A block and tackle with a velocity ratio of 5 is used to raise a mass of 25kg through a vertical distance of 400M at a steady rate.if the effort is equal to 60N,determine (a)distance moved by the effort (b)work done by lifting the load(c)the loss in energy involved in operating the machine
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To find the solutions to the given problem, we can use the formulas for velocity ratio, effort, distance moved by the effort, work done, and energy loss. Let's calculate them step-by-step:
Step 1: Calculate the distance moved by the load.
Given:
Velocity ratio (VR) = 5
Distance moved by the load (d load) = 400 m
Since the velocity ratio is defined as the ratio of the distance moved by the effort to the distance moved by the load, we can use the formula:
VR = distance moved by effort / distance moved by load
Substituting the given values:
5 = distance moved by effort / 400
Rearranging the equation:
distance moved by effort = VR * distance moved by load
distance moved by effort = 5 * 400
distance moved by effort = 2000 m
Therefore, the distance moved by the effort is 2000 meters.
Step 2: Calculate the work done by lifting the load.
Given:
Load mass (m load) = 25 kg
Distance moved by the load (d load) = 400 m
The work done is defined as the product of the force applied and the distance moved. In this case, the force applied is the effort.
Work done = effort * distance moved by the effort
Work done = 60 N * 2000 m
Therefore, the work done by lifting the load is 120,000 joules (J).
Step 3: Calculate the energy loss involved in operating the machine.
In an ideal machine, there is no energy loss. However, in real machines, energy is lost due to factors such as friction.
Energy loss = work done - output energy
Energy loss = work done - input energy
Since the input energy is equal to the output energy in the case of a block and tackle machine, the energy loss is equal to zero. Therefore, there is no loss of energy involved in operating the machine.
To summarize:
(a) The distance moved by the effort is 2000 meters.
(b) The work done by lifting the load is 120,000 joules (J).
(c) There is no loss in energy involved in operating the machine.
To solve this problem, we will use the formula:
Velocity Ratio = Distance moved by effort / Distance moved by load
Given:
Velocity Ratio (VR) = 5
Mass of load (m) = 25 kg
Vertical distance (d) = 400 m
Effort (E) = 60 N
(a) Distance moved by the effort:
Using the formula for velocity ratio, rearrange it to solve for the distance moved by effort:
Distance moved by effort = Velocity Ratio * Distance moved by load
Distance moved by load (D) = Vertical distance = 400 m
Distance moved by effort = VR * D
Distance moved by effort = 5 * 400 m
Distance moved by effort = 2000 m
Therefore, the distance moved by the effort is 2000 m.
(b) Work done by lifting the load:
Work done = Force * Distance
Force (F) = Effort = 60 N
Distance (d) = Vertical distance = 400 m
Work done = F * d
Work done = 60 N * 400 m
Work done = 24000 J (Joules)
Therefore, the work done by lifting the load is 24000 Joules.
(c) The loss in energy involved in operating the machine:
For an ideal machine, there should be no loss in energy. However, in real machines, some energy is lost due to friction and other factors.
The work done by the effort represents the energy input, and the work done in lifting the load represents the useful work or energy output.
So, the loss in energy involved in operating the machine is given by:
Loss in energy = Energy input - Energy output
Energy input = Work done by the effort = 24000 J
Energy output = Work done in lifting the load = 24000 J
Loss in energy = Energy input - Energy output
Loss in energy = 24000 J - 24000 J
Loss in energy = 0 J
Therefore, the loss in energy involved in operating the machine is 0 Joules.