Question

An orange sphere is attached to a string and also resting on a post as shown below. The x and y coordinates are defined as shown. String Wall 25T Post

Please answer part(a) to part(d)

We initially want to express the tension (T), the normal force (N) and the Weight (W) in terms of polar coordinates

(a) what is the polar angle of the tension in degrees?

(b) what is the polar angle of the normal force in degrees?

(c) what is the polar angle of the weight in degrees?

(d) Suppose the weight W is known to be 20 N and we want to determine the tension T and the normal force N.

Write down a few steps for the general procedure you would use to determine T and N using MatLab. Start out with the fact that you know the polar angles of the three forces.

Hints: How do we use Newton's second law in a static equilibrium situation and in what coordinate system should we write Newton's second law? Do we need to convert from polar coordinates to some other coordinate system? If we use conversion commands in MatLab, which one would we use. What would be the units in which the conversion commands expect the arguments?

Answer 1

a) Polar angle for tension - 090+25 = 1150 = 2950 b) Polar angle for normal force = 90-20= 70' c) polar angle for weight = 270º d) By D'alembert enneople, the body is in rest and so net force is zero. for accomponent, & Nos 700 & Tos 185 = 0. - N-– T cos115 - +1.23T cos 70 For y-component, Noin 70 + T sin 115 & wsin 270 20. --) 1237.(sin 70 ) + Tsinll15) = 20. - T- 20 9.732 N. 1. 155 +0.90 Thus, No 1.23 49.732 = Clogn