The hay baler and trailer are stationary Bales weigh 30 lb a

The hay baler and trailer are stationary. Bales weigh 30 lb and need to achieve a height h = 10 ft and distance d = 15 ft from the launching arm of the baler. The arm starts from rest and moves over a range delta y = 1.5 ft vertically and delta x = 1.0 ft horizontally. Calculate the necessary launching velocity vector v and the maximum power input P if the system operates with a n = 60% efficiency. Assume no drag forces are present during the flight of the bales.

Solution

We know the projectile motion formulae

Max Height = H= Vo2 * sin²(theta)/(2g)….equation 1

Range= R= Vo2 * sin(2*(theta))/g……...equation 2

H=h=10ft= 3.048m (given)

R=d= 15ft= 4.572m

Deviding equation 1 by equation 2 we get

H/R= tan(theta)/4

10/15 = tan(theta)/4

Therefore theta= 69.44 degrees

Substituting theta in eqution 1 and solving for Vo, we get

Launching velocity is Vo=8.26 m/s

Power required to launch= Farm* Vo= W*g* Vo= 13.6*9.81*8.26= 1102 Watts ( W- Weight in kg)

Since efficiency= 60 percent

Therefore maximum power required= 1102/0.6= 1836.7 W= 1.837 kW