Balancing a spring and arm at 45 degrees

[Ziv7]

I need to find what spring will balance an arm at 45 degrees
the arm is 5m and can be considered as a UDL of 1.6kg/m
the situation is that the arm starts upwards at 90 degrees and as it goes down it puts tension on the extension spring


5*1.6 = 8kN
acting 2.5m along the beam
which is 1.77m in direction x (horizontal)
8000*1.77 = 14160Nm (the moment acting at 45degrees)

how do I find the details on the spring? (diameter, length etc)
Maybe I'm approaching it wrong, any advice would be appreciated :)

 

[CWatters]

What two points is the spring connected between ? Diagram might help.

 

[Ziv7]

Here is what i mean

 

[CWatters]

Ok. I reckon the spring needs to produce a torque about the pivot of

= 8 * 9.8 * 2.5 * cos(45)
= 138.6 NM

PS: Normally we like you to have a go at the solution first.

 

[rezeew]

I would suggest approaching this problem using the principles of engineering mechanics and specifically, statics. In order to find the details of the spring needed to balance the arm at 45 degrees, we need to first determine the forces and moments acting on the system.

From the given information, we know that the arm is 5m long and has a uniform distributed load (UDL) of 1.6kg/m. This means that the total weight of the arm is 8kN (1.6kg/m * 5m = 8kN). Since the arm is at a 45 degree angle, the weight can be resolved into two components: a vertical component of 8kN*cos(45) = 5.66kN and a horizontal component of 8kN*sin(45) = 5.66kN.

Next, we need to consider the tension force acting on the extension spring as the arm moves downwards. This tension force is equal to the weight of the arm at that position, which we have already determined to be 8kN.

Now, using the principle of moments, we can find the moment acting on the system at 45 degrees. This moment is equal to the sum of the moments of all the forces acting on the system. In this case, the only force with a moment arm is the weight of the arm, which has a moment arm of 2.5m (half the length of the arm). Therefore, the moment acting on the system is 8kN * 2.5m = 20kNm.

Finally, we can use the equation for the moment of a spring (M = k*x, where k is the spring constant and x is the displacement) to find the required spring constant for the given moment. Rearranging the equation, we get k = M/x = 20kNm/1.77m = 11.3kN/m.

Now that we have the spring constant, we can use it to find the details of the spring such as the diameter and length. This will depend on the specific type of spring being used. For example, if we are using a helical spring, we can use the equation k = G*d^4/8*D^3*N, where G is the shear modulus, d is the wire diameter, D is the mean coil diameter, and N is the number of active coils. This