A machine has velocity ratio 6 and is 75% efficient. What effort would be needed to lift a load of 300N with the aid of this machine
To determine the effort needed to lift a load using this machine, we need to first understand the concept of velocity ratio and efficiency.
Velocity ratio (VR) is the ratio of the distance moved by the effort to the distance moved by the load. It tells us how much the machine multiplies the effort applied.
Efficiency is a measure of how well a machine converts the input work to useful output work. In this case, an efficiency of 75% means that only 75% of the input work is converted to useful output work, with the remaining 25% being lost to friction, heat, or other factors.
Now, let's calculate the effort needed to lift the given load using the provided velocity ratio and efficiency.
Efficiency = Output work / Input work
Since the efficiency is 75%, the output work is 75% of the input work. Therefore, the equation becomes:
0.75 = Output work / Input work
Now, let's use the velocity ratio to establish a relationship between the effort and the load:
Velocity Ratio (VR) = Load distance / Effort distance
Given the velocity ratio is 6, we know that for every 6 units of distance the load moves, the effort moves 1 unit of distance.
To find the effort needed, we can set up the following proportion:
VR = Load / Effort
6 = 300N / Effort
Cross-multiplying:
6 * Effort = 300N
Effort = 300N / 6
Effort = 50N
So, the effort required to lift the load of 300N using this machine with a velocity ratio of 6 and an efficiency of 75% is 50N.