Rod and Pin Apparatus: Friction, Acceleration, and Velocity
Not what you're looking for?
Rigid rod OA is 2 ft long and rotated around fixed pt O. This rod is pinned at A to rigid connecting rod AB, 6 ft long, which in turn is pinned at B to piston C. This piston moves without friction along the y axis. The pins are also frictionless.
Rod OA is positioned so that it is pi/3 radians above the x-axis and angular velocity = 2 rad/sec counterclockwise and its angular acceleration is 0. What are the velocity and acceleration of the piston in this case?
and...
Weights of the three components are as follows: W(OA)=64.4 lb, W(AB) = 16.1 lb, W(C) = 5 lb. A constant counterclockwise torque is applied to rod OA at O. The system starts from rest with rod OA horizontal to the right. What torque is needed to give rod OA an angular velocity of 5 rad/sec when rod OA is vertical, along the y axis?
Purchase this Solution
Solution Summary
A Rod/pin apparatus is discussed. The friction, acceleration and velocity of an apparatus is given.
Solution Preview
please, see the attached .doc file.
<br>please, don't forget to rate my solution!
SOLUTION.
Here is a diagram of the rods and the piston.
a) So, lets denote the angle between OA and x-axis as .
Then, for the vertical position of the piston, Y, we can write down:
Y=OA*sin + AB*cos(OBA)
We know that = /3 + *t, where is rod OA's angular
Velosity and t is time.
Now we need to find OBA. For that, we can write down that:
OA*cos = AB*sin(OBA)
sin(OBA) = OA/AB* cos
cos(OBA) = (1 - { OA/AB* cos }2)1/2
So we can write down that:
Y = OA*sin + AB*(1 - { OA/AB* cos }2)1/2
Y = OA*sin + (AB 2 - {OA* cos }2)1/2
Now, in order to find piston's velocity and acceleration, we need to find first and second derivatives of Y:
V = dY/dt = OA * cos * d/dt +
+ ((-OA2)*2*cos * (-sin ) * d/dt) / (AB 2 - {OA* cos }2)1/2 .
Now we remember that d/dt = and we ...
Purchase this Solution
Free BrainMass Quizzes
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.
Introduction to Nanotechnology/Nanomaterials
This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.
Classical Mechanics
This quiz is designed to test and improve your knowledge on Classical Mechanics.
The Moon
Test your knowledge of moon phases and movement.
Variables in Science Experiments
How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.