A weight driven catapult is used to launch a plane along a rail The following ar

Question

A weight driven catapult is used to launch a plane along a rail The following are the givens:

the weight=1400 lbs. it is dropped 16.5 feet; weight is connected to plane through a 3:1 pulley. This pulley means the plane is pulled (3)(16.5)=49.5 feet before the pilot releases the rope. The tug of the rope is weight/3; plane motor=21 hp and drives the plane up to 35mph; plane weight=780 lbs pilot weight=160 lbs;...I know, tons of info.

1]how much work is being done by the falling weight?(W=FxD)

2]work done by the weight is same as work done by the plane, but the distance is tripled by the pulley system. What is the force pulling the plane when the weight is falling?

3]power is work per unit time. can also be expressed as Force x Velocity. The motor is 21hp and achieves 35mph. What thrust can the motor achieve? (convert mph to ft/sec; one hp=550 ft.lb/sec).

4]F=ma where m=W/g(g=32.2 ft/sec^2) Add the two forces - thrust & pull - and find the acceleration of the plane with pilot aboard.

5]This accel. is applied along the entire length of the rail(49.5 feet). What is the final speed of the plane? 28mph is the required min. to achieve flight. Is the plane airborne?

I have no picture or illustrations, what I gave you is what I have. I changed the link below to a verified working video of the launch, I sure hope it helps.

If interested a video of this system can be found @ http://www.criticalpast.com/video/65675051256_Wright-Brothers_Wright-Flyer_catapult_Wilbur-at-controls       Thanks!!

Explanation / Answer

1. Work done by falligh weight = W*d ( where W is the weight and d is the distance through which it falls)
Work = mg*d
m = 1400 lbs = 635.0293 kg
d = 16.5 ft = 5.0292 m
Work = mgd = 31.33 kJ [ g = 9.1 m/s/s]

2. Force pulling the plane = F
work done by this force = F*3d
work done by this force = work done by falling weiht
3Fd = 31.33*10^3
F = 2076.54 N
3. Thrust form motor = T
then T*v = P ( P is power, v is velocity)
v = 35 mph = 15.6464 m/s
P = 21 hp = 15659.7 W
T = P/v = 1000.85 N
4. Acceleration = a
T = 1000.85 N = 225 lbf
F = 2076.54 N = 466.82 lbf
T + F = w*a/g
225 + 466.82 = 1400*a/32.2
a = 15.911 ft/s/s

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