# 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 F1 on 2 = ­‐F2 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 ﻿$F_{s}\leq f_{smax}=\mu F_{N}$﻿