Test Bank, Question 13
In a classroom demonstration, a 79.2-kg physics professor lies on a "bed of nails." 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 professor is lying down, approximately 1950 nails make contact with his body.
What is the average force exerted by each nail on the professor's body?
To find the average force exerted by each nail on the professor's body, we need to use the formula:
Average force = Total force / Number of nails
First, let's calculate the total force exerted by all the nails on the professor's body:
Total force = mass x acceleration
Since the professor is lying on the bed without any vertical acceleration, the net vertical force must be zero. Therefore, the total force exerted by all the nails must equal the weight of the professor:
Total force = weight of the professor
The weight of an object can be calculated using the formula:
Weight = mass x gravity
The mass of the professor is given as 79.2 kg. The value of gravity is approximately 9.8 m/s².
Weight of the professor = 79.2 kg x 9.8 m/s²
Now, we can calculate the total force exerted by all the nails:
Total force = Weight of the professor
Finally, we can find the average force exerted by each nail by dividing the total force by the number of nails (1950).
Average force = Total force / Number of nails
Using these calculations, we can determine the average force exerted by each nail on the professor's body.