Newton's laws form the foundation of classical mechanics and provide the framework for understanding force and motion.
An object remains at rest or in uniform motion unless acted upon by a net external force.
ΣF = ma
where:
For every action force, there is an equal and opposite reaction force.
A 2 kg block is pushed with a force of 10 N. If friction is 2 N, calculate the acceleration.
Solution:
Net force = 10 N - 2 N = 8 N
a = F/m = 8 N/2 kg = 4 m/s²
Fg = mg
where g = 9.81 m/s² on Earth
The perpendicular force exerted by a surface on an object.
Static Friction: fs ≤ μsN
Kinetic Friction: fk = μkN
where:
Free body diagrams (FBDs) are essential tools for visualizing and analyzing forces acting on objects.
Remember: The length of force arrows should be proportional to the magnitude of the forces!
Fx = F cos θ
Fy = F sin θ
ΣFx = max
ΣFy = may
Parallel component of weight: mg sin θ
Perpendicular component of weight: mg cos θ
A 5 kg block slides down a 30° incline. Calculate the acceleration if μk = 0.2.
Solution:
mg sin θ = 5(9.81)(sin 30°) = 24.525 N down slope
N = mg cos θ = 5(9.81)(cos 30°) = 42.47 N
fk = μkN = 0.2(42.47) = 8.494 N
Net force = 24.525 - 8.494 = 16.031 N
a = 16.031/5 = 3.21 m/s²
For an Atwood machine:
T - m₁g = m₁a
m₂g - T = m₂a
Fc = mv²/r = mω²r
where:
Centripetal force is not a new type of force - it's provided by friction, tension, or normal force!
Fs = -kx
where:
A 0.5 kg mass is attached to a spring with k = 20 N/m. If stretched 0.1 m, what is the acceleration?
Solution:
F = -kx = -20(0.1) = -2 N
a = F/m = -2/0.5 = -4 m/s²
W = F·d = Fd cos θ
Work-Energy Theorem: W = ΔKE = ½mv² - ½mv₀²
p = mv
F·Δt = Δp (Impulse-Momentum Theorem)
For AP Physics C, you should be able to:
