A force F=Fx ˆi + Fy ˆj + Fz ˆk acts on a particle located at X= (x, y, z). Given Fx=−88.3N, Fy=7.56N, Fz=60N, x= −3.65m, y=1.67m and z=7.03m,
calculate the three components of the torque vector ~� = �xˆi + �y ˆj + �z ˆk .
First, calculate the �x component.
Answer in units of Nm
Tx =Fx•X = (-88.3) •(-3.65) = 322.2 N,
Ty =Fy•Y = (7.56) •(1.67) = 12.63 N,
Tz = Fz•Z = 60•7.03 = 421.8 N
T = 322.2•I +12.63•j + 421.8•k
To calculate the x-component of the torque vector �x, we need to use the formula:
�x = y * Fz - z * Fy
Given that y = 1.67 m, Fz = 60 N, and Fy = 7.56 N, we can substitute these values into the formula:
�x = 1.67 m * 60 N - 7.03 m * 7.56 N
Now we can calculate the x-component of the torque vector:
�x = 100.2 Nm - 53.112 Nm
Finally, we subtract the two values:
�x = 47.088 Nm
Therefore, the x-component of the torque vector is 47.088 Nm.