Question

Firefighters need to go from their resting quarters on the second floor to their equipment, 10 feet below, in a hurry.

Answer 1

Answer:

a)  t = 0.622 s , v = 7.73 m / s , b)  K = 2539 J , c)  -2443.4 J , d)    fr = 803.75 N

Explanation:

A) when the fireman from the second floor is in a free fall motion the time to arrive, we can calculate it with kinematics

       y = v t + ½ g t²

When you jump your initial speed is zero

      y = ½ g t²

      t = √2y / g

Let's reduce the magnitude to the SI system

    y = 10 feet (0.3048 / 1 foot) = 3,048 m

    t = √ (2 3,048 /9.8)

    t = 0.622 s

The speed at this point is

   v² = v₀² + 2 g y = 0 + 2g y

   v = √ (2 9.8 3.048)

   v = 7.73 m / s

B) The kinetic energy is

    K = ½ m v²

    K = ½ 85 7.73²

    K = 2539 J

C) The relationship between work and kinetic energy is

   W = ΔK = $K_{f}$ - K₀

The initial kinetic energy is zero because when its high speed is zero.

   $K_{f}$ = ½ m v²

   $K_{f}$= ½ 85 1.5²

   $K_{f}$ = 95.6 J

 

  W2 = 95.6 - 0 = 95.6 J

The variation of work in free fall less with friction

    ΔW = W2 -W

    Δw = 95.6 -2539

   ΔW = -2443.4 J

This is the work done by the friction forces

C)

   W2 = fr d cos θ

The angle is 180º because the friction opposes the movement

   W2 = - fr d = -2443.4

   fr = 2443.4 / d = 2443.4 / 3,048

   fr = 803.75 N