Inclined Ramp A 2-pound weight is attached to a 3-pound
weight by a rope that passes over an ideal pulley. The smaller
weight hangs vertically, while the larger weight sits on a
frictionless inclined ramp with angle 0. The rope exerts a
tension force T on both weights along the direction of the
rope. Find the angle measure for that is needed to keep
the larger weight from sliding down the ramp. Round your
answer to the nearest tenth of a degree.
alt
opers
:34
of
4
3 pounds
2 pounds
Answers
The angle measure for the inclined ramp needed to keep the larger weight from sliding down the ramp is 42⁰.
The given parameters;
mass of the small block, m = 2 lb = 0.91 kgmass of the larger block, = M = 3 lb = 1.36 kgThe normal force on the larger weight (3 lb) is calculate as;
[tex]F_n = Mgcos(\theta)[/tex]
The net force on the larger weight is calculated as;
[tex]Mgsin(\theta) - T = 0[/tex]
where;
T is the tension on the wire due to the smaller weight pulling up the 3 lb weight.T = mg
[tex]Mgsin(\theta) - mg = 0\\\\(1.36\times 9.8)sin\theta \ - \ (0.91 \times 9.8) = 0\\\\13.328 sin(\theta) = 8.918\\\\sin(\theta) = \frac{8.918}{13.328} \\\\sin(\theta) = 0.669\\\\\theta = sin^{-1} (0.669)\\\\\theta = 42\ ^0[/tex]
Thus, the angle measure for the inclined ramp needed to keep the larger weight from sliding down the ramp is 42⁰.
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