Suppose you push on a flexible piece of stretched fabric...

Suppose you push on a flexible piece of stretched fabric with a force of $5.0 \mathrm{~N}$ as shown in Fig. 6- $83 a$. The fabric assembly is fixed and does not move. (a) What are the direction and magnitude of the normal force exerted back on the finger by the sheet? Is this normal force zero? If not, is it larger, smaller, or the same as the normal force would be if the fabric did not stretch? (b) Discuss the role the stretching of the fabric plays in regard to this normal force. (c) Suppose you push in the same way on a wall as shown in Fig. 6-83b. What are the direction and magnitude of the normal force exerted back on the finger by the wall? (d) Does the wall stretch noticeably? What causes the wall to be able to exert a force on the finger? How does the wall "know" what force to exert back on the hand?

Suppose you push on a flexible piece of stretched fabric with a force of $5.0 \mathrm{~N}$ as shown in Fig. 6- $83 a$. The fabric assembly is fixed and does not move.
(a) What are the direction and magnitude of the normal force exerted back on the finger by the sheet? Is this normal force zero? If not, is it larger, smaller, or the same as the normal force would be if the fabric did not stretch?
(b) Discuss the role the stretching of the fabric plays in regard to this normal force.
(c) Suppose you push in the same way on a wall as shown in Fig. 6-83b. What are the direction and magnitude of the normal force exerted back on the finger by the wall?
(d) Does the wall stretch noticeably? What causes the wall to be able to exert a force on the finger? How does the wall "know" what force to exert back on the hand?

Key Concepts

Elasticity and Material Deformation

Elasticity is the property of a material that enables it to deform under an applied force and then return to its original shape when the force is removed. In scenarios involving a flexible or stretched fabric, the degree of deformation (i.e., stretching) influences the distribution and magnitude of internal forces, including the normal reaction force. The material’s elastic response determines how effectively it resists deformation and distributes the applied force.

Static Equilibrium

Static equilibrium occurs when an object or system experiences no net force or net moment, meaning all the forces acting on it balance each other out. When a force is applied to a fixed object — whether a stretched fabric or a wall — the ensuing equilibrium requires that the reactive normal force exactly counterbalances the applied force, ensuring that the object remains stationary.

Normal Force

The normal force is the contact force exerted by a surface perpendicular to the object applying another force. It is the reaction force that balances the externally applied force, ensuring that the objects in contact do not interpenetrate. In any interaction where one object exerts a force on another, the normal force responds in the opposite direction to prevent overlap.

Newton's Third Law

Newton's Third Law of Motion states that for every action there is an equal and opposite reaction. This law is fundamental in understanding contact interactions; when one body exerts a force on another — whether pushing against a flexible fabric or a rigid wall — the second object exerts a force of equal magnitude and opposite direction back on the first object.

Microscopic Basis of Contact Forces

The microscopic origin of contact forces lies in electromagnetic interactions between atoms and molecules. When two surfaces come into contact, the electrons in the atoms of one surface repel the electrons in the atoms of the other surface. This repulsion creates the macroscopic normal force that we observe, allowing solids to exert reactive forces even without significant bulk deformation.

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