Question

A normal force is a contact force that acts at the surface between two objects. Which of the following statements concerning the normal force is not correct? a) The normal force is always equal to the force of gravity. b) The normal force is just large enough to keep the two objects from penetrating each other. c) The normal force is not necessarily equal to the force of gravity, d) The normal force is perpendicular to the plane of the contact surface between the two objects.

Short answer

a) The normal force is always equal to the force of gravity. b) The normal force is just large enough to keep the two objects from penetrating each other. c) The normal force is not necessarily equal to the force of gravity. d) The normal force is perpendicular to the plane of the contact surface between the two objects. Answer: a) The normal force is always equal to the force of gravity.

Step-by-step solution

Option A

The normal force is always equal to the force of gravity. This statement is not always true. The normal force is equal to the force of gravity only when an object is lying flat on a horizontal surface with no other forces acting on it. In any other situation, such as the object being on an inclined plane or with other forces at play, the normal force is not equal to gravitational force.

Option B

The normal force is just large enough to keep the two objects from penetrating each other. This statement is true. The normal force occurs due to contact between objects and is equal to the force required to prevent the objects from interpenetrating or sinking into each other.

Option C

The normal force is not necessarily equal to the force of gravity. This statement is true. As mentioned before, the normal force is only equal to gravitational force when an object is lying on a completely horizontal surface, and no other forces are applied. If other forces or inclinations are introduced, the normal force will be different from the gravitational force.

Option D

The normal force is perpendicular to the plane of the contact surface between the two objects. This statement is true. By definition, the normal force always acts perpendicular to the surface where the two objects are in contact. This is an important property of normal force that aids in analyzing the behavior of objects under various forces. The incorrect statement is: a) The normal force is always equal to the force of gravity.

Key concepts

Gravitational Force

Imagine an apple falling from a tree; this is a classic example of gravitational force at work. The force of gravity is an attractive force that acts between any two masses. In most cases, one of these masses is our planet Earth, which pulls objects towards its center.

Gravitational force can be described by Isaac Newton's law of universal gravitation, which states that every point mass attracts every other point mass by a force pointing along the line intersecting both points. The formula for gravitational force is given by \( F = G \frac{m1 \cdot m2}{r^2} \) where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m1 \) and \( m2 \) are the masses of the two objects, and \( r \) is the distance between the centers of the two masses.

It's important to note that gravitational force is a field force, meaning it can act over a distance without direct contact. Students can often confuse this with the normal force, which, as pointed out in the textbook solution, is not always equal to the gravitational force. This distinction is fundamental and can help avoid misconceptions in physics problems.

Contact Forces

A contact force, as the name suggests, requires physical contact between two objects. When an object is placed on a surface, it experiences a contact force known as the normal force. This normal force is one component of the support force that prevents solid objects from passing through each other, hence sustaining their structural integrity.

Contact forces can vary greatly depending on the nature of the interaction and the materials involved. They include not only the normal force but also friction, tension, and applied forces. For example, when you push a book across a table, you're exerting an applied force, and the resistance you feel is due to friction – another contact force. These forces are crucial when calculating motion and equilibrium since they are responsible for initiating, sustaining, or resisting the movement of objects.

Understanding the role of contact forces is invaluable when solving physics problems, and as the exercise solutions demonstrate, normal force is just one important example of a contact force that needs to be understood in the context of its reaction to other forces, including gravitational force.

Force Vectors

Force vectors are critical in the study of physics because they allow us to represent forces graphically and calculate them quantitatively. Vectors are mathematical objects characterized by both a magnitude and a direction, which makes them perfect for describing forces. The magnitude of a vector represents how strong the force is, while the direction shows where the force is applied.

For example, when analyzing the force vectors on a block resting on an inclined plane, we must consider both the gravitational force pulling the block down the slope and the normal force pushing perpendicularly from the plane's surface. These force vectors are crucial in determining resultant forces, which in turn dictate the motion of the block.

Force vectors are essential in properly understanding physical situations, for instance, when facing the task to resolve forces into their components or when adding multiple forces together. The concept of force vectors is implicitly used in the textbook solution when describing the normal force as perpendicular to the surface, which illustrates its directional aspect, a fundamental property of vector quantities.