A scene in a movie has a stuntman falling through a floor onto a bed in the room below. The plan is to have the actor fall on his back, but a researcher has been hired to investigate the safety of this stunt. When the researcher examines the mattress, she sees that it effectively has a spring constant of 65144 N/m65144 N/m for the area likely to be impacted by the stuntman, but it cannot depress more than 11.79 cm11.79 cm without injuring him. To approach this problem, consider a simplified version of the situation. A mass falls through a height of 3.72 m3.72 m before landing on a spring of force constant 65144 N/m.65144 N/m. Calculate the maximum mass that can fall on the mattress without exceeding the maximum compression distance.

Question

contestada

Respuesta :

boffeemadrid boffeemadrid · Answer 1 · 2019-10-29T10:57:41+01:00

Answer:

24.06 kg

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

[tex]v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 9.81\times 3.72+0^2}\\\Rightarrow v=8.54\ m/s[/tex]

[tex]v^2-u^2=2as\\\Rightarrow a=\frac{v^2-u^2}{2s}\\\Rightarrow a=\frac{0^2-8.54^2}{2\times 0.1179}\\\Rightarrow a=-309.29\ m/s^2[/tex]

[tex]m(a-g)=-kx\\\Rightarrow m=-\frac{kx}{a+g}\\\Rightarrow m=-\frac{65144\times 0.1179}{-309.29-9.81}\\\Rightarrow m=24.06\ kg[/tex]

Maximum mass of the person is 24.06 kg