Final answer:
The force required to produce a torque on a rod about the origin is calculated using the formula F = T/r, where F is the force, T is the torque, and r is the distance. In this case, the force required is 4.0 kN.
Step-by-step explanation:
The force F required to produce a torque on a rod can be calculated using the formula:
F = T/r
where F is the force, T is the torque, and r is the distance from the origin to the point where the force is applied.
In this case, the torque is given as 8.0 kN.m and the distance is 2.0 m, so the force required is:
F = 8.0 kN.m / 2.0 m = 4.0 kN
Therefore, a force of 4.0 kN must be applied to the end of the rod along the x-axis to produce a torque of 8.0 kN.m about the origin.