In a physics demonstration, a performer lies motionless on a horizontal board supported only by an array of identical vertical nails. Each nail has a tip that can be approximated as a circle of radius 0.70 mm. The performer has mass 70 kg and her weight is distributed uniformly among the nails. Assume g = 9.8 m/s² and ignore the weight of the support board.
(a) If the board rests on 400 nails, calculate the force exerted on a single nail tip.
(b) Determine the pressure exerted on the performer’s skin by a single nail tip in pascals.
(c) A pressure of 1.5 MPa will puncture human skin. Does the performer risk injury under these conditions? Justify quantitatively.
(d) The performer removes the board so that only 10 nails support her weight. Repeat parts (a) and (b) for this scenario and evaluate the risk of injury.
(e) Based on your calculations, determine the minimum number of nails required to keep the pressure on each nail tip below 1.0 MPa, providing clear reasoning.