Question

"What is the mass of the heaviest book this person can hold onto vertically before it slips out of his or her fingers? The coefficient of static friction of the surface between the fingers and the book cover is 0.80."

Answer 1

Answer: 9.6kg

Explanation:

According to research, a person with compromised strength in his finger can apply a normal force of 6N to either side of a pinch held object like a notebook.

Since the person is holding onto to the book vertically, the force applied on both sides of the book slightly is 6 + 6 = 12N.

If the coefficient of friction of the surface between the finger and the book cover is given as 0.80.

From the relationship,

F = uR, u is the frictional force, R is the slight resultant force exerted on both side of the book.

Therefore,

F = 0.8 × 12 = 9.6N

The max mass of book this person can hold onto vertically before it slip off his finger will be derived from the formula

F = Mg

If we take acceleration due to gravity as 10m/s², and make M the subject of formula, we have

M = F/g = 9.6/10 = 0.96kg.

Answer 2

Answer: The mass of the heaviest book the person can hold is 0.0157 kilogram

Explanation:

From Force F = Coefficient of friction * length

Note, average length of human fingers is 7.6inches = 0.19304 meters

F= 0.8 *0.19304

F= 0.1544 N

But F = mass m * acceleration g

Mass m = F/g

m = 0.1544/9.81

m = 0.0157 kg