- #1
e2m2a
- 354
- 11
I need help with this problem. This is not a homework assignment, so please don’t send it over to the homework forum.
It involves mechanical engineering dynamics that probably are more subtle and advanced then first year mechanical engineering dynamics. It might involve tensor analysis. I don’t know.
We let a mass, designated as ##m_2##, slide along a straight track with one degree of freedom with no friction. The track is rigidly attached to the earth. There is a wire attached to ##m_2## so that it can be pulled at a constant acceleration. Attached on the other end of the wire is a second mass, designated as ##m_1##. A known force of magnitude F is applied to ##m_1##, such as a magnetic force, accelerating ##m_1## and ##m_2## along the track. We define the motion of ##m_1##-##m_2## to be in the positive y-direction. The wire makes an angle ##\theta## with respect to the x-axis, and for this problem we keep the angle ##\theta## constant. Thus, the givens are: ##m_1##, ##m_2##, F, and the angle ##\theta##. I want to know the tension in the wire for any constant angle ##\theta## between 0 and 90 degrees with the above givens.
On the surface this might seem like a trivial problem, but when I do a deeper analysis, it seems to be more complicated than I can handle. For example, when ##\theta## is zero degrees, intuitively, the tension in the wire would be at a maximum, and there would be no acceleration of ##m_1##-##m_2## in the positive y-direction, and when ##\theta## is 90 degrees, the tension would be a minimum, and there would be a maximum acceleration of m1-m2. But what would the tension in the wire be at any angle between zero and 90 degrees? I can’t get my head around this. Could someone please help me with this?
It involves mechanical engineering dynamics that probably are more subtle and advanced then first year mechanical engineering dynamics. It might involve tensor analysis. I don’t know.
We let a mass, designated as ##m_2##, slide along a straight track with one degree of freedom with no friction. The track is rigidly attached to the earth. There is a wire attached to ##m_2## so that it can be pulled at a constant acceleration. Attached on the other end of the wire is a second mass, designated as ##m_1##. A known force of magnitude F is applied to ##m_1##, such as a magnetic force, accelerating ##m_1## and ##m_2## along the track. We define the motion of ##m_1##-##m_2## to be in the positive y-direction. The wire makes an angle ##\theta## with respect to the x-axis, and for this problem we keep the angle ##\theta## constant. Thus, the givens are: ##m_1##, ##m_2##, F, and the angle ##\theta##. I want to know the tension in the wire for any constant angle ##\theta## between 0 and 90 degrees with the above givens.
On the surface this might seem like a trivial problem, but when I do a deeper analysis, it seems to be more complicated than I can handle. For example, when ##\theta## is zero degrees, intuitively, the tension in the wire would be at a maximum, and there would be no acceleration of ##m_1##-##m_2## in the positive y-direction, and when ##\theta## is 90 degrees, the tension would be a minimum, and there would be a maximum acceleration of m1-m2. But what would the tension in the wire be at any angle between zero and 90 degrees? I can’t get my head around this. Could someone please help me with this?