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 F\sum F .

Fx=FcosΘF_{x}= F\cos\Theta 

Fy=FsinΘF_{y}= F\sin \Theta 

Directed by the free body diagram


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

Hooke’s law:

F=KSF = -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-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.
  • F=0,\sum F=0, therefore, acceleration =0= 0 \rightarrow VconstantV_{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, F\sum F , acts on an object of mass m, results in an acceleration, a, that:
  • Directly Proportional to the F\sum F
  • Has a magnitude inversely proportional to the m
  • The direction of the acceleration is the same as the direction of the acting F\sum F
  • Therefore a=F/ma=\sum F/m

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

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

Use FBD; if FBD is unbalanced, F\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; Fx=0\sum F_{x}= 0 and Fy=0\sum F_{y}= 0 None‐equilibrium: Fx=max,Fy=may\sum F_{x}=ma_{x}, \sum F_{y}=ma_{y}


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

FK=μKFNF_{K}=\mu _{K}F_{N} ,, 0<μ<10 < \mu <1- where μ\mu is the coefficient of kinetic friction Fsfsmax=μFNF_{s}\leq f_{smax}=\mu F_{N}

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