E139 Week 1 Forces (Lecture 2)

newton’s first law

a body maintains a constant velocity if the net force acting on it is 0

newton’s second law

net force = mass x acceleration

• F = MA

newton’s third law

to every force, there is an equal and opposite force

types of forces

gravitational force

inertial force

gravitational force

F = mg

• g = 9.81 m/s²

inertial force

F = ma

units = N

newtons

kg m /s²

energy

potential and kinetic energy

potential energy

PE = mgh

units = J

kinetic energy

velocity

KE = 0.5mv²

units = J

joules

Nm = kg m²/s²

momentum

p = mv

conservation of momentum

applies 3rd law

• F1 = -F2

• t1 = t2

• F1t1 = -F2t2

applies 2nd law

• m1a1t1 = -m2a2t2

• m1v1 = m2v2

spring stiffness

k = spring constant

△L

length that the spring is stretched from rest

spring force

F = k△L

force and length relationship

proportional

• high k = high stiffness = lower length with more force

• low k = low stiffness = greater length with less force

elastic strain energy

E = F△L

E = ½ k (△L)²

area under the curve

steps for calculations

1. sketch picture to define variables

2. define governing equations

3. solve for variable of interest

4. define knowns

5. plug in using consistent units and solve

6. write the answer in a sentence

7. state any assumptions made