A young work crew is trying to quickly finish some touch‑up painting to complete a job. Rather than setting up a secure work area, they decide to try a shortcut. Worker A will hold the far end of a 8.98 m work plank which weighs 115 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.11 m from worker A. Worker B also brings up his paint can, mc=3.42 kg, which he places 0.295 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 522 N of force to hold the end of the plank. How much does worker B weigh? The acceleration due to gravity is ????=9.81 m/s2.

Respuesta :

Answer:

Wb = 820.929N      mb = 83.68 kg

Explanation:

The given values are:

Fa = 522N                              Da = 8.98m

Wp = 115N                               Dp = 8.98/2 = 4.49m

Wb = ?                                     Db = 8.98 - 4.11 = 4.87m

Wc = 3.42*9.81 = 33.55N       Dc = 8.98 - 4.11+0.295 = 5.165m

Net torque on the plank will be:

Wp*Dp + Wb*Db + Wc*Dc - Fa*Da = 0

Solving for Wb:

[tex]Wb=\frac{Fa*Da-Wp*Dp-Wc*Dc}{Db} =820.929N[/tex]

The weight of worker B is 820.929N

Dividing by gravity we get the mass of worker B: 83.68kg