four decimal places.) The force supported by cord EF is 11.5253 N. The reactions RC and RD between the sphere and sides Cand D, respectively, of the channel are as follows: RC= RD=arrow_forwardWhen it hails, each golf ball-sized chunk of hail rained down with a mass of 0.025 kg mass and impacted my car with a velocity of 400 m/s. The hood of the car is made out of 1040 steel. The modulus of elasticity is 207 GPa, the YS is 490 MPa, and the UST is 590 MPa. A. Determine the amount of energy (or work) that the steel hood of my car could absorb before being Plasticly deformed. Assume that the cross-sectional area impacted by the hail is 0.0005 m2 and that the thickness of the steel is 0.005 m. B. Determine the amount of energy (or work) that the steel hood of my car could absorb before being fractured. Assume that the cross-sectional area impacted by the hail is 0.0005 m2 and that the thickness of the steel is 0.005 m.arrow_forwardA. A motorcycle and rider have a combined mass of 350kg. The wheels each have a mass of 20kg, diameter of 500mm and radius of gyration of 200mm. The rider accelerates uniformly from 5m/s to 25m/s over a distance of 100m, whilst climbing a hill of slope 1 in 20. The average resistance to motion, including drag, is 105 N. 1. Determine the total work done as the motorcycle ascends the incline. 2. Calculate the amount of power developed during the climb. B. At another point in its journey, the motorcycle and rider travel at 80 km/h around a left-hand bend of radius 30m. Calculate: 1. The angular velocity of each of the wheels. 2. The moment of inertia of each wheel. 3. The magnitude and effect of the gyroscopic torque produced on the bike.arrow_forward
- A conservative mechanical system consists of a mass m that is constrained to move along a circle of radius R. The centre of the circle is at the origin O of the coordinate system. The mass is connected to a point A along the â-axis at a distance 2R from the centre of circle with a spring of elastic constant k, so that the corresponding elastic potential has the form Vspring = (k/2)ď², where d is the (varying) distance between the mass and point A. Gravity acts, as usual, along the vertical direction. See the figure for a depiction of the system. 0 m (b) Write down the Lagrangian of the system. (a) How many degrees of freedom does the system have? Indicate generalised coordinates to describe the motion of the system. X (c) Write down the corresponding Euler-Lagrange equation(s).arrow_forwardFour bodies are located in a region where g=9.67 m/s2 = 31.7148 ft/s2 Body1=750gm; Body2=4 slugs; Body3=4.5N and Body4=32.2 lbf (2.2lbm=1kgm, 1slugm=32.2lbm) a. What is the total mass expressed in lbm?arrow_forwardA wheel with a radius of 1.86 m and a mass of 0.242 kg rolls without sliding down a plane that is inclined at an angle φ = 21 °. g = 9,806 m/s². Calculate the kinetic energy of the wheel after the time 0.862 s if it has a moment of inertia 1.59 kg · m², starts from rest and a force acts on the wheel so that its angular velocity varies with time according to ω(t) = 1.98 · t^2 rad/s .arrow_forward
- . A nonconducting container filled with 25 kg of water at 20°C is fitted with a stirrer, which is made to turn by gravity acting on a weight of mass 35 kg. The weight falls slowly through a distance of 5 m in driving the stirrer. Assuming that all work done on the weight is transferred to the water and that the local acceleration of gravity is 9.8 m·s−2, determine:(a) The amount of work done on the water.(b) The internal energy change of the water.(c) The final temperature of the water, for which CP = 4.18 kJ·kg−1·°C−1.(d) The amount of heat that must be removed from the water to return it to its initial temperature.(e) The total energy change of the universe because of (1) the process of lowering the weight, (2) the process of cooling the water back to its initial temperature, and (3) both processes togetherarrow_forwardStep by step answer please help mearrow_forwardChannel AB is fixed in space, and its centerline lies in the xy plane. The plane containing edges AC and AD of the channel is parallel to the xz plane. The surfaces of the channel are frictionless and the sphere E has 1.9 kg mass. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. N N E 30° x F 20° B ᎠᏓ C 30°/A 30° Determine the force supported by cord EF, and the reactions RC and RD between the sphere and sides C and D, respectively, of the channel. (Round the final answers to four decimal places.) The force supported by cord EF is The reactions RC and Rp between the sphere and sides Cand D. respectively, of the channel are as follows: RC= RD= z N. 4arrow_forward
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