Conical Definition and 136 Threads

Homework Statement A round cone A of mass ##m## and half-angle ##\alpha## rolls uniformly and without slipping along a round conical surface B so that its apex O remains stationary. The centre of gravity of the cone A is at the same level as point O and at a distance ##\ell## from it. The...

Homework Statement [10marks] A water tank has the shape of a vertex-down right circular cone. The depth of the tank is 9 meters, and the top of the tank has radius 6 meters. Water flows into the tank from a hose at a constant rate of 14 cubic metres per hour, and leaks out of a hole at...

Here is the question: Here is a link to the question: Applying integration to physics and engineering? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I am working on a paper at the moment which has to do with draining tanks. I have already set up a differential equation which explains the drain from a tank where the cross-sectional areas of the container and of the outflow are constants. But now I have to set up one which explains the drain...

Homework Statement A particle moves under the action of gravity on a conical surface z^2 = 4(x^2+ y^2), z ≥ 0, where z is the vertical axis. For initial position r = (1, 0, 2) and initial velocity ṙ = (0, 2, 0) find the extremal values of z along the trajectory. Take g = 10. Homework...

Homework Statement A particle of mass 15g is attached to the end of a string of length 50cm, rotating at 6rads-1 to form a conical pendulum. Find a) The tension in the string Find b) The angle 2. The attempt at a solution Okay I get that Tcosθ= mg & TSinθ=...

Homework Statement A metal sphere is attached to the end of a string and then set in motion such that it rotates in a horizontal circle as shown in the sketch. The metal sphere has a mass of 0.5kg and the radius of the circle is .2m. 1)Find the tension in the string 2)Calculate the radial...

I've been trying to figure out where my mistake lies in the first solution. Some help would be appreciated. I did notice I got the same solution twice, so I assume I just calculated dr/dt twice and I need to use a different equation for dh/dt? Is dh/dt=(3/4)*dr/dt? 1. Sand falls from a...

Homework Statement By resolving forces horizontally and vertically and using Newton's second Law, find an expression for the angle swung out of a Chair-o-plane ride. Im just not really sure how to resolve the forces vertically and horizontally. Homework Equations So far I know that...

Conical pendulum question help!? Homework Statement By resolving forces horizontally and vertically and using Newtons second law, find an expression for the angle swung out. You must use calculus where needed. Use this analysis to answer questions 1-3 Q1: Will a child swing at a greater...

For a conical pendulum, there is an instantaneous centripetal acceleration. Does this mean there is an instantaneous angular acceleration of the pendulum towards the center?

Homework Statement A particle of mass 6 kg is attached to the centre B of a light inextensible string of length 10m. One end of the string is attached to a point A and the other end to a point C which is distance 8m directly below A. The particle is moving in a horizontal circle, with both...

Homework Statement Given that the conical shell has uniform density and thickness is made of one sheet, has mass M, height h, and base radius R, derive the moment of inertia about its axis of symmetry. Homework Equations I = MR^2 for a ring about its central axis. I = ∫dI - my approach The...

Homework Statement Find the work required to empty a 10m high conical tank with a radius at the top of 4m by pumping the water out the top of the tank. The water level is 2m below the top of the tank. Homework Equations \pi r^2 Similar triangles The Attempt at a Solution...

Homework Statement A great conical mound of height h is built by the slaves of an oriental moarch, to commemorate a victory over the barbarians. If the slaves simply heap up uniform material found at ground level, and if the total weight of the finished mound is M, show that the work they...

3.(a) A particle P, of mass 0.03kg, is attached to one end of a light inextensible string OP, of length 1 m. The other end of the string is attached to a fixed point O. The particle moves in a horizontal circle, with centre vertically below O, at an angular speed of 2 revolutions per second. The...

Homework Statement A ball (mass m = 250 g) on the end of an ideal string is moving in circular motion as a conical pendulum as in the figure. The length L of the string is 1.85 m and the angle with the vertical is 37°. What is the magnitude of the torque exerted on the ball about the...

Good Morning to all I saw this problem in one of the courses that I am taking this semester. It is very simple, it consists of an open conical tank being filled in the upper part with an stream (which is assumed to be cylindrical) of water (flow Qi through an area Ai). At the bottom of the...

Design the optimal conical container that has a cover and has walls of negligible thickness. The container is to hold 0.5 m^3. Design it so that the areas of its base and sides are minimized. information : 1) areas of the sides = (pi) x r x s 2) areas of the base = (pi) x (r^2) 3)volume of...

I am researching water clocks through history. At some point, it was realized that for the container the water drips from, a conical container with the hole at its point was superior to a cylindrical container with the hole in its side. Could someone explain to me why conical containers are...

Hi everybody, I am designing conical shells in the aim to better understand the launch vehicle adapter and what changing thickness of conical shells will do to buckling load and natural frequency. I have an issue with certain equations I have characteristic equations with a critical axial...

Homework Statement Fig. 6-53 shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.012 kg, the string has length L = 0.86 m and...

Homework Statement A conical pendulum is formed by attaching a 0.900 kg ball to a 1.00 m long string, then allowing the mass to move in a horizontal circle of radius 20.0 cm . What is the ball's angular velocity, in rpm? Homework Equations v=\sqrt{}L*g*sin(\vartheta)*tan(\vartheta)...

I am working on a Hydro project. Just can't get this right. I have a water tank (cone shaped) with Radius 60 Inches and height 120 Inches. The Tip of the cone has a nozzle with a 3 inch opening. If the Air pressure is ignored. What will be the flow rate of water and pressure. ?

Homework Statement Suppose there is a Conical section (of a right circular cone) of total height 'l' and radii 'a' and 'b' (a>b). How do we derive the formula for the radius at a height 'h' (h<l) ?Homework Equations The Attempt at a Solution

This is a problem that my lecturer gave us in class and it has been bugging me ever since. I have been unsuccesful in finding or calculating a proper solution so I am hoping PF will be able to help... This is the Q: Let H be the height of a conical glass which is filled to a height h. Find...

Homework Statement Find the work done in pumping all the water out of a conical reservoir of radius 10ft at the top and altitude 8ft if at the beginning the reservoir is filled to a depth of 5ft and the water is pumped just to the top of the reservoir. Homework Equations None The Attempt at a...

Homework Statement This is a problem I've been pondering, and I simply need some recommendations for texts to read on the topic. Suppose you have an enclosed air chamber with an acoustic source on one end (http://beckerexhibits.wustl.edu/did/images1/hatpatent.jpg" ). How can one predict...

Homework Statement This is a problem I've been pondering, and I simply need some recommendations for texts to read on the topic. Suppose you have an enclosed air chamber with an acoustic source on one end. How can one predict the amplification (most important), distortion, and...

Am looking to build a solar tunnel that would not only redirect solar visible light radiation, but also heat, with minimum losses. Basically need to deflect angle of incident radiation by around 30 degrees. Am considering an inverted truncated cone design, with a polished inner surface...

Homework Statement This setup of a conical pendulum is actually at the end of crane which is rotating, however I do not think that this should effect the situation: I need to calculate the radius so that I can then add this to the radius of the crane which will give my actual required...

hi i am posting a problem 2.26 from griffiths EM book third edition.i am also attaching the solution from the book's solution manual. in the solution, griffiths has taken the ring as the differential element. but i want to know if we can take the small rectangular patch on the conical surface...

hi i am posting a problem 2.26 from griffiths EM book third edition.i am also attaching the solution from the book's solution manual. in the solution, griffiths has taken the ring as the differential element. but i want to know if we can take the small rectangular patch on the conical surface...

Homework Statement A conical reservoir is 50m deep and 200m across the top. Water is being pumped in at a rate of 7000m^3/min, and at the same time, water is being drained out at a rate of 9000 m^3/min. What is the change in diameter when the height of the water in the reservoir is 20m...

1.The string of a conical pendulum is 1m long and the bob has mass 100g. It rotates at 0.5 revolutions per second. a) Find the angle that the string makes to the vertical. b) Find the tension in the string c) If the maximum tension which the string can bear is 2N, what is the maximum rate...

Homework Statement Q1. I am currently doing a physics assignment where i must answer some concept questions about a conical pendulum. So here they are: Does the centripetal acceleration and/or the net force alter if the launch angle changes? Q2. Would the centripetal acceleration and/or...

Homework Statement A particle of mass m is tied to the middle of a light, inextensible string of length 2L. One end of the string is fixed to the top of a smooth vertical pole. The other end is attached to a ring of mass m, which is free to slide up and down the pole. The particle moves in a...

Homework Statement A draining conical reservoir. Water is flowing at the rate of 50 m^3/min from a shalloe concrete conical reservoir (vertex down) of base radius 45m and height of 6m. a. How fast (centimeters per minute) is the water level falling when the water is 5m deep? b. How fast...

Hello , I have been wanting to find out the how heat generation of a tubular solenoid (pull-type)actuator is calculated? Secondly, why do most solenoid design use a plunger with a flat face/conical surface area . If I am looking for 1mm of stroke.. and a force output of 2500N, what apex...

Homework Statement A .30kg ball is swung in a conical pendulum whose length is 95cm. If the string makes an angle of 22 degrees with the vertical, what are (a) the balls speed and (b) the tension in the string Homework Equations The Attempt at a Solution I drew a freebody...

http://img25.imageshack.us/my.php?image=77494342.jpg I can do the first part, however am unsure of how to deduce the motion cannot take place unless the inequality is satisfied. Can someone please explain this part? Thanks

A right circular conical tank of height 3 feet and radius 1 foot at the top is filled with water to a height of 2 feet. Find the work required to pump all the water up and over the top of the tank. similar triangles : x=y/3 water 62.5 lb/ft^3 ?? am i setting this up right

Please help me with the following simple and dumb questions: First, assumptions: - Ignore atmospheric pressure. - The liquid in the tanks is water with uniform density = 1g/cc. - all tanks are sealed at the bottom and are vertically positioned. - cross sections of the tanks are circular...

Homework Statement okay here is the problem: A conical pendulum is formed by attaching a 500g ball to a 1.0m long string, then allowing the mass to move in a horizontal circle of radius 20cm. What is the tension in the string? Homework Equations My professor gave a hint that said use the...

I'm supposed to find the shortest path between the points (0,-1,0) and (0,1,0) on the conical surface z=1-\sqrt {{x}^{2}+{y}^{2}} So the constraint equation is: g \left( x,y,z \right) =1-\sqrt {{x}^{2}+{y}^{2}}-z=0 And the function to be minimized is...

Homework Statement A conical pendulum is formed by attaching a 0.900 kg ball to a 1.00 m-long string, then allowing the mass to move in a horizontal circle of radius 10.0 cm. The figure (Intro 1 figure) shows that the string traces out the surface of a cone, hence the name. (Figure Attached)...

Homework Statement A water tank is in the shape of an inverted conical cone with top radius of 20m and depth of 15m. Water is flowing into the tank at a rate of 0.1m^3/min. (a) How fast is the depth of water in the tank increasing when the depth is 5m? Water is now leaking from the...

HELP ME i tried spliting the forces of the tension of the string but I don't know how exactly

Conical Pendulum--- did I do this right? Homework Statement A ball is attached to a string with length of L. It swings in a horizontal circle, with a constant speed. The string makes an angle (theta) with the vertical, and T is the magnitude of the tension in the string. 1)Determine the...

It's not a problem, it's a proof. The trouble being that I'm not entirely sure what I'm supposed to be proving, which is why I'm getting so confused. Our instructor told us to verify F=ma using the equations that we got from a conical pendulum lab. When further prompted, he said to divide them...