find the amount of force valid to keep the system in equilibrium

Question

A rope is being pulled with a force of 366 N parallel to the horizontal surface toward the right, five men are pulling the same rope parallel to the horizontal surface but toward left, what amount of force should an individual apply towards the left to keep the rope in the equilibrium position? (suppose that each of the men is contributing the same amount force).

Answer 1

The acceleration is the rate of change of velocity.

 

Since both the acceleration and initial velocity are on vectors pointing in the j direction, then the motion will continue to be straight in the j direction.

 

The formula for velocity at time t given constant acceleration is v = v₀ + at, so it will be (500 + 3t) j m/s.

 

The formula for position is 1/2 at² + v₀t + s₀.  (s_t is position at time t.)  Since the initial position is the origin (0 in the j direction), the position will be 1/2 * 3 * t² + v₀t = (1.5 t² + 500t) j