Question

using the free-body diagram, calculate the net force acting on the sled. is the sled in a state of dynamic equilibrium?
forces: ( f_f = -225 , \text{n} ) (left), ( f_i = 225 , \text{n} ) (right), ( f_n = 50 , \text{n} ) (up), ( f_g = -50 , \text{n} ) (down)

Explanation:

Step1: Calculate net force in x - direction

Forces in x - direction: \(F_f=- 225\space N\) (frictional force, negative as it opposes motion) and \(F_i = 225\space N\) (applied force by dogs). The net force in x - direction \(F_{net,x}=F_f + F_i\)
\(F_{net,x}=-225 + 225=0\space N\)

Step2: Calculate net force in y - direction

Forces in y - direction: \(F_N = 50\space N\) (normal force, upward) and \(F_g=-50\space N\) (gravitational force, downward). The net force in y - direction \(F_{net,y}=F_N+F_g\)
\(F_{net,y}=50+( - 50)=0\space N\)

Step3: Calculate total net force

The total net force \(F_{net}=\sqrt{F_{net,x}^2+F_{net,y}^2}\) (since \(F_{net,x} = 0\) and \(F_{net,y}=0\))
\(F_{net}=\sqrt{0^2 + 0^2}=0\space N\)

Step4: Determine dynamic equilibrium

Dynamic equilibrium occurs when the net force is zero and the object is moving with a constant velocity. Since the net force is zero, if the sled is moving with constant velocity, it is in dynamic equilibrium. But from the calculation of net force, we first find the net force.

Answer:

The net force acting on the sled is \(0\space N\). If the sled is moving with a constant velocity, it is in a state of dynamic equilibrium (because net force is zero).