A block and tackle of 5 pulleys is used to raise a load of 5o kgf steadily through a height of 20m. The work against friction is 2000J.Calculate the work done by effort, efficiency and mechanical advantage.
SCIENCE
To calculate the work done by effort, efficiency, and mechanical advantage, we first need to understand the formulas related to these concepts.
1. Work done by effort (W): Work done is equal to the force applied (effort) multiplied by the distance over which it is applied. The formula is W = Force × Distance.
2. Efficiency (η): Efficiency is a measure of how effectively a machine converts input work to output work. It is calculated by dividing the output work by the input work and multiplying by 100 to express it as a percentage. The formula is η = (Output work / Input work) × 100.
3. Mechanical Advantage (MA): Mechanical advantage is a measure of the amplification of force gained by using a machine. It is calculated by dividing the output force by the input force. The formula is MA = Output force / Input force.
Now, let's calculate the values.
Given:
Load = 50 kgf (kilogram-force)
Height = 20 m
Work against friction = 2000 J (joules)
Number of pulleys = 5
1. Work done by effort (W):
Since the work done against friction is provided, we can calculate the total work done by adding the work done against friction to the work done to lift the load. The work done to lift the load can be calculated using the formula W = Force × Distance.
Work done against friction (W_friction) = 2000 J
Work done to lift the load (W_load) = Force × Distance = 50 kgf × 9.8 m/s² × 20 m
Total Work done by effort (W_total) = W_load + W_friction
2. Efficiency (η):
Efficiency is calculated by dividing the output work (work done to lift the load) by the input work (total work done by effort) and multiplying by 100.
Efficiency (η) = (W_load / W_total) × 100
3. Mechanical Advantage (MA):
Mechanical Advantage is calculated by dividing the output force (load) by the input force (effort). Since the load is given as weight, we need to convert it to force by multiplying by the acceleration due to gravity (9.8 m/s²).
Input force (effort) = Load / Number of pulleys = 50 kgf × 9.8 m/s² / 5
Mechanical Advantage (MA) = Load (force) / Input force
Now, using these formulas, we can calculate the values.