Subscribe to our Youtube Channel - https://you.tube/teachoo

Last updated at Feb. 6, 2020 by Teachoo

Transcript

Example 18 A beam is supported at its ends by supports which are 12 metres apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 1 cm? Beam is always facing upwards with the axis vertical Since, the axis is positive y-axis, its equation is x2 = 4ay First we find coordinates of point B Given Width of beam = 12 m Hence, AB = 12 m So, BC = ๐ด๐ต/2 = 12/2 = 6 m Also, there is a deflection of 3 cm from centre So, OC = BD = 3 cm OC = BD = 3 cm = 3/100 m Hence point B is B(6, ๐/๐๐๐) Now, Since point B(6, 3/100) lies on the parabola Putting x = 6, y = 3/100 in equation x2 = 4ay (6)2 = 4a (3/100) 36 = (3๐ )/25 3/25 a = 36 a = (36 ร 25)/3 a = 12 ร 25 a = 300 m Now, we need to find how far from the centre is the deflection 1 cm Hence RQ = 1 cm, We need to find OP QP = 3 cm โ 1 cm = 2cm = 2/100 m Let OP = x So, coordinates of point Q is Q (x, ๐/๐๐๐) Since point Q lies on parabola it will satisfy the equation of parabola Equation of parabola is x2 = 4ay Putting x = x & y = 2/100 m & a = 300 m x2 = 4 (300) (2/100) x2 = 1200 ร 2/100 x2 = 24 x = โ24 = โ(6 ร4) = 2โ6 ๐ Thus, the required distance is 2โ๐ ๐

Examples

Example 1

Example 2

Example 3 Important

Example 4 Important

Example 5

Example 6 Important

Example 7 Important

Example 8 Important

Example 9

Example 10 Important

Example, 11

Example 12 Important

Example 13 Important

Example 14 Important

Example 15

Example 16 Important

Example 17

Example 18 Important You are here

Example, 19 Important

Chapter 11 Class 11 Conic Sections

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.