How many prime mover is needed to pull the crane with velocity 10m/min?

[ainaz89]

Homework Statement

prime mover = 220 hp
crane = 2000 tonne
velocity crane = 10m/min = 0.17m/sec
acceleration crane = 0.017m/sec
every 100 tonne = 6 tonne of friction

1hp = 726 W
1 tonne = 1000 kg

Homework Equations

how many prime mover are needed to pull the crane?prime mover 220 hp = 164120W

for every 100 tonne = 6 tonne of friction
2000tonne = 120 tonne of friction

m = 2000tonne - 120 tonne = 1880 tonne

P = F*v
= mg * v
= (1880*1000)(9.81)*(0.17)
= 3135276W

so, total of PM = 3135276/164120
= 19 units.

the answer should be less than 10 units.

 

[RTW69]

I need some clarification for this problem. Can I assume that the crane accelerates from rest to a final velocity of .17 m/s at an acceleration of .017 m/s^2? Friction forces are in Newtons not Kg (or tonne). Is 120 tonne friction 120,000 Kg * 9.8 M/s^2= 1.18 x 10^6 Newtons? 1 prime mover unit is 164,120 watts?

 

[ainaz89]

RTW69: yes..the acceleration of the crane is 0.017m/s^2.and u can change the parameters into SI unit.as i calculated, the prime mover power is 164120 watts.

 

[RTW69]

OK, there are two parts to this problem. Part 1 is how much power is required to get the crane from rest to a final velocity given the acceleration. You need to do a free body diagram oft he accelerating crane, sum of the forces in x-direction=M*a. Use your one-dimensional motion equations to find distance and time for crane to reach final velocity. Power= F*D/t

The second part of the problem is how much power is required to keep the crane moving at final velocity. There is no acceleration so sum of forces in x-direction=0. The motor just needs to overcome the friction forces. Power=F*Vel. Which power requirement is larger, part 1 or part 2? convert larger to power units.

Your P=F*V equation is incorrect

 

[rwisz]

Based on the given information, it seems that the crane would require at least 19 units of the prime mover to pull it with a velocity of 10m/min. However, this number may vary depending on the efficiency and power of the prime mover and the specific details of the crane's design and operation. It is also important to consider the safety and stability of the crane while it is in motion. Further analysis and calculations may be needed to determine the exact number of prime movers required for this scenario.