Why is My Calculation of Force on the Door Incorrect?

In summary, the question asks for the steady force needed to move a very large door with a mass of 44,000kg and a rotational inertia of 8.7*10^4 kg*m^2. The door has a front face of 2.4m and needs to be moved from rest through an angle of 90 degrees in 30 seconds. After attempting the problem, the incorrect solution yielded a force of 304.5 N, but the correct answer is actually 130N. The error was in converting degrees to radians.
  • #1
SEG9585
34
0
Hey all--
Can someone try to ifnd what I'm doing wrong with this question, I must have sort of brain lapse in the middle of a 4-day weekend and all:

Question: A (very large) door has a mass of 44,000kg, and a rotational inertia about a vertical axis through its hingesof 8.7*10^4 kg*m^2, and has a front face of 2.4m. NEglecting friction, what steady force perpendicular to the door can move it from rest through an angle of 90 degrees in 30s?

My incorrect solution: ("@" refers to the angle in radian measure), and "&" refers to angular acceleration)

@ = 2(pi)*r/4 @=2.4(pi)/2 radians

@ = .5(&)(t^2)
1.2(pi) = .5(&)(30^2)
& = .0084 rad/s^2

I(&) = r x F = rFsin90
(8.7*10^4)(.0084) = (2.4)(F)(1)
F= 304.5 N

However, the actual answer is apparently 130N. What did I do wrong?
 
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  • #2


Originally posted by SEG9585
However, the actual answer is apparently 130N. What did I do wrong?
How many radians in 90 degrees?
 
  • #3
hah oops...yeah i knew i had a brain fart there (thinks all the way back to trig)
of course...radians don't change proportionally to radius...duhhh
Thanks Doc
 
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FAQ: Why is My Calculation of Force on the Door Incorrect?

What is rotation physics?

Rotation physics is a branch of mechanics that studies the motion of objects as they spin or rotate around an axis.

How is rotational motion different from linear motion?

Rotational motion involves objects moving around an axis, while linear motion involves objects moving in a straight line. Rotational motion also involves concepts such as angular velocity and angular acceleration, while linear motion involves concepts such as velocity and acceleration.

What is the relationship between rotational motion and torque?

Torque is the measure of a force's ability to cause rotational motion. The greater the torque applied, the greater the rotational acceleration.

How do we calculate the moment of inertia?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It can be calculated by taking the sum of the mass of each particle in an object multiplied by the square of its distance from the axis of rotation.

How does rotational motion affect an object's stability?

Rotational motion can affect an object's stability by changing its center of mass. If an object's center of mass is above its base of support, it is more stable. However, if an object's center of mass is outside its base of support, it is less stable and may topple over.

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