# Statics of a particle Watch

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Two forces P and Q act on a particle at the origin O. Force P acts along the 0x, Q makes an angle with 0x. Calculate the Magnitude of the resultant force and the angle it makes with 0x when:

P = 4N, Q=3N feta =60

We are given the angle 60, according to my drawing this angle is outside the right angled triangle, and so therefore to find the inner angle that is opposite to the angle we are eventually to find - I did this:

180 - 60 = 120

We are given two lengths, so in order to find R we must use the cosine rule:

R^2=b^2+c^2 - 2bc cos A

R^2 = 3^2 + 4^2 - 2(3)(4) * cos120

= 9+ 16 - 24 * cos120

R = sqrt37

=6.08

According to my diagram, it would be wise to the sine rule as this traingle is not a <ABC triangle.

R / sin120 = 3/sin feta

sin feta therefore equals = 3 sin120 / sqrt37

which is wrong the angle should be 25.3

Thank you v much!

P = 4N, Q=3N feta =60

We are given the angle 60, according to my drawing this angle is outside the right angled triangle, and so therefore to find the inner angle that is opposite to the angle we are eventually to find - I did this:

180 - 60 = 120

We are given two lengths, so in order to find R we must use the cosine rule:

R^2=b^2+c^2 - 2bc cos A

R^2 = 3^2 + 4^2 - 2(3)(4) * cos120

= 9+ 16 - 24 * cos120

R = sqrt37

=6.08

According to my diagram, it would be wise to the sine rule as this traingle is not a <ABC triangle.

R / sin120 = 3/sin feta

sin feta therefore equals = 3 sin120 / sqrt37

which is wrong the angle should be 25.3

Thank you v much!

0

(Original post by

It's theta, not feta. That's a type of cheese

**juno_the**)It's theta, not feta. That's a type of cheese

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(Original post by

If you tell me whether P and Q act towards or away from the origin, then I can answer the question I think.

**Nima**)If you tell me whether P and Q act towards or away from the origin, then I can answer the question I think.

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(Original post by

The question already gives you the angle. Why are you trying to find another one?

**dvs**)The question already gives you the angle. Why are you trying to find another one?

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(Original post by

I am trying to find the inner angle of the triangle , I will draw picture of what I think the question looks like, bare with me for a sec.

**DOJO**)I am trying to find the inner angle of the triangle , I will draw picture of what I think the question looks like, bare with me for a sec.

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#10

The resultant force equals sqrt[37] N. Apply the sine rule to get:

(sinT)/3 = (sin120)/sqrt[37] [120 is from 180-60 -- draw the diagram and complete a parallelogram]

sinT = 3(sin120)/sqrt[37]

T = 25.3

(sinT)/3 = (sin120)/sqrt[37] [120 is from 180-60 -- draw the diagram and complete a parallelogram]

sinT = 3(sin120)/sqrt[37]

T = 25.3

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(Original post by

The resultant force equals sqrt[37] N. Apply the sine rule to get:

(sinT)/3 = (sin120)/sqrt[37] [120 is from 180-60 -- draw the diagram and complete a parallelogram]

sinT = 3(sin120)/sqrt[37]

T = 25.3

**dvs**)The resultant force equals sqrt[37] N. Apply the sine rule to get:

(sinT)/3 = (sin120)/sqrt[37] [120 is from 180-60 -- draw the diagram and complete a parallelogram]

sinT = 3(sin120)/sqrt[37]

T = 25.3

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(Original post by

Here's my interpretation. (I appologize for the crappy drawing.)

**dvs**)Here's my interpretation. (I appologize for the crappy drawing.)

sinT = 3(sin120)/sqrt[37]

T = 25.3

It comes out as 0.427121098 and not 25.3. My calc is set in degrees mode.

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#14

(Original post by

It comes out as 0.427121098 and not 25.3. My calc is set in degrees mode.

**DOJO**)It comes out as 0.427121098 and not 25.3. My calc is set in degrees mode.

First time, I read that the question only wanted you to find the resultant force, so I got confused when I saw you trying to find an angle. Second time, I thought you didn't know how to do the question. And now, I finally know what's wrong... You're finding sinT, and not T. Try finding arcsin(0.427121098) (inverse sine). If your calculator's one of those scientific Casios, press shift and sin, then = (after you get 0.427121098 on the screen).

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(Original post by

I really should start reading the entire post before replying...

First time, I read that the question only wanted you to find the resultant force, so I got confused when I saw you trying to find an angle. Second time, I thought you didn't know how to do the question. And now, I finally know what's wrong... You're finding sinT, and not T. Try finding arcsin(0.427121098) (inverse sine). If your calculator's one of those scientific Casios, press shift and sin, then = (after you get 0.427121098 on the screen).

**dvs**)I really should start reading the entire post before replying...

First time, I read that the question only wanted you to find the resultant force, so I got confused when I saw you trying to find an angle. Second time, I thought you didn't know how to do the question. And now, I finally know what's wrong... You're finding sinT, and not T. Try finding arcsin(0.427121098) (inverse sine). If your calculator's one of those scientific Casios, press shift and sin, then = (after you get 0.427121098 on the screen).

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