How Does Cart Acceleration Affect Tension in a Moving Pendulum?

[phlegmy]

hey guys
i'm writing a computer prog in visual basic that models a gantry crane.
(basically modeling a pendulum that has a moving point of suspension)

the point of suspension, the cart, has a mass
the bob of the pendulum, the load, has a mass also

in order to calculate the net forces (horizontal) on the cart and load, to determine their accelerations, velocities and displacements, it is nescessary to know the tension in the cable that connects them.

what i need is a formula for calculating the tension in the cable given the two masses , the length of cable and the driving force F on the cart!

so far i have gotten the programme to work but am worried that my formula for tension is not complete

i have taken the tension= loadmass*g*cos(angle) + loadmass*cablelength*angularvelocity
, where the angle is the angle incurred by the cable to the verticle
which i think is correct for a pendulum with a fixed point of suspension
the second term is the centripedal force due to angular velocity

the net horizontal force on the load = tension*sin(angle)
and net horizontal force on cart = F- tension*sin(angle)



has anyone got any suggestions
i can "picture" it in my head;
the faster i accelerate the cart (very large F)
the greater the tension in the cable
is this greater tension accounted for in the fact that if the cart accelerates very quicly, the anglular velocity will be much greater and as a result tension will be much greater?
OR is it nescessary (as i suspect) to add another term containing F, the driving force on the cart, to the formula for tension?

any suggestions or insights appreciated
james!

 

[quinn]

tension on cable = mg*(cos(angle of cable with normal)) + m*(v^2)/(cable length)

Force on mass= mg*(sin(angle of cable with normal)

 

[charng]

I can provide some insights into the tension in a moving pendulum. First, it is important to understand that the tension in the cable is a result of the forces acting on the pendulum. In this case, the tension is a combination of the weight of the load and the centripetal force due to the angular velocity. Your formula for tension is correct for a pendulum with a fixed point of suspension.

However, as you mentioned, when the cart accelerates quickly, the angular velocity will also increase, resulting in a greater tension in the cable. This is because the centripetal force is directly proportional to the angular velocity. So, yes, the tension will increase as the cart accelerates quickly.

In addition, the driving force on the cart (F) should also be taken into account in the formula for tension. This is because the driving force is also a factor in determining the net horizontal force on the load and cart. So, adding another term containing F to the formula for tension would be necessary to accurately calculate the tension in the cable.

Overall, it seems like you have a good understanding of the forces at play in a moving pendulum and how they affect the tension in the cable. Keep in mind that there may be other factors to consider, such as friction and air resistance, which could also affect the tension. I would suggest continuing to refine your formula and considering all the forces involved to accurately model a gantry crane in your program. Good luck!