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Hello,
I hope this is a suitable forum, it's a million miles from homework but it may be on the same sort of level.
A picture is worth a thousand words so please have a look at the attached picture. When the rope is pulled there isn't just the issue of gravity, but also of the friction of the rope over the metal bar. What I am wanting to calculate is the actual force that must be applied to stop the weight from falling, taking into account the friction.
I really don't know where to start with this, but from the searching that I've done, this page seems to be using diagrams and words that seems applicable. http://www.engineeringtoolbox.com/bollardforced_1296.html
The equation given is:
S = F e^{μα}
Where:
S = effort force in the rope (N)
F = load (N)
e = 2.718
μ = friction coefficient (approximately 0.3  0.5 is common for a rope around a steel or cast iron bollard)
α = angle where the rope is in contact with the bollard (radians)
So, plugging in the following data (assuming the rope is only in contact with half the bollard):
F = 300N
e = 2.718
μ = 0.4
α = ∏
I get:
300 * ( 2.718 ^{0.4 * ∏} ) = 85.39 N
Which seems to imply that the force that is needed to stop the weight from falling is 214.6 1N (30085.39). However, I've got a feeling that I might be messing up the calculation, would somebody be kind enough to take a look for me?
Thank you.
I hope this is a suitable forum, it's a million miles from homework but it may be on the same sort of level.
A picture is worth a thousand words so please have a look at the attached picture. When the rope is pulled there isn't just the issue of gravity, but also of the friction of the rope over the metal bar. What I am wanting to calculate is the actual force that must be applied to stop the weight from falling, taking into account the friction.
I really don't know where to start with this, but from the searching that I've done, this page seems to be using diagrams and words that seems applicable. http://www.engineeringtoolbox.com/bollardforced_1296.html
The equation given is:
S = F e^{μα}
Where:
S = effort force in the rope (N)
F = load (N)
e = 2.718
μ = friction coefficient (approximately 0.3  0.5 is common for a rope around a steel or cast iron bollard)
α = angle where the rope is in contact with the bollard (radians)
So, plugging in the following data (assuming the rope is only in contact with half the bollard):
F = 300N
e = 2.718
μ = 0.4
α = ∏
I get:
300 * ( 2.718 ^{0.4 * ∏} ) = 85.39 N
Which seems to imply that the force that is needed to stop the weight from falling is 214.6 1N (30085.39). However, I've got a feeling that I might be messing up the calculation, would somebody be kind enough to take a look for me?
Thank you.
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