Question

2. During a play, Peterpan is lowered from above the stage using the following setup (see figure below) He cannot descend too quickly to avoid being hurt and must land on the stage not moving any faster than 4.4 m/s (which is equivalent to free falling from a 1 m height). If the stage crew is using sandbags as their counterweight with μ = 0.54, Peterpan weighs 160 lbs, and must be lowered a distance of 50 ft,how heavy must the sandbags be so that he reaches the ground safely? How long will it take him to reach the stage? Does this seem like a realistic setup, explain l 50ft θ-600

Answer 1

First, look at the free body diagram

Let

$m \longrightarrow \text{mass of Peterpan,}\\ M \longrightarrow \text{mass of the counterweight,}\\ T \longrightarrow \text{Tension in the string,}\\ l \longrightarrow \text{height at which Peterpan is hanging,}\\ a \longrightarrow \text{acceleration,}\\ g \longrightarrow \text{acceleration due to gravity.}$

I will work in SI units, so

$l=50\text{ft}=15.24\text{m}, \\ m=160\text{lbs}=72.57\text{kg},\\ u=0\text{m/s,}\\ v=4.4\text{m/s}, \\ \theta=60^{\circ}.$

and Mt M

Now, remember that the Maximum allowed velocity is 4.4m/s.