How Can I Calculate the Force Needed to Push a Trolley Over a Bumpy Floor?

[rookie37]

Will somebody please help me with a physics problem?

At work we have very heavy carts. The floor is in terrible shape. Management knows that they need to fix the floor but don't know if it will be cost effective. I.E. money spent on floor vs. increased production.I want to make a spreadsheet. I don't know the math and I need your help.I want to have 3 variablesThe mass of the cart. the diameter of the wheel, and the size of the bumps on the floor will all change. I want to find out how many Newtons it takes to push this trolley.

M mass

D dia of wheel

H height of bump on floorstep 1

I need the math formula of how many Newtons will it take to get this trolley moving from a stationary position?step 2

How many Newtons will it take to push this trolley over a bump on the floor? H
please see this drawing

http://content.screencast.com/users/dchristensen777/folders/Default/media/60586f4a-cedd-4117-8698-04afc5060eaa/trolly.bmp

 

[mfb]

That will depend on details of the bump structure, the size and typical mass and speed of the trolleys, the way they absorb shocks, and various other factors that are impossible to include in a pen&paper solution with reasonable effort (i.e. significantly cheaper than getting a new floor).
Experiments are probably easier - you can measure the time and effort needed to push a trolley over flat and bumpy ground, for example.

 

[rookie37]

Suspension on the trolley is impossible. $10 million worth of machinery is designed for this trolley. If suspension was added, it would not fit in the machines.

I understand that bump size, shape, and speed are a big factor. I'm not worried about that. I only want a rough idea. I'm doing this on my own, without pay. The managers don't know that I'm even doing this. Trials are not an option for political reasons. Half of the management don't even want to know how bad the floor is. 30% of the workers on the shop floor (including me) have health problems from pushing hundreds of these trolleys around all day. The intention of this spreadsheet is not to have an accurate rate of force required. It is to show that the bumps in the floor and the size of the wheels make a big difference. (and will give the managers that want the floor repaired some ammunition. At the moment, some of the managers are being an ostrich and are trying not to realize that the floor causes injury.

'It can't be done because ...' is an automatic response. Managers are not the only ones that do it. Some people that hang out on forums do it as well.

 

[mfb]

You can try to use some geometry to estimate the angle the trolleys have to take to get up to a bump (or out of a hole) and then calculate the force needed for this angle - similar to an inclined plane, a standard textbook question. I doubt the result will help much, but that's probably the best you get without experiments or with a lot of effort.

If the trolleys carry sensitive or expensive material around, there could be another argument to fix the floor.

 

[pmacias]

Thank you for reaching out for help with this physics problem. I understand your concern about the heavy carts and the condition of the floor. It is important to consider the cost-effectiveness of fixing the floor versus the potential increase in production.

To help you with your spreadsheet, I suggest using the following equation to calculate the force needed to push the trolley:

F = μmg

Where:
F = force needed (in Newtons)
μ = coefficient of friction between the wheels and the floor
m = mass of the trolley
g = acceleration due to gravity (9.8 m/s^2)

To calculate the force needed to overcome a bump on the floor, you can use the following equation:

F = mg(sinθ + μcosθ)

Where:
θ = angle of the bump
μ = coefficient of friction between the wheels and the floor
m = mass of the trolley
g = acceleration due to gravity (9.8 m/s^2)

Using these equations, you can input the variables of mass, diameter of the wheel, and height of the bump to determine the force needed to push the trolley in both scenarios.

I hope this helps you with your spreadsheet. If you need further assistance, please don't hesitate to ask. I am always happy to help with physics problems. Good luck with your project!