A rope is used to host an object with a mass of 1,3 tons vertically through a distance of 100m. The mass of the rope is 2kg per metre.
Determine: the work done.the average tension in the rope and the power used if it takes 2minutes to host the object.
W=200×9.8= 1960N
W=1300×9.8= 12740 N
W=f×s=980×100= 98000
To determine the work done, we can use the formula:
Work = Force * Distance
Since the object is being lifted vertically, the force required to lift it is equal to the weight of the object. The weight can be calculated using the formula:
Weight = Mass * Gravity
Given that the mass of the object is 1.3 tons and the acceleration due to gravity is approximately 9.8 m/s^2, we can convert the mass to kilograms:
Mass = 1.3 tons * 1000 kg/ton = 1300 kg
Now we can calculate the weight:
Weight = 1300 kg * 9.8 m/s^2 = 12740 N
The force required to lift the object is equal to the weight:
Force = 12740 N
Next, we can calculate the work done:
Work = Force * Distance = 12740 N * 100 m = 1274000 J
Therefore, the work done is 1,274,000 Joules.
To determine the average tension in the rope, we can use the formula:
Tension = Weight + (Mass of the rope per meter * Length of the rope)
Given that the mass of the rope is 2 kg per meter and the length of the rope is 100 m, we can calculate the tension:
Tension = 12740 N + (2 kg/m * 100 m) = 12740 N + 200 kg = 32940 N
Therefore, the average tension in the rope is 32,940 Newtons.
To calculate the power used, we can use the formula:
Power = Work / Time
Given that it takes 2 minutes to lift the object, we need to convert the time to seconds:
Time = 2 minutes * 60 seconds/minute = 120 seconds
Now we can calculate the power:
Power = 1274000 J / 120 s = 10616.67 W
Therefore, the power used is approximately 10,616.67 Watts.