A machine uses an effort of 5N to lift a load of 14N.Calculate it's velocity ratio,if it has an efficiency of 65%.
What is the answer
To calculate the velocity ratio of a machine, you need to divide the load force (output force) by the effort force (input force).
In this case, the load force is 14N and the effort force is 5N, so the velocity ratio is:
Velocity Ratio = Load Force / Effort Force
Velocity Ratio = 14N / 5N
Velocity Ratio = 2.8
Now, let's calculate the actual mechanical advantage (AMA) of the machine using the efficiency given. Efficiency is calculated by dividing the AMA by the velocity ratio and multiplying by 100.
Efficiency = (AMA / Velocity Ratio) * 100
We can rearrange the formula to find AMA:
AMA = (Efficiency / 100) * Velocity Ratio
Given that the efficiency is 65%, we have:
AMA = (65 / 100) * 2.8
AMA = 1.82
Therefore, the velocity ratio of the machine is 2.8, and its actual mechanical advantage is 1.82.
To calculate the velocity ratio of the machine, we need to determine the input force and the output force.
The efficiency of the machine is given as 65%. Efficiency is defined as the ratio of output work to input work, expressed as a percentage. Therefore, we can calculate the output work of the machine using the efficiency formula:
Efficiency = (Output Work / Input Work) * 100
Given that the efficiency is 65%, we can write the equation as:
65 = (Output Work / Input Work) * 100
Now, let's find the output work. Output work is defined as the product of output force and the distance moved by the output force:
Output Work = Output Force * Output Distance
In this case, the output force is the load being lifted, which is 14N.
Now, let's find the distance moved by the output force. Since the machine is lifting the load vertically, the distance moved by the output force is equal to the distance the load is lifted.
Since we don't know the distance the load is lifted, we can't calculate the exact value of the output work. So, we'll use a symbolic value, "d," to represent the distance lifted.
Hence, the output work is given by:
Output Work = 14N * d (Equation 1)
Next, let's find the input work. Input work is defined as the product of input force and the distance moved by the input force.
In this case, the input force is 5N.
Again, since we don't know the distance moved by the input force, we'll use a symbolic value, "D," to represent it.
Hence, the input work is given by:
Input Work = 5N * D (Equation 2)
Now, we need to solve for D in terms of d.
Efficiency is defined as the ratio of output work to input work. So, we can rewrite the efficiency equation as:
65 = (Output Work / Input Work) * 100
Substituting the values of output work and input work from Equations 1 and 2, respectively, we get:
65 = (14N * d / 5N * D) * 100
Simplifying this equation, we can cancel out the Ns and rearrange the equation to solve for D:
65 = (14d / 5D) * 100
65 = (14d / 5D) * 100 / 100
65 / 100 = (14d / 5D)
0.65 = (14d / 5D)
0.65 * 5D = 14d
3.25D = 14d
D = (14d / 3.25)
Now that we have D in terms of d, we can calculate the velocity ratio.
Velocity ratio is defined as the ratio of distance moved by the input force to the distance moved by the output force.
In this case, the distance moved by the input force is D, and the distance moved by the output force is d.
So, the velocity ratio is given by:
Velocity Ratio = D / d
Substituting the value of D we found earlier, we get:
Velocity Ratio = (14d / 3.25) / d
Velocity Ratio = 14 / 3.25
Therefore, the velocity ratio of the machine is 4.3077 (rounded to four decimal places).