Vector projection to find a force

[rachelmaddie]

Hi. I need my work checked please!

The force must balance the component of the weight that is parallel to the surface of the hill inclined at 15°.
F = W sin15° = (90 Ibs) sin15° = 23.29 Ibs

 

[yoscar04]

You should also include a draw of the situation including the angle of inclination of the hill and the force. Your result looks almost correct. What about the units?

 

[rachelmaddie]

You should also include a draw of the situation including the angle of inclination of the hill and the force. Your result looks almost correct. What about the units?

What units?

 

[yoscar04]

What units?

lbs are not unit of force.

 

[rachelmaddie]

lbs are not unit of force.

Oh i see. Would it be Newtons?

 

[yoscar04]

Oh i see. Would it be Newtons?

Yes. But remember you have lbs that need to be transformed into kg and then use F=mg, m in kgs and g=9.8 m/sec². Then the answer will be in Newtons.

 

[rachelmaddie]

Yes. But remember you have lbs that need to be transformed into kg and then use F=mg, m in kgs and g=9.8 m/sec². Then the answer will be in Newtons.

Wouldn’t that give me a different solution?

 

[yoscar04]

Yes.

 

[rachelmaddie]

Yes.

So I get 90 Ibs = 40.823 kilograms
(40.823 kg) sin15 = 26.54 N

 

[yoscar04]

So I get 90 Ibs = 40.823 kilograms
(40.823 kg) sin15 = 26.54 N

No. You have to multiply by 9.8. Then the result will be in Newton.

 

[rachelmaddie]

No. You have to multiply by 9.8. Then the result will be in Newton.

You mean 90 * 9.8 * sin15?

 

[yoscar04]

No. We got rid of the lbs to have kg. So why do you want to go back to lbs?
F=(40.823 kg) sin15 [MATH]\cdot[/MATH]9.8

 

[Deleted member 4993]

lbs are not unit of force.

Beg to differ. In FPS system, "pound" (lb) is the unit of force. The unit of "mass" in FPS is "slug".

I think in this problem, the expected unit of force to answer would be "lb".

So the answer should be:

F = 90 * sin(15^o) = 90 * 0.83237 = 7.4913 = 7.49 lb = 90 * 0.258819 = 23.293 = 23.3 lb ......... edited to correct the angle conversion

However, the answer in "N" is not incorrect - but kind of convoluted.

 

[yoscar04]

Beg to differ. In FPS system, "pound" (lb) is the unit of force. The unit of "mass" in FPS is "slug".

I think in this problem, the expected unit of force to answer would be "lb".

So the answer should be:

F = 90 * sin(15^o) = 90 * 0.083237 = 7.4913 = 7.49 lb

However, the answer in "N" is not incorrect - but kind of convoluted.

Thanks for the observation, I assumed that SI or MKS system was already worldwide used. In any event, your point is well taken.