# Chapter 4: Newton's Law of Motion and its Application

Classes of forces: **Contact / Field Forces,** consist of Force and Mass

**Net force**: the vector sum of all the forces acting on an object, written as $\sum F$ .

$F_{x}= F\cos\Theta$

$F_{y}= F\sin \Theta$

Directed by the free body diagram

#### FREE BODY DIAGRAM:

Drawing a systematic FBD, only consider the external force and not the internal force.

### Hooke’s law:

$F = -KS$ a restoring force that exerts in the opposite direction of force applied K is the spring constant

S is the change in the length caused by shift of the spring’s natural length

$-K$ Represents the negative displacement by a stretch

**Normal Force - **A force exerted in the opposite direction to the surface of the contact.

*Can also be a representation of the pressure between the surfaces of any two objects

**Friction - **It is a force between the surfaces of any two objects in the direction that opposes the motion.

**μ -** represents the friction constant.

Weight is always considered - mg

### Newton’s Law of Motion

- An object continues in a state of rest or in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force – forces on the object.
- $\sum F=0,$ therefore, acceleration $= 0 \rightarrow$ $V_{constant}$
- Inertia
- Inertial frame of reference; FoR when @ constant velocity
- Inertial Mass: m of object is a quantitative measure of inertia
- M inversely proportional 1/a; m1/m2 = a2/a1
- The net external force, $\sum F$ , acts on an object of mass
*m*, results in an acceleration, a, that: **Directly Proportional**to the $\sum F$- Has a magnitude
**inversely proportional**to the*m* - The
**direction**of the acceleration is the same as the direction of the acting $\sum F$ - Therefore $a=\sum F/m$

When the velocity of a body is constant / at rest: It’s at **Equilibrium**

The weight is the typical component of $\sum F$ acting upon an object by 2nd law.

Use FBD; if FBD is unbalanced, $\sum F$ is not 0.

- To every action, there is a reaction in the opposite direction of the original force applied. Where
**F**_{1 on 2}**= ‐F**_{2 on 1} - Force applied from A on B, reaction force can be found at center of B
- The reaction force is not included in the FBD.
- The Weight to Normal force are not Action to Reaction
- Both act on the same object
- Tensions and springs are considered.

### Equilibrium Application of Newton’s Law of Motion

An object is at equilibrium when it has 0 acceleration; $\sum F_{x}= 0$ and $\sum F_{y}= 0$ None‐equilibrium: $\sum F_{x}=ma_{x}, \sum F_{y}=ma_{y}$

### Friction:

$\ast$ The static friction $>$ kinetic friction where both base off of normal force

$F_{K}=\mu _{K}F_{N}$ $,$ $0 < \mu <1-$ where $\mu$ is the coefficient of kinetic friction $F_{s}\leq f_{smax}=\mu F_{N}$

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