Question

using the free - body diagram, calculate the net force acting on the sled. is the sled in a state of dynamic equilibrium
(diagram labels: $f = - 225\\ n$, $f_n = 50\\ n$, $f_t = 225\\ n$, $f_g = - 50\\ n$)

Explanation:

Step1: Calculate net force in x - direction

For the horizontal (x - direction) forces, we have \(F_1=- 225\space N\) (negative because it is in the left - ward direction) and \(F_2 = 225\space N\) (positive because it is in the right - ward direction). The net force in the x - direction, \(F_{net,x}=F_1 + F_2=-225 + 225=0\space N\)

Step2: Calculate net force in y - direction

For the vertical (y - direction) forces, we have \(F_N = 50\space N\) (positive, upward) and \(F_g=- 50\space N\) (negative, downward). The net force in the y - direction, \(F_{net,y}=F_N+F_g = 50+( - 50)=0\space N\)

Step3: Calculate the total net force

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

Step4: Determine dynamic equilibrium

Dynamic equilibrium occurs when the net force acting on an object is zero and the object is in motion with a constant velocity. Since the net force \(F_{net} = 0\space N\), if the sled is moving with a constant velocity, it is in dynamic equilibrium. From the calculation of net force, we see that the net force is zero.

Answer:

The net force acting on the sled is \(0\space N\). The sled is in a state of dynamic equilibrium (yes).