Two forces 5Newton and T act on a stone and are directed due northwest and northeast respectively. If the 5Newton force makes an angle 60degree with the vertical and the vertical and the weight of the stone I 4Newton, find the magnitude of the force T

Dear Student
The force of 5 N making 60 degrees with the vertical means that it is 150 degrees from east. The east direction is where zero degrees starts i.e x-axis.


There are 3 forces that will put the stone in equilibrium.
These forces have x and y components.
These forces are the 5 N, the T and the weight W.
The 3 x-components will sum up to zero and the 3 y-components will also sum up to zero.

The x – components are the 5 * cos 150, T * cos 45 and 4 * cos 270. The 3 y -components are the 5 * sin 150, T * sin 45 and 4 * sin 270.

Solving for the value of T

ΣX = 5 * cos 150 + T * cos 45 + 4 * cos 270

ΣX = 0.7071 * T + −4.3301 + 0

ΣX = 0.7071 * T + −4.3301 and to obtain zero sum, 0.7071 * T must be so that

0 = 0.7071 T + −4.3301

0.7071 T = 4.3301

T = 4.3301 / 0.7071

T = 6.1237 N
Thanks

Approved