A bucket filled with water weighing 50kg is raised from a well of depth 100m.if the linear density of the rope is 1kg per metre.then the work done is
50kg is not a weight....
work= 50*9.8*100 joules
To calculate the work done in raising the bucket, you need to consider the following components: the work done against gravity to lift the bucket, and the work done against the weight of the rope.
Let's break down the problem step by step:
1. Calculate the work done against gravity:
The weight of the bucket can be calculated using the formula: weight = mass * gravitational acceleration. In this case, the mass of the bucket is 50 kg.
The gravitational acceleration is approximately 9.8 m/s^2.
Therefore, the weight of the bucket is: 50 kg * 9.8 m/s^2 = 490 N.
The work done against gravity is given by the formula: work = force * distance.
In this case, the force is equal to the weight of the bucket, which is 490 N, and the distance is 100 m (the depth of the well).
So, the work done against gravity is: work = 490 N * 100 m = 49,000 J.
2. Calculate the work done against the weight of the rope:
The linear density of the rope is given as 1 kg/m. Since the length of the rope is equal to the depth of the well (100 m), the mass of the rope is 100 kg (mass = linear density * length).
The weight of the rope is equal to the mass of the rope multiplied by the gravitational acceleration, which is 100 kg * 9.8 m/s^2 = 980 N.
The work done against the weight of the rope is calculated similarly: work = force * distance.
In this case, the force is equal to the weight of the rope, which is 980 N, and the distance is also 100 m (the depth of the well).
Therefore, the work done against the weight of the rope is: work = 980 N * 100 m = 98,000 J.
3. Calculate the total work done by adding the work done against gravity and the work done against the weight of the rope:
Total work done = work done against gravity + work done against weight of the rope
Total work done = 49,000 J + 98,000 J = 147,000 J.
So, the total work done in raising the bucket is 147,000 Joules.