Question

In a circus act a 64.3 kg magician lies on a bed of nail. The bed consists of a large number of evenly spaced, relatively sharp nails mounted in a board so that the points extend vertically outward from the board/while the magician lying down, approximately 1900 nails make contact with hisbody.

1. What is the average force exerted by each nail on the magician's body?
2. If the area of contact at the head of each nail is1.26x10-6 m2 , what is the average pressure at each contact?

Answer 1

(a) Fn = 0.33 N

(b) Pn = 263.22 x 10³ Pa = 263.22 KPa

Step-by-step explanation:

(a)

First, we need to calculate the total force exerted by all nails on the magician. This force must be equal to the weight of magician:

F = W

where,

F = Total Force exerted by all nails = ?

W = Weight of magician = mg = (64.3 kg)(9.8 m/s²) = 630.14 N

Therefore,

F = 630.14 N

Now, we calculate the force exerted by each nail:

Fn = F/n

where,

Fn = force exerted by each nail = ?

n = Total no. of nails = 1900

Therefore,

Fn = 630.14 N/1900

Fn = 0.33 N

(b)

The pressure exerted by each nail is given as:

Pn = Fn/An

where,

Pn = Pressure exerted by each nail = ?

An = Area of contact for each nail = 1.26 x 10⁻⁶ m²

Therefore,

Pn = 0.33 N/1.26 x 10⁻⁶ m²

Pn = 263.22 x 10³ Pa = 263.22 KPa