How do I calculate the weight expected on each end of a ramp as the load moves specific distances up the ramp?

Without knowing the specifics of the problem you're working on: have you considered setting sum of torque = 0 about one end or the other?

I'm trying to weigh a small trailer on a bathroom scale using a ramp 8 ft long with one end on the ground and the other end sitting on the bathroom scale. If I know the distance the trailer tire is up the ramp, know the height the ramp is off the ground and know the weight registered on the bathroom scale am I right in the following:
sum the weight of the scale times 8 ft times the cos of the angle included by the ramp and the ground plus the ramp wt times 4ft times the angle included by the ramp and the ground and make it equal to the distance the trailer tire is up the ramp times x times the cos of the angle included by the ramp and the ground and solve for x?

No need for the cosines, since all forces here act vertically. The equation to use is this:


W = S (\frac L x )- \frac 1 2 W_r

where 'W' = the weight of the load on the ramp,'S' is the indicated weight on the scale, 'L' = total length of the ramp (8 feet), 'x' = distance up the ramp from the ground that the weight is placed, and W_r is the weight of the ramp. So for example if the weight is placed two feet up the ramp, then W = 4S - (1/2)W_r.

No need for the cosines, since all forces here act vertically. The equation to use is this:


W = S (\frac L x )- \frac 1 2 W_r

where 'W' = the weight of the load on the ramp,'S' is the indicated weight on the scale, 'L' = total length of the ramp (8 feet), 'x' = distance up the ramp from the ground that the weight is placed, and W_r is the weight of the ramp. So for example if the weight is placed two feet up the ramp, then W = 4S - (1/2)W_r.

All I need is a little help from my friends. Thanks!