The diameter of the head of a screw nail is 4 cm and its pitch 0.5cm. If the nail can magnify the applied effort 20 times calculate its MR VR and efficiency.
How
To calculate the mechanical advantage (MA) of the nail, you can use the formula:
MA = Diameter of the head / Pitch
In this case, the diameter of the head is 4 cm and the pitch is 0.5 cm. Therefore, the mechanical advantage is:
MA = 4 cm / 0.5 cm = 8
Next, to calculate the velocity ratio (VR) of the nail, you need to consider the magnification of the applied effort. The velocity ratio can be given as:
VR = Magnification of applied effort
Given that the nail can magnify the applied effort 20 times, the velocity ratio is:
VR = 20
Finally, to calculate the mechanical advantage (MR) of the nail, you can use the formula:
MR = MA / VR
Substituting the values:
MR = 8 / 20 = 0.4
The efficiency of the nail can be found using the formula:
Efficiency = (MR / VR) x 100%
Substituting the values:
Efficiency = (0.4 / 20) x 100% = 2%
Therefore, the mechanical advantage (MA) of the nail is 8, the velocity ratio (VR) is 20, the mechanical advantage (MR) is 0.4, and the efficiency is 2%.
To calculate the mechanical advantage (MA) of the screw nail, we can use the following formula:
MA = (pi * d) / p
Where:
- MA is the mechanical advantage
- pi is a mathematical constant (approximately 3.14159)
- d is the diameter of the head of the screw nail
- p is the pitch of the screw nail
Given that the diameter of the screw nail head (d) is 4 cm and the pitch (p) is 0.5 cm, we can substitute these values into the formula:
MA = (pi * 4) / 0.5
MA = 25.13274 / 0.5
MA = 50.26548
Therefore, the mechanical advantage (MA) of the screw nail is 50.26548.
To calculate the velocity ratio (VR) of the screw nail, we can use the following formula:
VR = p / d
Where:
- VR is the velocity ratio
- p is the pitch of the screw nail
- d is the diameter of the head of the screw nail
Given that the pitch (p) is 0.5 cm and the diameter of the head (d) is 4 cm, we can substitute these values into the formula:
VR = 0.5 / 4
VR = 0.125
Therefore, the velocity ratio (VR) of the screw nail is 0.125.
To calculate the efficiency of the screw nail, we can use the following formula:
Efficiency = (MA / VR) * 100
Where:
- Efficiency is the efficiency of the screw nail
- MA is the mechanical advantage of the screw nail
- VR is the velocity ratio of the screw nail
Given that the mechanical advantage (MA) is 50.26548 and the velocity ratio (VR) is 0.125, we can substitute these values into the formula:
Efficiency = (50.26548 / 0.125) * 100
Efficiency = 402.1248
Therefore, the efficiency of the screw nail is approximately 402.12%.