In a machine ,a load of 160Newton is lifted up by an effort of 25Newton.the velocity ratio is 8,what is the efficiency of the machine
160/25 = 6.4 = real mechanical advantage
8 = ideal mechanical advantage
100 * 6.4/8
eff. = L/(E*Vr) = 160/(25*8) = 0.80 = 80%.
Well, well, well, it seems we have a machine lifting some weight! Let's calculate its efficiency, shall we?
Efficiency is given by the formula: Efficiency = (Output Work / Input Work) x 100%
Now let's figure out the input work. The input work is the effort force (25 N) multiplied by the input distance. But wait a minute, we don't have the input distance! How will we solve this problem?
*Cue the clown music*
Why did the machine become friends with the math teacher? Because it wanted a little help with its input distance!
*Cue the laughter*
Okay, okay, let's get back on track. Remember the velocity ratio? It tells us how a force applied to the machine is multiplied to lift the load. In our case, the velocity ratio is 8. This means that for every 8 units of input distance, the load is lifted by 1 unit.
So, to calculate the input distance, we divide the output distance (160 N / 8 = 20 N) by the velocity ratio (8). Therefore, the input distance is 20 N / 8 = 2.5 N.
Now that we know the input distance, we can calculate the input work. Input Work = Input Force x Input Distance = 25 N x 2.5 N = 62.5 N
Next, we need to calculate the output work. Output Work = Output Force x Output Distance = 160 N x 20 N = 3200 N
Finally, let's put it all together and calculate the efficiency:
Efficiency = (Output Work / Input Work) x 100%
Efficiency = (3200 N / 62.5 N) x 100% ≈ 5120%
Wowza, that's quite the efficient machine! I hope that calculation brought a smile to your face!
To calculate the efficiency of a machine, we need to use the formula:
Efficiency = (Output Work / Input Work) × 100
Here's how to calculate the efficiency:
Step 1: Calculate the Output Work:
Output Work = Load × Distance Moved by Load
Given:
Load = 160 N
Distance Moved by Load = ?
Velocity Ratio = 8
Distance Moved by Effort = Distance Moved by Load / Velocity Ratio
Since the machine is lifting the load, the distance moved by the effort is equal to the distance moved by the load.
Hence, Distance Moved by Effort = Distance Moved by Load
So, Distance Moved by Load = Distance Moved by Effort = ?
We need the actual distance moved to continue the calculation.
Step 2: Calculate the Input Work:
Input Work = Effort × Distance Moved by Effort
Given:
Effort = 25 N
Distance Moved by Effort = Distance Moved by Load / Velocity Ratio = ?
Step 3: Calculate the Efficiency:
Efficiency = (Output Work / Input Work) × 100
Now, let's calculate the missing values for Distance Moved by Load and Distance Moved by Effort:
Distance Moved by Load = Distance Moved by Effort × Velocity Ratio
Substituting the known values:
Distance Moved by Load = ? × 8
Since the actual distance moved is not given, we cannot calculate the efficiency without this value. Please provide the value of "Distance Moved by Load" to proceed further.
To find the efficiency of the machine, we first need to understand the concept of efficiency in machines. Efficiency is a measure of how well a machine converts input work or energy into useful output work or energy. Mathematically, efficiency is expressed as a ratio of output work to input work, multiplied by 100 to express it as a percentage.
The formula for efficiency is:
Efficiency = (Output work / Input work) x 100
In this case, the input work is the effort applied to the machine, which is 25 Newtons. The output work is the load lifted by the machine, which is 160 Newtons.
Now, let's determine the velocity ratio. The velocity ratio is a measure of how much the machine multiplies the input force and is calculated as the ratio of the output distance to the input distance. In this case, the velocity ratio is given as 8.
To find the output distance and the input distance, we can use the formula:
Velocity ratio = Output distance / Input distance
Since we are given the velocity ratio as 8, and the input distance and output distance are the same, we can set up the equation:
8 = Output distance / Input distance
To solve for the output distance and input distance, we can set them equal to each other:
Output distance = Input distance
Substituting this into the velocity ratio equation, we get:
8 = Output distance / Output distance
Simplifying this equation, we find:
8 = 1
Now, since it doesn't make sense for the velocity ratio to be 1 when we are given it as 8, it seems there might be an error or missing information in the problem. If you can provide more details or double-check the given values, I can assist you further in finding the efficiency of the machine.