Finding Force to Accelerate a Wheel Cart for Bending Moment Calculation

[1988ajk]

I am having trouble trying to find the force required to accelerate a wheeled cart. so that i can calculate the bending moment in a stopping bracket,

the bit I am stuck on is The Acceleration of the cart, the situation is;

An 80,000Kg Wheeled cart runs on rails from rest and hits a stop after 7.8m at a velocity of 0.1m/s

what is the acceleration of the cart at 7.8m?,

this would allow me to find the force F=MA

I would be very grateful for your input,

*Note, this is not a homework question


Adam.

 

[Naty1]

d = 1/2at.t is one relationship to get a.

But you do NOT need that to determine the stopping force. All that matters at the moment of impact is the velocity (momentum) of the cart.

F =ma is NOT the relationship you think on the stopping side ...The "a" there would be the deceleration experienced and has nothing to do with the "a" that caused the cart to accelerate in the first place...

Try an approach like FT= MV for stopping force...you'll have to decide how long that fixed constant force "F" acts..pick a "T" during which time the cart stops...say 0.1 or 0.01 seconds or whatever you like. And recognize that because the cart may crumple..deform...upon impact, the force is not really constant...

 

[Naty1]

formula above is supposed to be d = 1/2at²

 

[1988ajk]

thanks for that,

however I think I haven't put enough detail into my problem. to find the impact stress I am using an expression from the Roark book on stress and strain where the impact stress can be calculated from a theoretical static stress.

this is the reason I was interested in the acceleration. If I use the expression for acceleration you gave, putting in time taken for the bogie to reach the stop from rest, will this value be able to be used to find the force to push the cart. F=ma

 

[PJC01]

I would suggest approaching this problem by using the principles of Newton's laws of motion. The first law states that an object at rest will remain at rest unless acted upon by an external force. In this case, the cart is initially at rest and is then acted upon by a force (presumably from a pushing or pulling mechanism) that accelerates it.

To find the acceleration of the cart, we can use the second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). In this case, the mass of the cart is given as 80,000 kg and the final velocity is given as 0.1 m/s. We can also assume that the initial velocity is 0 m/s since the cart starts from rest.

So, using the equation F=ma, we can rearrange it to solve for the acceleration (a=F/m). Plugging in the values we have, we get a= 0.1 m/s^2. This means that the cart is accelerating at a rate of 0.1 m/s^2 as it travels 7.8 m.

To find the force required to accelerate the cart, we can use the same equation F=ma and plug in the values we have for mass and acceleration. This will give us a force of 8,000 N (newtons).

Once we have the force required to accelerate the cart, we can use this value to calculate the bending moment in the stopping bracket. This can be done by using the formula for bending moment, which is M=F*d, where F is the force and d is the distance from the point of application of the force to the point of rotation (in this case, the stopping bracket). So, by plugging in the force of 8,000 N and the distance of 7.8 m, we can calculate the bending moment.

I hope this helps in your calculations and understanding of the problem. Remember to always use the principles of physics and equations to solve problems like these. Good luck!