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

Answer 1

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)