Ch. 1 1D Problems

Question 1

How to solve forces which are dependent on velocity to get x(t)

Answer 1

ma = m(dv/dt) = F(v)
–> ∫m (dv/F(v)) = ∫ dt = t + c
This gives v = v(t)
Solve v = dx/dt = v(t) to find x(t)

Question 2

How to solve forces which are dependent on velocity to get v(x)

Answer 2

ma = v(dv/F(v)) = dx = x + c

Question 3

Conservation of Energy

Answer 3

E = (1/2)mv^2 + V(x) is conserved

Question 4

Potential energy V(x) =

Answer 4

• ∫F(x) dx

Question 5

What is a conservative force?

Answer 5

A force with the property that the work done in moving a particle from a to b is independent of the path taken

Question 6

Spring constant equation

Answer 6

F = -kx

Question 7

Newton’s equation for springs:

Answer 7

mẍ = -mg - kx
–> ẍ + (ω^2)x = -g
(w^2 = k/m)

Question 8

Integral of 1/ (a^2 + b^2x^2)

Answer 8

(m/ab) arctan(bx/a)

Question 9

Integral of 1/ √(a^2 - x^2)

Answer 9

arcsin(x/a)

Question 10

If a particle exhibits simple harmonic motion its motion is of the form…

When do maxima and minima occur?

Answer 10

x(t) = Acos(ωt) + Bsin(ωt)

Maxima and minima occur when 0 = xdot

Question 11

Solution to simple harmonic oscillator, mass on a spring, extension x =

Answer 11

g/ω^2 + Acos(ωt) + Bsin(ωt)

first term may be negative, depends if measuring x up or down

Question 12

How to get v(x) from f(v,x)

Answer 12

F = ma = v(dv/dx)

Question 13

tan values

Answer 13

nπ = 0
π/6 = sqrt(3)/3
π/4 = 1
π/3 = sqrt(3)
π/2 = infinity

Question 14

Frequency =

Answer 14

ω/2π

Question 15

Period =

Answer 15

2π/ω