A machine with v.r requires 1000J of work to raise a load of 500N through a vertical distance of 1.7m . find the efficiency and m.a of the machine.
W = Fd
1000 = 500d
d=2 for perfectly efficient. You only got 1.7 so
1.7/2 = .85 or 85% efficient.
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To find the efficiency and mechanical advantage (MA) of the machine, we need to understand some basic concepts:
1. Work (W): Work is defined as the product of the applied force and the distance over which the force is applied. Mathematically, work (W) is calculated as W = F * d, where F is the force applied, and d is the distance over which the force is applied.
2. Efficiency (η): Efficiency is the ratio of useful work output to the total work input. It is a measure of how effectively a machine converts input energy into useful output energy. Mathematically, efficiency (η) is calculated as η = (useful work output / total work input) * 100%.
3. Mechanical Advantage (MA): Mechanical advantage is the measure of the amplification of force achieved by a machine. It is defined as the ratio of the output force to the input force. Mathematically, mechanical advantage (MA) is calculated as MA = output force / input force.
Now, let's calculate the efficiency and mechanical advantage of the machine:
Given:
Work required (W) = 1000 J
Load (F) = 500 N
Distance (d) = 1.7 m
1. Efficiency (η):
Since efficiency is the ratio of useful work output to the total work input, we need to find the useful work output and the total work input.
Total work input (W_input) = Work required (W) = 1000 J
To calculate the useful work output, we need to determine the output force and the output distance.
Output force = Load (F) = 500 N
Output distance (d_output) = Distance (d) = 1.7 m
Useful work output (W_output) = Output force * Output distance = F * d_output
Now, we can calculate the efficiency using the formula:
Efficiency (η) = (useful work output / total work input) * 100%
= (W_output / W_input) * 100%
= (F * d_output / W) * 100%
Substituting the given values:
Efficiency (η) = (500 N * 1.7 m / 1000 J) * 100%
2. Mechanical Advantage (MA):
Since mechanical advantage is the ratio of the output force to the input force, we can directly calculate it using the formula:
Mechanical Advantage (MA) = output force / input force
= F / Input force
Substituting the given values:
Mechanical Advantage (MA) = 500 N / Input force
You will need to provide the input force to calculate the mechanical advantage.