Vectors/equilibrium in AS Physics

Could someone pls help me with these Qs? For the first two, I just need the theory, not calcs. themseleves. I was away when they studied this, and can't find much information on it. Also, does anyone know of a gd website about resultant and resolving forces???

1) A mass of 5 kg is suspended in equilibrium, by 2 light inextensible strings which make angles of 30 degrees and 45 degrees with the horizontal. Calculate the tensions in the strings.

2) A body of weight 10N supported in equilibrium by 2 light inextensible strings. The tensions in the strings are 7N and T and the angles the stings make with the upward vertical are 60 degrees and q respectively. Calculate T and q.

3) The diagram shows a light inextensible string with one end fixed at A and a mass of 5Kg suspended at the other end. The mass is held in equilibrium at an angle q to the downward vertical by a horizontal force P. Find q by trigonometry to find the magnitude of the force P and the tension T.

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Reply 1

thefish_uk

*girlie*

1) A mass of 5 kg is suspended in equilibrium, by 2 light inextensible strings which make angles of 30 degrees and 45 degrees with the horizontal. Calculate the tensions in the strings.

2) A body of weight 10N supported in equilibrium by 2 light inextensible strings. The tensions in the strings are 7N and T and the angles the stings make with the upward vertical are 60 degrees and q respectively. Calculate T and q.

3) The diagram shows a light inextensible string with one end fixed at A and a mass of 5Kg suspended at the other end. The mass is held in equilibrium at an angle q to the downward vertical by a horizontal force P. Find q by trigonometry to find the magnitude of the force P and the tension T.

Helps to draw a diagram...

1. if we call the tension in the string at 30 degrees T1 and the tension in the string at 45 degrees T2...

object's weight is 50N
Resolving(horizontally): T2 cos 45 - T1 cos 30 = 0 so T2cos45 = T1cos30
Resolving(vertically): T2sin45 + T1sin30 - 50 = 0 so T2sin45 + T1sin30 = 50
Difficult to explain without a diagram, basically you want the vertical and horizontal components of each force.

2.
R(vert): 7cos60 + Tcosq - 10 = 0
R(horiz): 7cos60 - Tcosq = 0

Very hard to explain without a diagram... hmmm...

Googling returns this: http://library.thinkquest.org/28388/Maths/Vector/Vector3.htm

Reply 2

john !!

1. You can take the vertical component of the forces on the mass. Obviously there are 5g N acting down and there are also (from trig.) A sin 30 + B sin 45 N acting upwards. You can then take the horizontal components and say that A cos 30 = B cos 45 (since there is no resultant force horizontally as well as vertically). Drawing a diagram will really help. You can then solve the simultaneous equations in variables A and B.

2. Do the same as above (take vertical and horizontal components to get 2 equations with the two variables T and q.. solve!) again a diagram really helps.

3. I'm not sure since the diagram doesn't match up with the question in terms of labelling, but use the same things and the answer will probably fall out again.

Try this for a website ... its the only one I could find to use in AS:
http://www.bearwoodphysics.com/asa2revision1.htm