Applications of Newton’s Laws
Net force affects the motion, position and/or shape of objects (some important and commonly used forces are friction, drag and deformation).
Learning Objectives
Explain the effect of forces on an object’s motion and shape
Key Takeaways
Key Points
- Friction is the force that resists relative motion between two surfaces sliding across each other. Friction converts kinetic energy into heat.
- Drag force is the force that resists motion of an object traveling through a fluid such as air or water. Drag force is proportional to the velocity of the object traveling.
- Deformation forces are forces caused by stretching or compressing a material. Some examples would be springs or elastics.
Key Terms
- kinetic energy: The energy possessed by an object because of its motion, equal to one half the mass of the body times the square of its velocity.
We know that a net force affects the motion, position and shape of an object. It is useful at this point to look at some particularly interesting and common forces that will provide further applications of Newton’s laws of motion. Specifically, we will discuss the forces of friction, air or liquid drag, and deformation.
Friction
Friction is a force that resists movement between two surfaces sliding against each other. When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have a dramatic effect, as seen in the use of friction created by rubbing pieces of wood together to start a fire. Friction is not itself a fundamental force, but arises from fundamental electromagnetic forces between the charged particles constituting the two contacting surfaces.
Drag
Another interesting force in everyday life is the force of drag on an object when it is moving in a fluid (either gas or liquid). You feel this drag force when you move your hand through water, or through the wind. Like friction, the force of drag is a force that resists motion. As we will discuss in later units, the drag force is proportional to the velocity of the object moving through it. We see an illustrated example of drag force in.
Deformation
We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. The change in shape of an object due to the application of a force is a deformation. Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed. First, the object returns to its original shape when the force is removed (that is, the deformation is elastic for small deformations). Second, the size of the deformation is proportional to the force.
Friction: Kinetic
If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction.
Learning Objectives
Explain the dynamics of energy for friction between two surfaces
Key Takeaways
Key Points
- Kinetic (or dynamic) friction occurs when two objects are moving relative to each other and rub together (like a sled on the ground).
- The force of friction can be represented by an equation [latex]\text{F}_{\text{friction}} = \mu \text{F}_\text{n}[/latex]where [latex]\mu[/latex] is the coefficient of friction and is a unitless number that represents the strength of the friction of the surface.
- Kinetic friction and static (stationary) friction use two different coefficients for the same material.
Key Terms
- kinetic energy: The energy possessed by an object because of its motion, equal to one half the mass of the body times the square of its velocity.
When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to heat whenever motion with friction occurs, for example when a viscous fluid is stirred.
Kinetic (or dynamic) friction occurs when two objects are moving relative to each other and rub together; a sled on the ground would be a good example of kinetic friction.
The force of friction is what slows an object sliding over a surface. This force is what makes the brakes on cars work or causes resistance when you slide your hand across a surface. The force of friction can be represented by an equation: [latex]\text{F}_{\text{friction}} = \mu \text{F}_\text{n}[/latex]. In this equation [latex]\mu[/latex] is something called the coefficient of friction. This is a unitless number that represents the strength of the friction of the object. A very “grippy” surface like rubber might have a high coefficient of friction, whereas a slippery surface like ice has a much lower coefficient. [latex]\text{F}_\text{n}[/latex] is called the normal force and is the force of the surface pushing up on the object. In most cases on level ground, the normal force will be the equal and opposite of the object’s weight. In other words, it is the force that the surface must exert to keep the object from falling through.
The coefficient of kinetic friction is typically represented as [latex]\mu_\text{k}[/latex] and is usually less than the coefficient of static friction for the same materials.
Friction: Static
Static friction is a type of friction that occurs to resist motion when two objects are at rest against each other.
Learning Objectives
Demonstrate the relationship of maximum force of static friction
Key Takeaways
Key Points
- Static friction is a force that acts to resist the start of motion. It is borne of macroscopic inconsistencies in the surfaces of materials in contact as well as intermolecular interactions between the materials, such as hydrogen bonding, Van der Waal’s interactions and electrostatic interactions.
- Static friction uses a different, usually higher, coefficient than kinetic friction does.
- The force of static friction is [latex]\text{F}_{\text{fs}} = \mu_\text{s} \text{F}_\text{n}[/latex]. Where [latex]\mu_\text{s}[/latex] is the coefficient of static friction which varies by material and [latex]\text{F}_\text{n}[/latex] is the normal force.
Key Terms
- static: Fixed in place; having no motion.
- kinetic: Of or relating to motion
- friction: A force that resists the relative motion or tendency to such motion of two bodies in contact.
Static Friction
Another type of frictional force is static friction, otherwise known as stiction. Like all friction, it acts to resist the motion of an object moving over a surface. Unlike kinetic friction, however, static friction acts to resist the start of motion.
Static friction is friction between two objects that are not moving relative to each other. This frictional force is what prevents a parked car from sliding down a hill, for example. Before an object at rest on a surface can move, it must overcome the force of static friction.
Static friction originates from multiple sources. For any given material on another material of the same composition, friction will be greater as the material surfaces become rougher (consider sandpaper) on the macroscopic level. Additionally, intermolecular forces can greatly influence friction when two materials are put into contact. When surface area is below the micrometer range, Van der Waals’ forces, electrostatic interactions and hydrogen bonding can cause two materials to adhere to one another. A force is required to overcome these interactions and cause the surfaces to move across one another.
Circular Motion
An object in circular motion undergoes acceleration due to centripetal force in the direction of the center of rotation.
Learning Objectives
Develop an understanding of uniform circular motion as an indicator for net external force
Key Takeaways
Key Points
- An object that is undergoing circular motion has a velocity vector that is constantly changing direction.
- The force that is needed to maintain circular motion points toward the center of the circular path. It is therefore known as the centripetal force.
- The velocity of an object in circular motion is always tangent to the circle, and the centripetal force is always perpendicular to the velocity.
Key Terms
- tangent: a straight line touching a curve at a single point without crossing it at that point
- perpendicular: at or forming a right angle (to).
Uniform circular motion describes the motion of an object along a circle or a circular arc at constant speed. It is the basic form of rotational motion in the same way that uniform linear motion is the basic form of translational motion. However, the two types of motion are different with respect to the force required to maintain the motion.
Let us consider Newton’s first law of motion. It states that an object will maintain a constant velocity unless a net external force is applied. Therefore, uniform linear motion indicates the absence of a net external force. On the other hand, uniform circular motion requires that the velocity vector of an object constantly change direction. Since the velocity vector of the object is changing, an acceleration is occurring. Therefore, uniform circular motion indicates the presence of a net external force.
In uniform circular motion, the force is always perpendicular to the direction of the velocity. Since the direction of the velocity is continuously changing, the direction of the force must be as well.
The direction of the velocity along the circular trajectory is tangential. The perpendicular direction to the circular trajectory is, therefore, the radial direction. Therefore, the force (and therefore the acceleration) in uniform direction motion is in the radial direction. For this reason, acceleration in uniform circular motion is recognized to “seek the center” — i.e., centripetal force.
The equation for the acceleration [latex]\text{a}[/latex] required to sustain uniform circular motion is:
[latex]\displaystyle \text{a} =\frac{\text{v}^2}{\text{r}}[/latex]
where [latex]\text{m}[/latex] is the mass of the object, [latex]\text{v}[/latex] is the velocity of the object, and [latex]\text{r}[/latex] is the radius of the circle. Consequently, the net external force [latex]\text{F}_{\text{net}}[/latex] required to sustain circular motion is:
[latex]\displaystyle \text{F}_{\text{net}}=\frac{\text{m}\cdot \text{v}^2}{\text{r}}[/latex]
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