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Mechanics: Manual Drill Eccentricity

  • Thread starter JohanM
  • Start date
  • #1
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Homework Statement


In order to manually drill a hole, as shown below, it is important to keep the drill perpendicular to the surface. The drill is spun by a 30-lbf force applied downward at the handle at B, while pressure on the bit at A is obtained by applying a 10-lbf force along the x-axis at C. The handle currently lies along the x-z plane and the wall does not supply a reaction moment at A.

a) Find the other axial components of the force applied at C that are required to keep the bit at A oriented solely along the x-axis.
b) Find the equivalent force and moment couple at A that results from the applied forces at B and C.
2m34369.jpg

Homework Equations


[itex]\vec{M}=\vec{r}\times\vec{F}[/itex]

The Attempt at a Solution



My approach was to determine the moments of B and C about point A first.

[itex]\vec{M}^{F_{B}}_{A}=\left\langle 8,0,-6 \right\rangle \times \left\langle 0,-30,0 \right\rangle [/itex]
[itex]=\left\langle -180,0,-240 \right\rangle [/itex]

[itex]\vec{M}^{F_{C}}_{A}=\left\langle 16,0,0 \right\rangle \times \left\langle -10,C_{y}, C_{z} \right\rangle [/itex]
[itex]=\left\langle 0, -16C_{z}, 16C_{y} \right\rangle [/itex]

I then assumed that only the x-component of the moments about A should be non-zero, and said that Cz=0 and 16Cy=240, yielding Cy=15 lb.

However, when I calculate the resultant force and the moment couple at A, the moment couple equals zero:

[itex]F_{R}=(-10)\hat{i} + (-30+15)\hat{j} + 0\hat{k}[/itex]
[itex]\theta=tan^{-1}(\frac{15}{10})=56.3^{\circ}[/itex]

[itex]M_{A}=(10)(0)+(-15 lb)(16 in)+(30 lb)(8 in)[/itex]
[itex]=0[/itex]

Clearly, the moment couple at point A is not zero, so my approach is wrong...
What should I change?

Thanks in advance,
Johan
 

Answers and Replies

  • #2
Spinnor
Gold Member
2,102
316
Why can't the moment couple at point A be zero? If it were not zero wouldn't the drill not stay on axis? Sorry if this is an obvious question.
 

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