To protect themselves from invading pirates, the good and quite funny folk of th

Question

To protect themselves from invading pirates, the good and quite funny folk of the humerus peninsula are building strange devices to launch giant pie shaped cannon balls. The launcher consists of a sled on an incline of 30 degree that leads up to a sled stopper that is 100m above the water. The sled (about 100kg including the pi ball) is pulled up the ramp by a strong rope and is suddenly stopped by the, yes you guessed it, sled stopper causing the pie to be launched at incoming wessels. To create tension in the rope a large mass is dropped off the edge of the cliff. The rope is connected to the sled over a series of two polished, rounded, and slotted stones. In experimental tests the humerus engineers determined: that the coefficient of friction between the sled and the ramp was 0.2, that pie shaped cannon balls fly much less hindered by the breeze than round ones, and that there is nothing humerus about an engineer! Your job is to determine the minimum tensile strength required in the rope for the launcher and to determine the hanging mass to fire shots at the pirate ships.

Explanation / Answer

PROJECTILE

1)

along horizantal

initial velocity vox = vo*costheta

ax = 0

from equaiton of motion

x = vox*T+ 0.5*ax*T^2

x = vo*costheta*T

T = x/(vo*costheta)......(1)

along vertical

voy = vo*sintheta

acceleration ay = -g = -9.8 m/s^2

from equation of motion

y = voy*T + 0.5*ay*T^2

y = (vo*sintheta*x)/(vo*costhetra) - (0.5*g*x^2)/(vo^2*(costheta)^2)

y = x*tantheta - ((0.5*g*x^2)/(vo^2*(costheta)^2))

given

y = -100 m

x = 300 + 10 = 310 m m

theta = 30

-100 = (310*tan30) - (0.5*9.8*310^2/(v0^2*(cos30)^2))

v0 = 47.4 m/s <<<--------answer

length of incline L = 100/sin30 = 200 m

along incline acceleration a = v0^2/(2*L) = 47.4^2/(2*200) = 5.62 m/s^2

along incline

for sled

Fnet = m*a

T - (m*g*sintheta) - uk*m*g*costheta) = m*a

T - (100*9.8*sin30) - (0.2*100*9.8*cos30) = 100*5.62

T = 1221.74 N <<<-------answer

for hanging mass M

Mg - T = M*a

M*9.8 - 1221.74 = M*5.62

M = 292.2 kg <<<---------answer

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