Question

A box is pulled up a rough ramp that makes an angle of 22 degrees with the horizontal surface. The surface of the ramp is the x-plane.There is a free body diagram drawing on a block on a 22 degree incline with 5 force vectors. The first force is pointing up and parallel to the surface of the incline, labeled F Subscript T Baseline. The second force is pointing down and parallel to the surface of the incline, labeled F Subscript f Baseline = 14.8 N. The third force is pointing away from and perpendicular to the surface of the incline, labeled F Subscript N Baseline = 65 N. The fourth force is pointing into and perpendicular to the surface of the incline, labeled F Subscript g y Baseline. The fifth force is pointing straight down to the center of the earth, labeled F Subscript g Baseline = 70 N. There is another force parallel to the surface of the incline and down the hill starting at the tip of the F Subscript g y Baseline vector; it is labeled F Subscript g x Baseline.

What is the magnitude of the force of tension if the net force in the x direction of 98 N?

57 N
139 N
178 N
183 N

Answer 1

Sum forces along the incline (positive up the ramp):

FT - Ff - Fgx = Fnet,x = 98 N.

Compute the downslope component of gravity: Fgx = 70 sin 22° ≈ 70(0.3746) ≈ 26.22 N.

So FT = 98 + 14.8 + 26.22 ≈ 139.02 N ≈ 139 N.

Answer: 139 N.