# Motion and Friction Problem

1. Jan 8, 2010

### fox2005eng

1. The problem statement, all variables and given/known data

Hi for all, basically I have a mass of 25Kg, want to move this mass with speed upto 12m/s for 15 meter long, where the mass held on 4 wheel (R= 50mm) and moving on aluminum alloy rails. I want to know the force needed and torque required, so I can be able to choose the suitable DC motor required.
actually I have tried most formulas but with no luck, as I don't know the friction coefficient.
However,
what is the suitable formulas are required here according to my question?
steps of calculations if possible?

2. Relevant equations

3. The attempt at a solution

1 – Find the time:
Given:
Velocity = 12 (m/s).
V: Velocity (m/s).
x: Distance (m).
t: Time (sec).
According to the rail length, which is = 14.9728 (m)
Time taken from the beginning of the rail until the end at speed of 12 (m/s) is:
t=V/x
= 1.2477 (seconds) taken from start of the rail until the end.
2- Find the acceleration:
V: Final velocity = 12(m/s)
V0: Initial velocity = 0 (m/s)
a: Acceleration (m/s2).
t: Time (seconds).
V=V0+2at
a = 9.62 (m/s2).
3- Find the Force:
Mass of the machine is 25 Kg , acceleration is 9.62 (m/s2), by using equation of motion can obtain the required force, by the following formula:
Newton second law:
F=ma
F: Force (N).
m: Mass = 25 Kg.
a: Acceleration = (m/s2).
Assume no friction "Ignore Friction":
F= 240.5 (N).
4- Find required torque:
Torque depends on force:
T = F x r sin theta ,
F= 240.5 (N)
r: wheel radius = 0.05 (m).
theta : Angle = 90.
T= 12 (N.m).

Last edited: Jan 9, 2010
2. Jan 9, 2010

### ideasrule

The first thing to do is to find the acceleration of the cart given a force F. To do this, draw free-body diagrams on the wheels as well as the body, write out Newton's second law and the rotational second law, and solve. This will get quite complicated, and you'll need to make some simplifying assumptions.

3. Jan 9, 2010

### ideasrule

You will, by the way, find that acceleration is independent of the coefficient of friction as long as the wheels don't slip.

4. Jan 9, 2010

### fox2005eng

it seems to complicated for me.

is it wrong ?