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I need to use this to find a motor that will be able to pull at most 2250 kg at a 1.5 m/s pace. At peak acceleration, I would like this to accelerate at 0.5 m/s2. The area that the load will be pulled is a concrete sidewalk with, at its most extreme, a 20° incline.

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    $\begingroup$ This is not a do your homework or project site - show what you have done so far. $\endgroup$ – Solar Mike Mar 15 '18 at 17:48
  • $\begingroup$ Welcome to Engineering! This looks like a "homework question" (notice the quotation marks). In order for such questions to be answered in this site, we need you to add details describing the precise problem you're having. What have you tried to solve this yourself? Please edit your question to include this information. $\endgroup$ – Wasabi Mar 15 '18 at 18:44
  • $\begingroup$ sliding, on wheels, or what? $\endgroup$ – agentp Mar 15 '18 at 18:55
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Ignoring friction, because you have not provided any details regarding this in your question, and assuming that the object starts from rest on a $20°$ incline, and accelerates at a peak rate of $0.5m/s^2$ on it's way to a max speed of $1.5m/s$

The force required to stop a static object from rolling down a hill is the same as that required to keep it at a constant speed on that hill, $F_1=mg\sin\theta$.

The additional resultant force required to provide an acceleration of $0.5m/s^2$ can then simply be added using $F=ma$, therefore,

$$F=m(g\sin\theta+a)$$

Which equates to a peak force in your case of:

$$F=2250(9.81\sin20+0.5)=8674=8.7kN$$

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Your question contradicts itself. Acceleration will mean infinitely increasing speed.

If we disregard that and assume a steady speed of 1.5m/s up a ramp of 20 degrees for a mass of 2250kg, you need:

$P= mgh/s= 2250(9.8)sin(20)1.5$

And force = P/vertical velocity= P/sin(20)1.5

This is the force needed. From here depending on the diameter of the winch's pulley you can calculate the torque needed. Just divide the power by the diameter.

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  • $\begingroup$ "At Peak acceleration" suggests that the acceleration will drop off after a certain time, i.e. speed does not increase infinitely. Acceleration is critical to calculating the force required - remember $F=ma$! $\endgroup$ – Jonathan R Swift Mar 16 '18 at 14:24

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