# What resistance in pounds is needed to pull this cart up the incline?

Or better yet what would be the formula when the angle of incline, cart weight and hanging weight vary?

Or better yet what would be the formula when the angle of incline, cart weight and hanging weight vary?

active| newest | oldestThen the hanging block would rise ΔL vertically, and the rolling block would move upward by (sin(21.8 deg))*ΔL.

So the work it takes to make these blocks move upward against their own weight is :

W = (50 lb)*ΔL + (165 lb)*(sin(21.8 deg))*ΔL

Next I am going to naively assume none of your rope-pulling work is lost to friction, so that:

W = F*ΔL = (50 lb)*ΔL + (165 lb)*(sin(21.8 deg))*ΔL

where F is the force with which you pull on the rope, and with which the rope pulls on you, at that place in the diagram labeled, "?? lbs to pull".

Divide both sides by ΔL, and get :

F = (50 lb) + (165 lb)*(sin(21.8 deg)) = 111.28 lb

Fp = W h/l

= W sin α

where:

Fp = pulling force (N, lbf)

W = m g = weight of body (N, lbf)

h = elevation (m, ft)

l = length (m, ft)

α = elevation angle (degrees)

m = mass of body (kg, slugs)

g = acceleration of gravity = 9.81 (m/s2) = 32.174 (ft/s2)