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
torque about origin
M = R cross F
i j k
x y z
Fx Fy Fz determinant
=(y Fz-z Fy)i+(z Fx-x Fz)j *(x Fy-y Fx)k
so x component
(y Fz-z Fy)
= 1.67*60 - 7.03*7.56
= 47.1 Nm
How do you calculate the �y component.
Answer in units of Nm.
How do you calculate the �z component.
Answer in units of Nm.
To calculate the ρx component of the torque vector, you need to multiply the respective force component (Fx) by the corresponding coordinate (y - y0), where y0 is the reference point.
Given:
Fx = -88.3 N
y = 1.67 m
To calculate ρx, use the formula:
ρx = Fx * (y - y0)
Substituting the given values:
ρx = -88.3 N * (1.67 m - y0)
However, the question does not provide the value of y0, which is necessary to compute the ρx component of the torque vector. Please provide the missing information, or if you have any other questions, feel free to ask.
To calculate the �x component of the torque vector, we need to use the equation:
�x = (y * Fz) - (z * Fy)
Given the values:
Fy = 7.56N
Fz = 60N
y = 1.67m
z = 7.03m
Substituting these values into the equation:
�x = (1.67m * 60N) - (7.03m * 7.56N)
Calculating this expression:
�x = (100.2Nm) - (53.1128Nm)
Subtracting the two values:
�x = 47.0872Nm
Therefore, the �x component of the torque vector is 47.0872 Nm.