Calculating Force Required to Pull 17N Spool Over 11cm Edge

In summary, a 17N spool with outside radius 20 cm and inside radius 6.4cm requires a horizontal force of 19N to pull it over an 11cm edge. The torque exerted by the weight of the spool is calculated by finding the perpendicular distance from the corner edge to the line of the force, which can be found using basic trigonometry.
  • #1
Fusilli_Jerry89
159
0

Homework Statement


A 17N spool has an outside radius of 20 cm and an inside radius of 6.4cm as shown. What horizontal force on the rope(wrapped around the inside radius) will be required to pull the spool over an 11cm edge?
http://img299.imageshack.us/img299/6105/27kl1.png


Homework Equations


FdL+/-FdL=0
F=force
d=distance to pivot
L=perpendicular

The Attempt at a Solution


0.154F-(17)(0.09)
F=10N
Is this right?
 
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  • #2
Can anyone help?
 
  • #3
Please include units in all of your equations, and please explain your reasoning for your attempted solution.
 
  • #4
Fusilli_Jerry89 said:

The Attempt at a Solution


0.154F-(17)(0.09)
F=10N
Is this right?
No. Where did you get the 0.09 m distance? (Remember: You need the perpendicular distance to the pivot point. Perpendicular to what?)
 
  • #5
wait instead of 0.09 should it be 0.20? I'm using the corner as the pivot point.
 
  • #6
Describe to me what distance you are trying to specify: The perpendicular distance from the corner to what? What's the orientation of that distance: horizontal, vertical, at some angle?
 
  • #7
the 0.20 is the horizontal distance from the middle of the spool to the edge. Just the radius.
 
  • #8
Fusilli_Jerry89 said:
the 0.20 is the horizontal distance from the middle of the spool to the edge. Just the radius.
Since you are trying to find the torque exerted about the corner edge by the spool's weight, what you need is the perpendicular distance from the corner to the line of the force. Since the weight is vertical, the perpendicular distance will be the horizontal distance between the corner and the center of the spool. That distance is not 0.20 m, although it may look like that since your diagram is not drawn to scale. 0.20 m is the radius of the spool, not the distance to the corner edge.
 
  • #9
ok I see how the distance would get less and less as you go down the circle. But Ihave no idea how to calculate it?
 
  • #10
Fusilli_Jerry89 said:
ok I see how the distance would get less and less as you go down the circle. But Ihave no idea how to calculate it?

Draw a radius from the center of the spool vertically downward. Draw another radius to the point of contact with the step. What is the angle between those radii?
 
  • #11
with that triangle i got 58 degrees from the origin and then two 61 degrees. Ur asking for that 58 degrees right?
 
  • #12
k I solved and got approx 0.17 instead of the 0.20 I said earlier: so instead would it be:

0.154F=(17)(0.17)
F=19N
 
  • #13
Fusilli_Jerry89 said:
with that triangle i got 58 degrees from the origin and then two 61 degrees. Ur asking for that 58 degrees right?

I got something a bit different for the angle. The center of the circle is 9cm above the contact point. The angle between a horizontal radius and the radius to the contact point is sin^-1(9/20) = 26.7° so the angle to the vertical is 63.3°. You can use either angle to get the distance between the line of gravity and the contact point as 17.9cm. That's not very different from what you got. The rest looks good.
 

Related to Calculating Force Required to Pull 17N Spool Over 11cm Edge

What is the formula for calculating force required to pull a 17N spool over an 11cm edge?

The formula for calculating force required to pull a 17N spool over an 11cm edge is: Force (F) = Mass (m) x Acceleration (a). In this case, the mass would be 17N and the acceleration would be the force needed to overcome the resistance of the edge, which can be calculated using the coefficient of friction and the angle of the edge.

What is the coefficient of friction and how does it affect the force required?

The coefficient of friction is a measure of how easily one surface slides over another. It is affected by factors such as the texture and material of the surfaces. The higher the coefficient of friction, the more force will be required to overcome the resistance of the edge.

Can the force required to pull the spool over the edge be reduced?

Yes, the force required can be reduced by decreasing the coefficient of friction or by changing the angle of the edge. Using a smoother surface or lubricant can also help reduce the force needed.

What units should be used for the calculation?

The units used for the calculation should be consistent. For example, if the mass is given in kilograms, the acceleration should be in meters per second squared. It is important to double check the units to ensure accuracy in the calculation.

What are some potential sources of error in this calculation?

Some potential sources of error in this calculation could include inaccurate measurements of the spool or edge, variations in the coefficient of friction due to changing surface conditions, and human error in inputting the values into the formula. It is important to be mindful of these potential errors and take steps to minimize them for more accurate results.

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