Exercise 2.36 Two sticks and a wall

Two sticks are connected, with hinges, to each other and to a wall. The bottom stick is horizontal and has length LL, and the sticks make an angle of θ\theta with each other, as shown in Figure above. If both sticks have the same mass per unit length, ρ\rho, find the horizontal and vertical components of the force that the wall exerts on the top hinge.

Also show that the magnitude goes to infinity for both θ\theta00 and θ\thetaπ2\frac{\pi}{2}

Note by Beakal Tiliksew
5 years ago

No vote yet
1 vote

</code>...<code></code> ... <code>.">   Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in </span>...<span></span> ... <span> or </span>...<span></span> ... <span> to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

alt text alt text

In the above figure, I have marked all the forces that are present in the system. Let the masses of the two rods be m1\displaystyle m_1 and m2\displaystyle m_2.

Thus,
m1=ρLsecθm_1 = \rho L\sec\theta m2=ρLm_2 = \rho L

Considering the torque about the point A,
h1(Ltanθ)=(m1+m2)gL2h_1(L\tan\theta) = (m_1+m_2)g\frac{L}{2}

h1(Ltanθ)=ρL(1+secθ)gL2h_1(L\tan\theta) = \rho L (1+\sec\theta)g\frac{L}{2}

h1=ρ1+secθtanθgL2\boxed{h_1 = \rho\frac{1+\sec\theta}{\tan\theta}\frac{gL}{2}}

Ill do the vertical force later..Ill post it as a comment

Anish Puthuraya - 5 years ago

Log in to reply

Nice explanation

Mardokay Mosazghi - 5 years ago

Log in to reply

Why are there no forces at the hinge joining the 2 sticks ??

CH Nikhil - 3 years, 10 months ago

Log in to reply

There are forces at the hinge joining the sticks, but they are internal forces. So, they cancel each other off..

Anish Puthuraya - 3 years, 10 months ago

Log in to reply

@Anish Puthuraya Got it ! Thanks a lot !!

CH Nikhil - 3 years, 10 months ago

Log in to reply

do you know any good book with exersises in rotational dynamics ;

aris nikolaidis - 4 years, 5 months ago

Log in to reply

Try IE Irodov or Krotov

Pranjal Jain - 4 years, 5 months ago

Log in to reply

The vertical force can be found using the pivot point B. It is -(rholg/2)(1+2sec(theta)).

Harsh Bhardwaj - 11 months, 2 weeks ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...