The man in the figure below is slowly pulling a drum over acircular hill. The dr

Question

The man in the figure below is slowly pulling a drum over acircular hill. The drum weighs 60 N, and the hill issmooth. Find the tension in the rope (which does not varyalong the rope if the hill is smooth) for every position ofthe drum, starting when the drum is on the ground at the left anduntil the rope attached to the drum is horizontal. The man in the figure below is slowly pulling a drum over acircular hill. The drum weighs 60 N, and the hill issmooth. Find the tension in the rope (which does not varyalong the rope if the hill is smooth) for every position ? ofthe drum, starting when the drum is on the ground at the left anduntil the rope attached to the drum is horizontal. Diameter of drum: 1meter distance from drum to the end of that triangle: 2 meters

Explanation / Answer

Thetangential force necessary to keep the ball in place at any pointis:

.

F.t =60N cos

.

But weknow that the drum has a radius 1m and that it is 2m before therope touches the surface of the hill. This means that the Radius ofthe hill is

(R+1m)^2 = R^2 + (2m)^2

R =3/2m

.

We canthen find the angle that the rope makes with the tangent to thehill. This will be

=90degrees - atan((3/2)/2)

=53.15 degrees

.

Thetension in the rope will therefore need to be:

F = T =F.t / cos

T = 60Ncos / .6

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