5-point star resultant force question

[jfletch]

Any help on where I start with this question. Need to convert each force into its horizontal and vertical components, but don't know any angles apart from the 70N force acting straight down.

 

[ehild]

Any help on where I start with this question. Need to convert each force into its horizontal and vertical components, but don't know any angles apart from the 70N force acting straight down.

The lines of the forces connect the vertices of a regular pentagon to the centre. What angle do they enclose with each other? What are their angles with respect to the positive x axis?

ehild

 

[voko]

Surely you can figure out the angles. The star is uniform, so the angle is the same between any two adjacent forces. And you know what the sum of all the angles is.

 

[jfletch]

Thanks for the help.

 

[Nickie]

To begin solving this question, we can first draw a diagram of the 5-point star and label the forces acting on it. From the given information, we know that there is a 70N force acting straight down. We can also label the other forces as A, B, C, and D.

Next, we need to find the horizontal and vertical components of each force. To do this, we can use trigonometric functions such as sine and cosine. Since we only know the angle of the 70N force, we can use this to find the horizontal and vertical components of that force. The horizontal component would be 70N*cos(0) = 70N and the vertical component would be 70N*sin(0) = 0N.

For the other forces, we can use the Pythagorean theorem to find their magnitudes. For example, for force A, we can use the equation A^2 = (70N)^2 + (70N)^2 to find that A = 99.0N. To find the horizontal and vertical components of A, we can use the angles formed by the force with the horizontal and vertical axes. This can be found by drawing a right triangle with A as the hypotenuse and using the inverse trigonometric functions.

Repeat this process for forces B, C, and D, and you will have the horizontal and vertical components for all the forces acting on the star. Then, to find the resultant force, we can use the vector addition method by adding all the horizontal components together and all the vertical components together. The resultant force would then be the square root of the sum of the squares of the horizontal and vertical components.

In summary, to solve this question, we need to use trigonometric functions, the Pythagorean theorem, and vector addition to find the horizontal and vertical components of each force and then find the resultant force. This process can be applied to other similar problems involving forces acting at different angles.