# Casting of molten metal is important in many industrialprocesses. Centrifugal casting is used for manufacturing pipes,bearings and many other structures. A veriety of sophisticatedtechniques have been invented. A cylindrical enclosure is rotated rapidly and steadily about a horizontal axis. Molten metal is poured into therotating cylinder and then cooled, forming the finished product.Turning the cylinder at a high rotation rate forces the solidifying metal strongly to the outside. Any bubbles are displace toward the axis, so unwanted voids will not be present in the casting. Sometimes it is desirable to form a composite casting, such as fora bearing. Here a stron steel outer surface is poured, followed byan inner lining of special low- friction metal. In some applications a very strong met

Question
Other
Casting of molten metal is important in many industrialprocesses. Centrifugal casting is used for manufacturing pipes,bearings and many other structures. A veriety of sophisticatedtechniques have been invented. A cylindrical enclosure is rotated rapidly and steadily about a horizontal axis. Molten metal is poured into therotating cylinder and then cooled, forming the finished product.Turning the cylinder at a high rotation rate forces the solidifying metal strongly to the outside. Any bubbles are displace toward the axis, so unwanted voids will not be present in the casting. Sometimes it is desirable to form a composite casting, such as fora bearing. Here a stron steel outer surface is poured, followed byan inner lining of special low- friction metal. In some applications a very strong metal is given a coating of corrosion-resistan metal. Centrifugal casting results in stronbonding between the layers.
Suppose that a copper sleeve of iner radius 2.10 cm and outer radius 2.20 cm is to be cast. To eleminate bubbles and give high structural intgrity, the centripetal acceleration of each bit of metal should be 100g what rate of rotation is required? State theanswer in revolutions per minute.

2021-02-02

.

### Relevant Questions

A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 $$\displaystyle\frac{{m}}{{s}^{{2}}}$$, moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
A high-speed sander has a disk 4.00 cm in radius that rotates about its axis at aconstant rate of 1265 rev/min.Determine
(a) the angular speed of the disk in radians persecond,
(b) the linear speed of a point 2.2 cmfrom the disk's center,
m/s
(c) the centripetal acceleration of a point on the rim, and
$$\displaystyle\frac{{m}}{{s}^{{{2}}}}$$
(d) the total distance traveled by a point on the rim in1.96 s.
m
There is a clever kitchen gadget for drying lettuce leavesafter you wash them. It consists of a cylindrical container mountedso that it can be rotated about its axis by turning a hand crank.The outer wall of the cylinder is perforated with small holes. Youput the wet leaves in the container and turn the crank to spin offthe water. The radius of the container is 13 cm. When the cylinder is rotating at1.6 revolutions per second, what isthe magnitude of the centripetal acceleration at the outerwall?
m/s2
Your town is installing a fountain in the main square. If thewater is to rise 25m(82feet)above the fountain,how much pressuremust the water have as it moves slowly toward the nozzle thatsprays it up into the air?
Rather than putting a pump in the fountain(previous question)the engineer puts a water storage tank in a nearby high risebuilding.How high up in that building should the tank be for itswater to rise 25m when spraying out thefountain?(neglect friction)
As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.
a)Assuming that Albertine's mass is 60.0kg , what is $$\displaystyle\mu_{{k}}$$, the coefficient of kinetic friction between the chair and the waxed floor? Use $$\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}$$ for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for $$\displaystyle\mu_{{k}}$$, since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.
Electrostatic precipitators use electric forces to remove pollutant particles from smoke, in particular in the smokestacks of coal-burning power plants. One form of precipitator consists of a vertical, hollow, metal cylinder with a thin wire, insulated from the cylinder, running along its axis. A large potential difference is established between the wire and the outer cylinder, with the wire at lower potential. This sets up a strong radial electric field directed inward. The field produces a region of ionized air near the wire. Smoke enters the precipitation at the bottom, ash and dust in it pick up electrons, and the charged pollutants are accelerated toward the outer cylinder wall by the electric field. Suppose the radius of the central wire is 90.0 u(m,the radius of the cylinder is 14.0 cm, and a potential difference of 50.0 kG is established between the wire and the cylinder. Also assume that the wire and cylinder are both very long in comparison to the cylinder radius.
(a) What is the magnitude of the electric field midway between the wire and the cylinder wall? (V/m)
(b) What magnitude of charge must a 30.0 u(gas particle have if the electric field computed in part (a) is to exert a force ten times the weight of the particle? (c)
Give a full and correct answer Why is it important that a sample be random and representative when conducting hypothesis testing? Representative Sample vs. Random Sample: An Overview Economists and researchers seek to reduce sampling bias to near negligible levels when employing statistical analysis. Three basic characteristics in a sample reduce the chances of sampling bias and allow economists to make more confident inferences about a general population from the results obtained from the sample analysis or study: * Such samples must be representative of the chosen population studied. * They must be randomly chosen, meaning that each member of the larger population has an equal chance of being chosen. * They must be large enough so as not to skew the results. The optimal size of the sample group depends on the precise degree of confidence required for making an inference. Representative sampling and random sampling are two techniques used to help ensure data is free of bias. These sampling techniques are not mutually exclusive and, in fact, they are often used in tandem to reduce the degree of sampling error in an analysis and allow for greater confidence in making statistical inferences from the sample in regard to the larger group. Representative Sample A representative sample is a group or set chosen from a larger statistical population or group of factors or instances that adequately replicates the larger group according to whatever characteristic or quality is under study. A representative sample parallels key variables and characteristics of the large society under examination. Some examples include sex, age, education level, socioeconomic status (SES), or marital status. A larger sample size reduced sampling error and increases the likelihood that the sample accurately reflects the target population. Random Sample A random sample is a group or set chosen from a larger population or group of factors of instances in a random manner that allows for each member of the larger group to have an equal chance of being chosen. A random sample is meant to be an unbiased representation of the larger population. It is considered a fair way to select a sample from a larger population since every member of the population has an equal chance of getting selected. Special Considerations: People collecting samples need to ensure that bias is minimized. Representative sampling is one of the key methods of achieving this because such samples replicate as closely as possible elements of the larger population under study. This alone, however, is not enough to make the sampling bias negligible. Combining the random sampling technique with the representative sampling method reduces bias further because no specific member of the representative population has a greater chance of selection into the sample than any other. Summarize this article in 250 words.
The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with $$\displaystyle\mu={1.5}$$ and $$\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}$$.
(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.
(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than $$\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}$$.
(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of $$\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}$$? Explain, based on theprobability of this occurring.
(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?
(e) What is the moment generating function for X?
Assume that a ball of charged particles has a uniformly distributednegative charge density except for a narrow radial tunnel throughits center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton any where along the tunnel or outside the ball. Let $$\displaystyle{F}_{{R}}$$ be the magnitude of the electrostatic force on the proton when it islocated at the ball's surface, at radius R. As a multiple ofR, how far from the surface is there a point where the forcemagnitude is 0.44FR if we move the proton(a) away from the ball and (b) into the tunnel?
The unstable nucleus uranium-236 can be regarded as auniformly charged sphere of charge Q=+92e and radius $$\displaystyle{R}={7.4}\times{10}^{{-{15}}}$$ m. In nuclear fission, this can divide into twosmaller nuclei, each of 1/2 the charge and 1/2 the voume of theoriginal uranium-236 nucleus. This is one of the reactionsthat occurred n the nuclear weapon that exploded over Hiroshima, Japan in August 1945.
C. In this model the sum of the kinetic energies of the two"daughter" nuclei is the energy released by the fission of oneuranium-236 nucleus. Calculate the energy released by thefission of 10.0 kg of uranium-236. The atomic mass ofuranium-236 is 236 u, where 1 u = 1 atomic mass unit $$\displaystyle={1.66}\times{10}^{{-{27}}}$$ kg. Express your answer both in joules and in kilotonsof TNT (1 kiloton of TNT releases 4.18 x 10^12 J when itexplodes).