A rope is used to hoist a skip with a 300kg mass,vertically through a distance of 100m.the mass of the rope is 2kg/m.draw the force distance curve and then determine
The total work done
The average tension in the rope
The power required if it takes 2minutes to hoist the skip
To determine the total work done, we can use the formula:
Work = Force x Distance
First, let's calculate the total mass of the skip and the rope:
Total mass = Mass of skip + Mass of rope
Total mass = 300 kg + (2 kg/m x 100 m)
Total mass = 500 kg
Since the force exerted by the rope is equal to the tension in the rope, we can calculate the average tension in the rope using the formula:
Tension = Total mass x g
Tension = 500 kg x 9.81 m/s^2
Tension = 4905 N
Next, we can calculate the total work done:
Work = Tension x Distance
Work = 4905 N x 100 m
Work = 490500 J
Therefore, the total work done to hoist the skip vertically through a distance of 100m is 490500 Joules.
To determine the power required, we can use the formula:
Power = Work / Time
Given that it takes 2 minutes to hoist the skip, we need to convert this time to seconds:
Time = 2 minutes x 60 seconds/minute
Time = 120 seconds
Power = 490500 J / 120 s
Power ≈ 4087.5 W
Therefore, the power required to hoist the skip vertically through a distance of 100m in 2 minutes is approximately 4087.5 Watts.