A machine lift a load of 500N what is the effort of the machine if the velocity ratio move vertically upward at 30° and efficiency is 75%
A machine lift a load of 500N what is the effort of the machine if the velocity ratio move vertically upward at 30° and efficiency is 75%..
The velocity ratio is ..... move
To find the effort of the machine, we can use the formula:
Efficiency = (Load * Load distance) / (Effort * Effort distance)
Given:
Load = 500N
Efficiency = 75% (0.75)
Velocity Ratio = vertically upward at 30°
First, let's calculate the load distance and effort distance:
Load distance:
The load distance is the vertical distance over which the load is lifted. Since the machine moves vertically upward, the load distance is equal to the height of the lift.
Effort distance:
The effort distance is the horizontal distance over which the machine moves. This distance can be found using the velocity ratio and the vertical height.
Effort distance = Load distance / sin(30°)
Now, let's calculate the effort:
Efficiency = (Load * Load distance) / (Effort * Effort distance)
Solving for Effort:
Effort = (Load * Load distance) / (Efficiency * Effort distance)
Substituting the given values:
Load = 500N
Efficiency = 0.75
Load distance = height
Effort distance = height / sin(30°)
Effort = (500N * height) / (0.75 * (height / sin(30°)))
Simplifying the equation:
Effort = (500N / 0.75) * sin(30°)
Effort = 666.67N * 0.5
Effort = 333.33N
Therefore, the effort of the machine is 333.33N.
To find the effort of the machine in this scenario, we need to consider the principles of force, velocity ratio, and efficiency.
1. Force: The force (F) refers to the load that the machine is lifting. In this case, the load is 500N.
2. Velocity Ratio: Velocity ratio (VR) is the ratio of the distance moved by the effort to the distance moved by the load. In this scenario, the machine moves vertically upward at an angle of 30°. However, since we are only concerned with the vertical motion, the velocity ratio can be considered as the ratio of the vertical distance moved by the effort to the vertical distance moved by the load.
3. Efficiency: Efficiency (E) is the ratio of the output work (load multiplied by its distance) to the input work (effort multiplied by its distance). In this case, the efficiency is given as 75%.
Let's calculate the effort using these principles:
Efficiency (E) = Output work / Input work
Output work = Load * Distance moved by load
Input work = Effort * Distance moved by effort
Given that the VR is the ratio of vertical distances, the distance moved by the load vertically is the same as the actual distance.
Therefore, we can write:
Efficiency (E) = Load * Distance moved by load / Effort * Distance moved by effort
Since Efficiency = 75%, we can substitute this value into the equation:
0.75 = 500 * Distance moved by load / Effort * Distance moved by effort
Now, we need to consider the velocity ratio.
Velocity Ratio (VR) = Distance moved by effort / Distance moved by load
If we take the inverse of VR, we can find:
1 / VR = Distance moved by load / Distance moved by effort
Substituting this value in the equation and simplifying:
0.75 = 500 * (1 / VR)
Now, we can rearrange the equation to solve for the Effort:
Effort = 500 * (1 / VR) / 0.75
Finally, plug in the values given in the question:
Effort = 500 * (1 / sin(30°)) / 0.75
Effort = 500 * (2 / 1.5)
Effort = 1000 / 1.5
Effort ≈ 666.67N
Therefore, the effort of the machine is approximately 666.67N to lift the load of 500N with a velocity ratio at 30° and an efficiency of 75%.