Question

a 40kg wagon is towed up a hill at 18.5degrees with respect to the horizontal. The tow rope is parallel to the incline and has a tension of 140N .Assume that the wagon starts from rest at the bottom of the hill and neglect friction. How fast is the wagon going after moving 80m up the hill

Answer 1

Starting with Newton's 2nd law (Fnet = mass*acceleration), 

F(net acting on wagon) = Tension - mgsin(18.5) = ma 

140 - 40.0 * 9.81 * sin(18.5) = 40.0 * a ...gives us the acceleration up the plane. 

Now "armed" with vo=0 (initial velocity of wagon), a in m/s^2 and distance = 80.0 meters, we use 

vf^2 = vo^2 + 2ad to find the velocity. 

vf = SQRT(2*80 * [140 - 40.0 * 9.81 * sin(18.5)]/40) 

vf = 2*SQRT(140 - 402.4 * sin (18.5)) in meters/sec