Calculating Minimum Force for Turning a Barrel over a Step

[tgpnlyt7095]

Homework Statement

Find the smallest horizontal force required to push the barrel over the step.

Homework Equations

n/a

The Attempt at a Solution

By the principle of moments,
F x 0.2 = 1500 x 0.5 .
Thus, F = 3750N.

I think that there's a smaller force, right??

 

[Doc Al]

By the principle of moments,
F x 0.2 = 1500 x 0.5 .

What's the height of the force F? Where's your pivot?

 

[tgpnlyt7095]

What's the height of the force F? Where's your pivot?

the height is 0.2 + 0.5 = 0.7m.

The pivot , i suppose is the edge of the step ??

 

[arkofnoah]

basically this.

http://img535.imageshack.us/img535/5620/screenshot20100806at013.png

 

[tgpnlyt7095]

basically this.

http://img535.imageshack.us/img535/5620/screenshot20100806at013.png

thanks :D

 

[Doc Al]

the height is 0.2 + 0.5 = 0.7m.

Your diagram shows the force level with the center of the barrel. I guess that's wrong? And the height of the step is labeled as 0.2, but it's drawn as being at the height of the force.

What's the height of the step? Where is the force applied? At h = .5? or .7?

The pivot , i suppose is the edge of the step ??

Right. So what's the moment arm (distance) for computing the torque due to F?

 

[tgpnlyt7095]

Your diagram shows the force level with the center of the barrel. I guess that's wrong? And the height of the step is labeled as 0.2, but it's drawn as being at the height of the force.

What's the height of the step? Where is the force applied? At h = .5? or .7?Right. So what's the moment arm (distance) for computing the torque due to F?

My apologies. the height of the step is 0.2m . And 0.5 represents the radius of the circle.
The force is applied at the height of 0.7m

 

[Doc Al]

My apologies. the height of the step is 0.2m . And 0.5 represents the radius of the circle.
The force is applied at the height of 0.7m

Excellent. So what's the torque due to that force about the pivot? And what's the torque due to the weight of the barrel?

 

[tgpnlyt7095]

Excellent. So what's the torque due to that force about the pivot?

It should be, F x D = 1500N x 0.7m = 1050Nm

 

[Doc Al]

It should be, F x D = 1500N x 0.7m = 1050Nm

What's the value of D? I assume the barrel weighs 1500 N? How far is the center of the barrel from the edge of the step?

 

[tgpnlyt7095]

What's the value of D? I assume the barrel weighs 1500 N? How far is the center of the barrel from the edge of the step?

Distance of Barrel from the centre to the edge of the step
= 0.5m

so is it F x D = 1500N x 0.5m
= 750Nm ??

 

[arkofnoah]

the weight (1500N) is not perpendicular to the distance so it's not 1500N x 0.5m.

you need to use some trigo here, i think (unless there's a shortcut method).

 

[tgpnlyt7095]

the weight (1500N) is not perpendicular to the distance so you can't do 1500N x 0.5m

But i thought its a circle ??

 

[tgpnlyt7095]

I think i got it.

F x D , = 1500N x ( 0.5m - 0.2m )
= 450Nm

 

[Doc Al]

Distance of Barrel from the centre to the edge of the step
= 0.5m

No. That's the radius of the barrel. (Use a bit of trig/geometry.)

so is it F x D = 1500N x 0.5m
= 750Nm ??

Again, D is the distance between the line of the applied force F and the pivot. So what is D?

 

[tgpnlyt7095]

No. That's the radius of the barrel. (Use a bit of trig/geometry.)


Again, D is the distance between the line of the applied force F and the pivot. So what is D?

0.5m - 0.2m = 0.3m

 

[arkofnoah]

No. That's the radius of the barrel. (Use a bit of trig/geometry.)

actually the distance of Barrel from the centre to the edge of the step is the radius of the circle :tongue:

 

[Doc Al]

actually the distance of Barrel from the centre to the edge of the step is the radius of the circle :tongue:

LOL... yeah, I should have said "What is the horizontal distance from barrel center to the edge of the step".

 

[tgpnlyt7095]

Sorry .. ;(

 

[Doc Al]

0.5m - 0.2m = 0.3m

What's the height of F? What's the height of the step? The vertical distance between them is D.

 

[tgpnlyt7095]

What's the height of F? What's the height of the step? The vertical distance between them is D.

Okay, so the torque is 1500 x 0.3 = 450N ?

 

[arkofnoah]

okay... you need to find the perpendicular component of both forces (in green).

http://img843.imageshack.us/img843/5620/screenshot20100806at013.png

and you'd probably need trigo to do that (though I suspect there's some form of symmetry here. hmmm).

 

[tgpnlyt7095]

okay... you need to find the perpendicular component of both forces (in green).

http://img843.imageshack.us/img843/5620/screenshot20100806at013.png

and you'd probably need trigo to do that (though I suspect there's some form of symmetry here. hmmm).

Gosh... I appreciate the opportunity u guys had given me to be involved in the thinking procedures of solving this question but i have not learned trigo in my elementary mathematics ... is there an alternative ?

 

[arkofnoah]

trigo is the surefire and easiest way to do this. i think you might somewhat bypass using trigo by falling back on geometry (from the look of that diagram) but it's probably very clumsy and non-intuitive, if it's possible at all.

 

[tgpnlyt7095]

trigo is the surefire and easiest way to do this. i think you might somewhat bypass using trigo by falling back on geometry (from the look of that diagram) but it's probably very clumsy and non-intuitive, if it's possible at all.

Can i take a look at the solution / steps involved??

 

[arkofnoah]

something like this using similar triangles:

http://img689.imageshack.us/img689/4745/screenshot20100806at025.png

just a rough sketch i don't know if i got the alternate angles right so do check it again. you should pick up trigo asap because the above method is rather crude.

 

[tgpnlyt7095]

something like this using similar triangles:

http://img689.imageshack.us/img689/4745/screenshot20100806at025.png

just a rough sketch i don't know if i got the alternate angles right so do check it again. you should pick up trigo asap because the above method is rather crude.

So, based on this diagram, what am i supposed to find ?

Can u show me the trigo way of doing it ?

 

[arkofnoah]

based on similar triangles (you learned this before right), find W' (the green one). Assuming that the net moment is zero when F is just enough to balance W, W' = F'. From F' get F using similar triangles again.

 

[tgpnlyt7095]

based on similar triangles (you learned this before right), find W' (the green one). Assuming that the net moment is zero when F is just enough to balance W, W' = F'. From F' get F using similar triangles again.

What about the trigo way ??

 

[arkofnoah]

OH! actually i just realized we don't need to do all that.

F x 0.3 = 1500 x 0.4

That's it (the sides of the triangle I've drawn is found using pythagoras' theorem). Sorry for complicating the matter :tongue:

 

[tgpnlyt7095]

OH! actually i just realized we don't need to do all that.

F x 0.3 = 1500 x 0.4

That's it (the sides of the triangle I've drawn is found using pythagoras' theorem). Sorry for complicating the matter :tongue:

where does 0.4 comes from ??

 

[tgpnlyt7095]

why do all these? from the centre of the barrel to the edge, its still the radius that is concerned , which is 0.5. is there a need to use pythagoras theorem ??

 

[arkofnoah]

you need to find the perpendicular distance from either of the forces to the fulcrum (i.e. the edge). Look at my diagram again the 0.4 is one of the sides of the triangle I've found using pythagoras' theorem. This is the simplest method.