A machine with a velocity ratio 5 was used to raise a load of 1.2kg mass through a height of 10m ,if the work done to raise the load is 800j .find the work output, efficiency and mechanical advantage
To find the work output, efficiency, and mechanical advantage, we need to understand some key concepts.
1. Work Done (W): It is the product of the force applied (F) and the distance traveled (d) in the direction of the force. Mathematically, W = F * d.
2. Velocity Ratio (VR): It is the ratio of the velocity of the effort (Ve) to the velocity of the load (Vl). Mathematically, VR = Ve / Vl.
3. Mechanical Advantage (MA): It is the ratio of the load (L) to the effort (E). Mathematically, MA = L / E.
4. Efficiency (η): It is the ratio of the useful work output (Wo) to the total work input (Wi) expressed as a percentage. Mathematically, η = (Wo / Wi) * 100.
Now, let's calculate each value step by step:
Given:
Velocity Ratio (VR) = 5
Load Mass (L) = 1.2 kg
Height (d) = 10 m
Work Done (Wi) = 800 J
1. Work Output (Wo):
To find the work output, we need to calculate the force applied by the machine using work done.
W = F * d => 800 = F * 10
F = 800 / 10 = 80 N
Now, the work output will be the product of the force applied and the distance traveled by the load (i.e., the height).
Wo = F * d = 80 * 10 = 800 J
Therefore, the work output is 800 J.
2. Efficiency (η):
Efficiency is the ratio of the useful work output to the total work input, expressed as a percentage.
η = (Wo / Wi) * 100 = (800 / 800) * 100 = 100%
Therefore, the efficiency is 100%.
3. Mechanical Advantage (MA):
Mechanical Advantage is the ratio of the load to the effort.
MA = L / E = L / (F * VR)
MA = 1.2 kg / (80 N * 5) = 1.2 / 400 = 0.003
Therefore, the mechanical advantage is 0.003.
To summarize:
- Work Output (Wo) = 800 J
- Efficiency (η) = 100%
- Mechanical Advantage (MA) = 0.003