Final answer:
To find the effort applied by a machine with a velocity ratio of 5 and 80% efficiency carrying a load of 200 kg, we first determine the mechanical advantage using the formula for efficiency, and then calculate the effort by dividing the load force by the mechanical advantage.
Step-by-step explanation:
If a machine has a velocity ratio of 5 and is 80 percent efficient while carrying a load of 200 kg, the effort applied can be calculated using the relationship between mechanical advantage, velocity ratio, and efficiency. The mechanical advantage (MA) is defined as the force output divided by the force input (effort), and efficiency (e) is the ratio of useful work output to total work input, expressed as a percentage. The velocity ratio (VR) is the ratio of the distance moved by the effort to the distance moved by the load.
The formula linking these quantities is:
Efficiency (e) = (Mechanical Advantage (MA) / Velocity Ratio (VR)) × 100%
Given that the efficiency is 80 percent, we can rearrange this formula to solve for Mechanical Advantage:
MA = (Efficiency × VR) / 100% = (80% × 5) / 100% = 4
Now, we can calculate the effort (E) by dividing the force output (which is the weight of the load) by the mechanical advantage:
Force output (load) = mass × gravity = 200 kg × 9.81 m/s²
E = Force output / MA = (200 kg × 9.81 m/s²) / 4
Therefore, the effort applied is (200 kg × 9.81 m/s²) / 4, which needs to be calculated to give the final value.