The diameter of the head of a screw nail is 4cm and it's pitch 0.5cm. If the nail can magnify the applied effort 20times .calculate it's MA, VR and efficiency
Need answer
MA = circumference/pitch = pi*diameter/pitch = ?
To calculate the Mechanical Advantage (MA), Velocity Ratio (VR), and efficiency of the screw nail, we need to use the following formulas:
MA = Diameter / Pitch
VR = Output Distance / Input Distance
Efficiency = (MA / VR) x 100
Given:
Diameter = 4cm
Pitch = 0.5cm
Magnification (effort multiplier) = 20
Let's calculate each value step-by-step.
1. Mechanical Advantage (MA):
MA = Diameter / Pitch
MA = 4cm / 0.5cm
MA = 8
Therefore, the Mechanical Advantage (MA) is 8.
2. Velocity Ratio (VR):
The VR for a screw nail is calculated using the concept of threads:
VR = Output Distance / Input Distance
Since the screw nail rotates while being driven in the material, we can consider a full rotation as the input distance (360° or 2π radians). The output distance is the distance the nail moves vertically down with one complete rotation.
Output Distance (pitch) = 0.5cm (given)
Input Distance (rotation) = 2π radians (a full rotation)
VR = Output Distance / Input Distance
VR = 0.5cm / (2π radians)
VR ≈ 0.08 cm/radian
Therefore, the Velocity Ratio (VR) is approximately 0.08 cm/radian.
3. Efficiency:
Efficiency = (MA / VR) x 100
Efficiency = (8 / 0.08) x 100
Efficiency ≈ 1000 %
However, the efficiency value is greater than 100% due to the magnification factor of 20 mentioned in the question. This implies that the given magnification of 20 times is not possible or does not comply with the definitions of MA and VR. Please double-check the magnification value provided.
In summary:
- MA (Mechanical Advantage) = 8
- VR (Velocity Ratio) ≈ 0.08 cm/radian
- Efficiency ≈ 1000% (Please double-check the magnification value provided)
To calculate the mechanical advantage (MA), velocity ratio (VR), and efficiency of the screw nail, we need to understand their definitions and the formulas used to calculate them.
1. Mechanical Advantage (MA):
The mechanical advantage of a screw is determined by the ratio of the circumference of the screw head (which is equal to its pitch) to its diameter.
MA = Pitch / Diameter
2. Velocity Ratio (VR):
The velocity ratio of a screw is the ratio of the distance moved by the load to the distance moved by the applied effort.
VR = Distance moved by the Load / Distance moved by the Effort
3. Efficiency:
The efficiency of a machine is calculated by dividing the work output by the work input, and then multiplying the result by 100 to express it as a percentage.
Efficiency = (Work Output / Work Input) * 100
Now, let's calculate the MA, VR, and efficiency using the given information:
Given:
Head diameter (D) = 4 cm
Pitch (P) = 0.5 cm
Applied effort magnification (ME) = 20
1. Mechanical Advantage (MA):
MA = Pitch / Diameter
= 0.5 cm / 4 cm
= 0.125
The mechanical advantage of the screw nail is 0.125.
2. Velocity Ratio (VR):
For a screw, the distance moved by the effort is equal to the circumference of the head (pitch), and the distance moved by the load is equal to the distance traveled along the inclined plane formed by the screw.
VR = Distance moved by the Load / Distance moved by the Effort
= Pitch / Length of the inclined plane
= Pitch / (Length of inclined plane per revolution × Number of revolutions)
Since the length of the inclined plane per revolution is the same as the pitch, we can simplify the VR calculation as follows:
VR = Pitch / (Pitch × Number of revolutions)
= 1 / Number of revolutions
As we know that the applied effort is magnified by 20 times, the number of revolutions can be calculated by dividing the applied effort magnification with the MA of the screw nail.
Number of revolutions = Applied Effort Magnification / MA
= 20 / 0.125
= 160
Therefore, the velocity ratio (VR) is 1/160.
3. Efficiency:
To calculate the efficiency, we need to consider the work done by the effort (work input) and the work done against the load (work output).
Work Input = Effort × Distance moved by the Effort
= Effort × Pitch
Work Output = Load × Distance moved by the Load
= Load × (Pitch × Number of revolutions)
Efficiency = (Work Output / Work Input) × 100
= (Load × Pitch × Number of revolutions) / (Effort × Pitch) × 100
= Number of revolutions × (Load / Effort) × 100
Given that the applied effort magnification is 20 times, the efficiency can be calculated as:
Efficiency = Number of revolutions × (1 / 20) × 100
= 160 × 0.05 × 100
= 800%
Therefore, the efficiency of the screw nail is 800%.
In summary:
- Mechanical Advantage (MA) = 0.125
- Velocity Ratio (VR) = 1/160
- Efficiency = 800%