- #1

whatdoido

- 48

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1. Homework Statement

1. Homework Statement

I drew a picture of this problem, which should show up below. Lengths x,a and b were given in the original picture.

A rotating closed cylinder is braked with a bar. Its brake shoe is pressed in respect of point B without friction. The bar AB presses the cylinder. Force [itex]F_1[/itex] is used in point A.

Calculate the needed force when cylinder stops from a rotational speed of 1200 RPM clockwise in 12 seconds. Cylinder's mass is 14 kg, radius 6,5 cm and frictional coefficient 0,33.

[itex]r=6,5 cm= 0,065m[/itex]

[itex]\mu=0,33[/itex]

[itex]x=7,0 cm=0,07m[/itex]

[itex]a=19 cm=0,19m[/itex]

[itex]b=1,2 cm=0,012m[/itex]

[itex]m=14kg[/itex]

[itex]\Delta t=12s[/itex]

[itex]n=1200 RPM=20r/s[/itex]

## Homework Equations

[itex]M=J\alpha[/itex]

[itex]M=Fr[/itex]

[itex]J=\frac{1}{2}mr^2[/itex]

[itex]\sum M=0[/itex]

## The Attempt at a Solution

Well I know how to calculate the force needed to stop the rotating cylinder

[itex]M=J\alpha\hspace{30mm}M=\mu Nr[/itex]

[itex]J\alpha=\mu Nr[/itex]

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[itex]N=\frac{mr2\pi n}{t \mu}[/itex]

[itex]=28,877... N[/itex]

[itex]F_1[/itex] can be calculated with torques I'm pretty sure, but this is the spot where I am stuck at. Something like [itex]F_2 x=F_1 (x+a)[/itex] won't do. I should somehow take in the consideration the clockwise movement of cylinder (in part b of this problem it is supposed to calculate [itex]F_1[/itex] in counter-clockwise movement). Cylinder has a torque [itex]F_3[/itex], right? So I thought that is what I am supposed to use, but I'm not sure how to proceed.. I tried using some angles and make it work, but I cannot think something that would make me think "oh of course! That's how I can solve it" and give me the correct answer, eventually.