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

1. Jun 16, 2011

### ainaz89

1. The problem statement, all variables and given/known data

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

2. Relevant 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.

Last edited: Jun 16, 2011
2. Jun 16, 2011

### 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?

3. Jun 17, 2011

### 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.

4. Jun 17, 2011

### 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.