FIND.................
Answers
Answer:
(-4,4) and (4,4)
Explanation:
According to the question, the deflected beam is in the shape of the parabola
x² = 4ay
and (0,0) is the point of maximum deflection.As deflection in the center is 9cm, y co-ordinate of the points of support is +9. Assuming the beam is symmetrically loaded and geometrically symetric about its center, x co-ordinates of the support points are -6 and 6.Hence (-6,9) and (6,9) lie on the beam and satisfy the given parabola.
So, 6² = 4a*9
or 36 = 36a
or a = 1
Thus the equation becomes
x² = 4y ...........(1)
Now deflection of the required points is 5cm. Therefore their y co-ordinate is 9-5 = 4
Putting this value of y in equation (1),we get
x² = 4*4
or x = ±4
Therefore (-4,4) , (4,4) are the points on the beam with deflection 5 cm.
Please mark it as brainliest answer.
Answer:
2 m far from the center is the deflection 1 cm.
To find : How far from the center is the deflection 1 cm?
Given :
A beam is supported at its ends by supports, 12 m apart.
Load is concentrated at its center.
Deflection occurs at the center of 3 cm.
Deflected beam is in the shape of parabola.
Note :
With the given data graph has drawn which is attached below, refer it for better understanding.
From the drawn graph it shows that parabola is formed in y-axis :
So, the parabola equation is x² = 4ay.
Here, "R" is the midpoint of P and Q.
PQ = 12 cm.
OR = 3 cm.
RQ = = = 6 cm.
Converting 6 m to 6 cm :
1 m = 100 cm
6 m = 6 × 100 = 600 cm.
Co-ordinates of Q = (600, 3)
Where, x = 600 ; y = 3
Applying the values of "x" and "y" in the equation of parabola we get,
x² = 4ay.
(600)² = 4 × a × 3
120000 = 12 a
a = = 30000
a = 30000.
Applying the values of "a" in the equation of parabola we get,
x² = 4ay.
x² = 4 × 30000 × y.
x² = 120000y.
Finding deflection :
AB = 1 cm.
AC = 3 cm.
OC = x cm.
BC = ?
BC = AC - AB
= 3 - 1 = 2
BC = 2 cm.
B(x, 2) lies on the parabola.
Applying the values of "B" in the equation of parabola, we get
B(x, 2)
x² = 4ay.
x² = 4 × 30000 × y.
x² = 4 × 30000 × 2.
x² = 240000
x =
x = 200 cm ⇒ 2 m.
x = 2 m.
Therefore, the distance is 2 m.