Question

A body of mass 10kg is suspended by inextensible string from a nail 0 and pulled by horizontal force F until the angle of inclination of the string to the vertical is 30° calculate the value of F and the tension T in the string.

Answer 1

By Newton's law, the body will be at rest if the sum of the projections of forces is equal. From here we get the angle of deviation from the vertical.

$$F_T​∗sinα−F∗cosα=0$$

Horizontal force balancing load is equal to:

$$F=F_T*tg\alpha=mg*tg\alpha=10*9.81*0.577=56.6N$$

The tension force of the thread is equal to:

$$T=F_T*cos\alpha+F*sin\alpha=85+28.3=113.3N$$

Answer: 56.6N, 113.3N