Engineering Crate lowered by two ropes and deceleration at each point of contact with rope

AI Thread Summary
The discussion revolves around the confusion regarding the application of relative motion and angular acceleration in a problem involving a crate lowered by two ropes. Participants clarify that only vertical forces induce torque, and thus only horizontal distances are relevant for calculating angular acceleration. The differences in braking forces at points A and B lead to unbalanced vertical deceleration, causing angular acceleration about the center of mass. The key takeaway is that when dealing with parallel accelerations, only perpendicular distances should be considered for torque calculations. Understanding these principles is crucial for solving rigid body kinematics problems accurately.
Pipsqueakalchemist
Messages
138
Reaction score
18
Homework Statement
Question and attempts below
Relevant Equations
Newton’s law
Relative acceleration
For this question, I don’t understand the steps for the relative motion part. When I try it I get angular acceleration to be zero which is obviously wrong. The solution doesn’t consider the Y distance between G and A but I don’t understand why. In the relative motion equation it’s suppose to be the position vector from G to A but if you consider that like I did it’s wrong. This is how I’ve been solving the problems so far and in rigid body kinematic so I’m very confused right now
 

Attachments

  • 11A36A71-4C5B-4E30-B16B-66DD93AA5708.png
    11A36A71-4C5B-4E30-B16B-66DD93AA5708.png
    31.8 KB · Views: 148
  • 262ACDC6-6597-4185-9D71-EE6625E01E8E.png
    262ACDC6-6597-4185-9D71-EE6625E01E8E.png
    19.1 KB · Views: 152
  • image.jpg
    image.jpg
    31.9 KB · Views: 162
Last edited:
Physics news on Phys.org
Pipsqueakalchemist said:
Homework Statement:: Question and attempts below
... I’m very confused right now
Sometimes it helps to type out the problem statement :rolleyes:
When I try it I get angular velocity to be zero which is obviously wrong
This isn't about angular velocity, but about angular acceleration

And I agree with
PeroK said:
PS You should try to learn latex
Micromass said:
##\ ##
 
Last edited:
Sorry I meant angular acceleration
 
So did I do something wrong and I’m not suppose to consider the Y component of the position vector from G to A?
 
Anyone?
 
Pipsqueakalchemist said:
... The solution doesn’t consider the Y distance between G and A but I don’t understand why.
The only forces inducing a moment or torque that induces the angular acceleration are all vertical.
The relative distances to be considered for calculating that torque should be all perpendicular to those forces; therefore, horizontal distances between fulcrums and projection of vertical forces are the only significant in this problem.

WrenchTorque2.gif
 
Lnewqban said:
The only forces inducing a moment or torque that induces the angular acceleration are all vertical.
The relative distances to be considered for calculating that torque should be all perpendicular to those forces; therefore, horizontal distances between fulcrums and projection of vertical forces are the only significant in this problem.

WrenchTorque2.gif
But I’m using relative acceleration so there’s no moments or torques in the equation.
 
Is it safe to say that when using two point on an rigid body whose velocity are parallel to each other that we only consider perpendicular distance? Bc I don’t think I’ve had an problem where the two points being parallel to each other so I always consider both horizontal and vertical distances.
 
Pipsqueakalchemist said:
But I’m using relative acceleration so there’s no moments or torques in the equation.
What is the reason for the angular acceleration about G then?
TA>TB because the brake of crane A is applied more strongly than the brake of crane B.

Wherever there is a mass under acceleration (positive or negative) there is a force.
There is no force without direction and intensity.

In this case, the upward braking forces applied at A and B are different in magnitude, so one side of the crate vertically deccelerates more than the other and its center of mass vertically deccelerates at a rate between those two, and at the same time it angularly accelerates because the unbalanced pair of vertical braking forces applied 3.3 feet on its left and 3.3 feet on its right side.
Hence, the member 3.3xalpha in the solution equations (3) and (4) of the book.
 
  • #10
Lnewqban said:
What is the reason for the angular acceleration about G then?
TA>TB because the brake of crane A is applied more strongly than the brake of crane B.

Wherever there is a mass under acceleration (positive or negative) there is a force.
There is no force without direction and intensity.

In this case, the upward braking forces applied at A and B are different in magnitude, so one side of the crate vertically deccelerates more than the other and its center of mass vertically deccelerates at a rate between those two, and at the same time it angularly accelerates because the unbalanced pair of vertical braking forces applied 3.3 feet on its left and 3.3 feet on its right side.
Hence, the member 3.3xalpha in the solution equations (3) and (4) of the book.
So is it the case that since all the acceleration are parallel I can just focus on the perpendicular distances. Bc as I said above I’ve always considered both the horizontal and vertical distances when considering the position vector (r_AB) and I’ve noticed in these scenarios A and B had acceleration, velocity that weren’t parallel
 
Back
Top