Dynamics problem - Box being pulled by a rope at an angle
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Dynamics problem - Box being pulled by a rope at an angle

[From: ] [author: ] [Date: 12-02-14] [Hit: ]
determine the numerical value of the maximum acceleration when the coefficient of friction is 0.20.Any help is appreciated! Thanks so much!-(This would be easier if I could draw a picture).Do a free body diagram of the block and you would find that the net horizontal force is F*cos(theta)-(coefficient of friction)*(Normal Force).......
Given: A force of 100 lb, with variable direction THETA, acts on an 85 lb block.

Find: If the acceleration of the block is maximum when THETA= 11.31 degrees, determine the numerical value of the maximum acceleration when the coefficient of friction is 0.20.

Any help is appreciated! Thanks so much!

-
(This would be easier if I could draw a picture).

Do a free body diagram of the block and you would find that the net horizontal force is F*cos(theta)-(coefficient of friction)*(Normal Force).

The normal force is the net vertical force which will = (Weight)-F*sin(theta)

Plugging in the numbers you provided,
normal force = 85-100*sin(11.31) = 65.39 lb.
Net horizontal force = 100*cos(11.31)-(.2)*(65.39) = 84.98 lb.

Using newton's second law, the acceleration of the block would then be (84.98 lbf)/(85 lbm) = 32.2 ft/(s^2). Note that the English units are a pain here and you need conversion factors to do newton's second law.
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