A beam whose centre of gravity divides it into two portions, a and s placed inside a smooth sphere; show that, if 0 be its inclination to the horizon che position of equilibrium and 2a be the angle subtended by the beam at the tre of the sphere, them b - a tan 0 = tan a. 6 + a

A beam whose centre of gravity divides it into two portions, a and s placed inside a smooth sphere; show that, if 0 be its inclination to the horizon che position of equilibrium and 2a be the angle subtended by the beam at the tre of the sphere, them b - a tan 0 = tan a. 6 + a

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter11: Addition And Subtraction Of Decimal Fractions

Section: Chapter Questions

Problem 18A: Refer to the plate shown in Figure 117 and determine the following distances. All dimensions are in...

See similar textbooks

Related questions

Q: By how much will f(x, y, z) = e" cos yz change as the point P(r, y, z) moves from the origin a…

A: Given function is At origin,

Q: 29. The shaded band shown here is cut from a sphere of radius R by parallel planes A units apart.…

A: To show: That the surface area of the band is 2πRh. Given: The shaded band is cut from a surface pf…

Q: Let P(cos t, sin t) be a point on the unit circle x2 + y2 = 1 in the first quadrant. Show that t is…

Q: Find the length of one turn of the helix given by…

A: Given: The parametric equation of the curve: .

Q: Find the angle 0 E [0, between the planes 2x - y+z= 1 and x + z = -3. Lütfen birini seçin:…

A: Given that the two planes: P1:2x-y+z=1P2:x+z=-3Normal are,Let, n^1: 2i-j+k=1n^2: i+k=-3

Q: A point is rotating with uniform circular motion on a circle of radius r.Find ω if r = 8 cm and v =…

A: Given linear velocity and radius are: Formula used for angular velocity in rad/sec is:

Q: A beam whose centre of gravity divides it into two portions, a and b. is placed inside a smooth…

Q: Find the length of the curve: "(1) =/21i +e'j+e°k, 0 si sl

Q: A point is rotating with uniform circular motion on a circle of radius r. Find ? if r = 10 cm and v…

Q: Assume that the two points (x1 y1) and (x2.y2) lie on the graph of the straight line y = mx + b. Use…

Q: Find the length of the curve r(t) (e" cos(2t), e" sin(2t), e"), -2 sts 2 %3D

A: I am attaching image so that you understand each and every step.

Q: "A denotes the area of the sector of a circle of radius r formed by the central angle u. Find the…

A: r=5 & A=3

Q: Find polar equaton or the curve represented by the given Cartesian equaton 5at +j=8x(ris not equal…

Q: Given that the distance of BC is 469 m and CD is 156 m, bearing of BC = 70° east of south and…

A: Given that the distance of BC is 469 m and CD is 156 m, bearing of BC = 70° east of south and…

Q: At points on a circle of radius a, line segments are drawn perpendicular to the plane of the circle,…

A: We have to find the area of the surface formed by the perpendiculars to the xy-plane of length ks…

Q: Find the length of the hypocycloid defined by the equations x = a cos° (0), y = a sin° (0), 0 < 0 <…

A: Here we have to find the length of the hypocycloid defined by the equation x=acos3(θ) , y=asin3(θ)

Q: A beam whose centre of gravity divides it into two portions, a and b. is placed insıde a smooth…

A: I am attaching image so that you understand each and every step.

Q: A beam whose centre of gravity divides it into two portions, a and b. is placed insıde a smooth…

Q: A beam whose centre of gravity divides it into two portions, a and b, is placed insıde a smooth…

Q: Consider the curve C parametrized byx = −1 + 6 sin t and y =(1/2)− 6 cos t for −π ≤ t ≤ 7π. What is…

A: First of all, consider the given parametrized equation of curve C. Rearrange the equations to write…

Q: Find the length of one arch of the cycloid 2(t – sin(t)), y = 2(1 – cos(t). х

Q: s denotes the length of the arc of a circle of radius r subtended by the central angle θ. Find the…

A: Since, we know that s=rθ, where θ is the central angle.s denotes the length of the arc of a circle…

Q: For which values of a E R the tangent plane to the graph of f(r, y) = 1+ sin(ar + y?) at the point…

A: Given a curve f(x,y)=1+sinαx+y2 We have to give value of Alpha such that the tangent plane to given…

Q: The curves r1(t) = (4t, t³, – 5t°) and i2(t) = (sin( – 2t), sin( – 5t), t – T) intersect at the…

A: Solve the following

Q: Given the cardioid r= 3(1+cosθ) 0 ≤ θ ≤ 2π Determine in wich points the cardiod has vertical…

A: Differentiate the equations r=31+cosθ and x=rcosθ with respect to θ, to find drdθ and dxdθ.…

Q: Find the length of one arch of the cycloid 8(t – sin(t)), y = 8(1 – cos(t)). %3D

A: Given: x = 8(t -sint(t)) y = 8 (1-cos(t)) To find the length of arc.

Q: If we ignore air vesistance, then the range RO) of 'a ves pect to the X axis base ball hit at an…

Q: A point is rotating with uniform circular motion on a circle of radius r. Find v if r 3 inches and w…

A: Given radius and ω are 3 inches and 5 rad/sec, respectively.

Q: Which of the following is an arc length parametrization of a circleof radius 4 centered at the…

Q: A curve is defined by the parametric equations cos z dz, sin z dz, t > 1. X= y= Find the length of…

A: Use the formula for the length of curve in parametric form.

Q: A plane travels from point A on a bearing 150° to a point B 10 km from A as illustrated above. How…

A: We are given the following information. We need to find AC.

Q: Ex. 3. the horizontal plane through the point of projection. If a and B are the possible angles of…

Q: Show that the surface area obtained when the arc of the parabola y? = 16az from I = 0 to r = h is…

A: Surface area

Q: Find the measure of the angle between planes x + y − z = 3 and 3x − y + 3z = 5. Give the answer in…

Q: Find the length of one arch of the cycloid a = 9(t – sin(t)), y = 9(1 – cos(t)). %3D

Q: 6. If AF = 23in find the length of arc EC and the area of that sector. %3D 87 148 F E D B.

Q: The unit circle a + y: =1 can be wrriten in parametric form as x = cos(0) and y= sin0. Find and…

Q: (a) Find the exact length of the curve (i) r = 1+ sin 0, (ii) r = 2(1+ sin 8), 0<0< 27, 0<0< 2n.…

A: We have to find arc length of give curve after that we have to find relationship between their…

Q: (b) Consider the cycloid C parametrized by x = t – sin t and y = 1 – cos t, for all real t. Find…

A: Solution x= t-sint, y =1-cost C(0) = (0,0) C(pi) = (pi-sin pi, 1-cos pi) = (pi, 2) C(2pi) = (2pi-0,…

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

Q: 12.The temperature at each boint of a metel plate i given by the functien %3D :) In What disection…

A: The temperature function is given by Tx,y=excosy+eycosx the Temperature rise will be given by…

Q: 1. AB and AC are tangent to 00 at B and C. If mBC = x, then m LBAC = (С) 360 - х %3D (А) x (B) 180 -…

A: Given a circle with center at O and there are two tangents at B and C from an external point A. Also…

Q: a cosece, y = b cot0, then %3D x? , y? A) ? b? 可 x? y? = 1 ? b? 1 B - a a If x = a sec0,y= b tan 0,…

A: Given:6. x=a cosecθ, y=b cotθ7.x=a secθ, y= b tanθ

Q: If the angle at which the radius vector cuts the √√²-a² 2 1 a curve 0 = COS be o, then a r cos o…

Q: Use the figure and the given information to answer the questions that follow. 1. If mPR = 45 and mQS…

Q: AT is tangent to oG. 8 10 Find: AN. AN = %3D units

Q: A bascboll is thrown with an nitial velocity of 45 myr = 6ol6 f%s at an angle morizontal and from…

A: Given: Initial height above the ground h0 = 5 feet Initial velocity v0 = 66 feet/second

Question

I need the answer as soon as possible

A beam whose centre of gravity divides it into two portions, a and
b, is placed inside a smooth sphere; show that, if 0 be its inclination to the horizon
in the position of equilibrium and 2a be the angle subtended by the beam at the
centre of the sphere, thom
b - a
tan 0 =
tan a.
b + a

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Refer to the plate shown in Figure 117 and determine the following distances. All dimensions are in inches. a. The horizontal center distance between the 0.265" diameter hole and the 0.150" diameter hole. b. The horizontal center distance between the 0.385" diameter hole and the 0.150" diameter hole. c. The distance between edge A and the center of the 0.725" diameter hole. d. The distance between edge B and the center of the 0.385" diameter hole. e. The distance between edge B and the center of the 0.562" diameter hole.
Refer to the prisms of Exercises 1 and 2. Which of these have symmetry with respect to one or more planes?
For compactness, the drop-down wheels of a stretcher or gurney are folded under it as shown. In order for the boards upper surface to be parallel to the ground when the wheels are dropped, what relationship must exist between AB and CD?
If MNPQ is a rhombus, which formula from this section should be used to calculate its area? Exercise 46
For Exercises 39 to 44, make drawings as needed. How many common tangent planes do two externally tangent spheres have?
aBecause point Q is their common center, these circles are known as _ circles. bIf RQ=3 and QV=5, find the length of chord TV which is also a tangent to the inner circle.
Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
Three spheres are externally tangent to each other in pairs. Their radii have lengths of 1 in., 2 in., and 3in., respectively. What type of triangle is formed by the lines of centers?