The diameter of the head of a screw nails is 4cm and it's pitch 0.5cm. If the nails can magnify the applied effort 20 times, calculate it's MA, VR and efficiency
The mechanical advantage (MA) of the screw nail can be calculated using the formula:
MA = (diameter of screw head) / (pitch of screw)
MA = 4cm / 0.5cm
MA = 8
The velocity ratio (VR) of the screw nail can be calculated using the formula:
VR = (distance moved by effort) / (distance moved by load)
In this case, the distance moved by the effort is equal to the pitch of the screw nail, which is 0.5cm. The distance moved by the load is equal to the distance traveled along the threads of the nail as it is screwed into the material.
Assuming a single turn of the nail (360 degrees), the distance moved by the load can be calculated as the circumference of a circle with a radius equal to the pitch of the screw:
C = 2πr
C = 2π x 0.5cm
C = 3.14cm
Therefore, the velocity ratio of the screw nail is:
VR = 0.5cm / 3.14cm
VR = 0.159
Finally, the efficiency of the screw nail can be calculated using the formula:
efficiency = (MA / VR) x 100%
efficiency = (8 / 0.159) x 100%
efficiency = 502.1% (or 5.021)
To calculate the MA (Mechanical Advantage), VR (Velocity Ratio), and efficiency of the screw nails, we can use the following formulas:
MA = Diameter of the head / Pitch
VR = 1 / MA
Efficiency = MA / VR * 100%
Given:
Diameter of the head = 4 cm
Pitch = 0.5 cm
Magnification of applied effort = 20 times
Calculating the values:
MA = 4 cm / 0.5 cm = 8
VR = 1 / 8 = 0.125
Efficiency = 8 / 0.125 * 100% = 6400%
Therefore, the MA of the screw nails is 8, the VR is 0.125, and the efficiency is 6400%. Note that efficiency is usually expressed as a percentage, so it should be divided by 100 to obtain a decimal value, but in this case, there seems to be an error. Please verify the provided values.