Final answer:
Yes, it is possible for a situation where 0=∑ f is satisfied and 0=∑ τ is not, indicating that the object is in translational equilibrium but not in rotational equilibrium.
Step-by-step explanation:
Whether it is possible for a situation to exist where 0=∑ f is satisfied while the equation 0=∑ τ is not satisfied depends on the conditions of the system. According to static equilibrium situations in physics, for an object or system to be in complete static equilibrium, it must satisfy both conditions: The net force must be zero (net F = 0), and the net torque must be zero (net τ = 0). These two conditions are necessary to ensure that the object is neither translating nor rotating. Therefore, it is possible to have 0=∑ f (no net force) and not have 0=∑ τ (net torque is not zero) at the same time. This would occur in a situation where the forces are balanced, but their application does not balance out the torques, possibly due to the forces being applied at different distances from a pivot point.