A block and tackle with a velocity ratio of 6 is used to lift a load of mass 30kg through a vertical distance of 40cm at a steady rate. If the effort is 60newtons, determine the loss in energy.
Work accomplished = 30 * 0.4 * g = 12 * 9.8 Joules =118 Joules
Work in = 60 * 0.4 * 6 = 144 Joules
so 144 - 118 Joules
To determine the loss in energy, we need to calculate the work done by the effort and the work done against gravity.
1. Calculate the work done by the effort:
The work done by the effort is given by the formula: work = force * distance
work = effort * distance
= 60 N * 40 cm
First, convert cm to meters:
distance = 40 cm = 0.4 m
Work = 60 N * 0.4 m
= 24 joules
2. Calculate the work done against gravity:
The work done against gravity is given by the formula: work = force * distance
work = weight * distance
First, calculate the weight:
weight = mass * gravity
= 30 kg * 9.8 m/s^2
= 294 N
Then, calculate the work done against gravity:
work = weight * distance
= 294 N * 0.4 m
= 117.6 joules
3. Calculate the loss in energy:
The loss in energy is the difference between the work done by the effort and the work done against gravity:
loss in energy = work done by effort - work done against gravity
= 24 joules - 117.6 joules
= -93.6 joules
The loss in energy is -93.6 joules, indicating that energy has been lost during the lifting process.
To determine the loss in energy, we need to calculate the work done by the effort force and the work done against gravity. The work done by the effort force is equal to the product of the effort force and the distance the effort force moves. The work done against gravity is equal to the product of the weight of the load and the vertical distance it is lifted.
First, let's determine the distance the effort force moves. The velocity ratio is defined as the ratio of the distance the effort force moves to the distance the load moves. In this case, the velocity ratio is 6.
Since the load is lifted through a vertical distance of 40 cm, the distance the effort force moves is given by:
Distance of effort force = Velocity ratio * Distance of load
Distance of effort force = 6 * 40 cm
Distance of effort force = 240 cm
Now let's convert the distance of the effort force to meters:
Distance of effort force = 240 cm * (1 m / 100 cm)
Distance of effort force = 2.4 m
Next, let's calculate the work done by the effort force:
Work done by effort force = Effort force * Distance of effort force
Work done by effort force = 60 N * 2.4 m
Work done by effort force = 144 Joules
Now, let's calculate the work done against gravity. The weight of the load is equal to the mass of the load multiplied by the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s^2.
Weight of the load = Mass of the load * Acceleration due to gravity
Weight of the load = 30 kg * 9.8 m/s^2
Weight of the load = 294 N
The work done against gravity is given by:
Work done against gravity = Weight of the load * Vertical distance lifted
Work done against gravity = 294 N * 0.4 m
Work done against gravity = 117.6 Joules
Finally, the loss in energy is given by the difference between the work done by the effort force and the work done against gravity:
Loss in energy = Work done by effort force - Work done against gravity
Loss in energy = 144 Joules - 117.6 Joules
Loss in energy = 26.4 Joules
Therefore, the loss in energy is 26.4 Joules.