Question

Friction and climbing SHOES. Shoes made for the sports of bouldering and rock climbing are designed to provide a great deal of friction between the foot and the surface of the ground. Such shoes on smooth rock might have a coefficient of static friction of 1.2 and a coefficient of kinetic friction of 0.90.

A person wearing these shoes stands on a smooth, horizontal rock. She pushes against the ground to begin running. What is the maximum horizontal acceleration she can have without slipping? (a) 20g; (b) 00.75g ; (c) 0.90g; (d) 1.2g.

Short answer

The maximum acceleration in horizontal direction is 1.2g. Therefore, the correct answer is (d).

Step-by-step solution

identification of given data:

• The coefficient of static friction is ${\mathrm{\mu }}_{\mathrm{s}}=1.2$.
• The coefficient of kinetic friction is ${\mathrm{\mu }}_{\mathrm{k}}=0.90$.

Concept/Significance of friction force:

The friction force always acts between two objects in contact. This force tries to restrict the motion of a particular object. Since the act of running starts with pushing on the ground, the greater the force exerted on the floor greater will be the acceleration. The value of maximum acceleration is constrained by static friction.

Find the maximum horizontal acceleration she can have without slipping:

The maximum force that can be exerted is the static friction which is given by,

$$\begin{gathered} \mathrm{F}={\mathrm{\mu }}_{\mathrm{s}}\mathrm{mg} \\ \mathrm{ma}={\mathrm{\mu }}_{\mathrm{s}}\mathrm{mg} \\ \mathrm{a}={\mathrm{\mu }}_{\mathrm{s}}\mathrm{g} \end{gathered}$$

Substitute 1.2 for ${\mathrm{\mu }}_{\mathrm{s}}$in the above equation.

a= 1.2g

The maximum acceleration in horizontal direction is 1.2 g. So, the options (a), (b), and (c) are incorrect. Therefore, the correct answer is (d).