Motion
Newton’s Laws
1. A body in motion will remain in motion or a
body at rest will remain at rest unless acted
on by an external force.
2. An external force on a body of mass m causes
an acceleration of that body, i.e.
F = ma
3. For every action, there is an equal and
opposite reaction.
Derivation of Laws of Motion
F = ma
a = F/m
Where a is the acceleration.
Acceleration is defined as the derivative with
respect to time of the velocity
a = dv/dt = Δv/Δt
Where both a and v are vectors.
dv = a dt
∫dv = ∫adt
If a = constant
v = vo + at
Where vo is the velocity at t=0.
v = vo + at
The definition of velocity is
v = Δ x/Δ t = dx/dt
dx/dt = v
dx = v dt
∫dx = ∫v dt
x = xo + vot + (1/2) at2
v = dx/dt
v/a = (dx/dt) / (dv/dt)
v/a = dx/dv
vdv = adx
∫vdv = ∫adx
v2 = (vo)2 + 2a(x – xo)
One Dimensional Motion
• Josh Avery climbs to the top of a 200 ft tall
tree carrying two metal spheres – the first
weighs 1 pound and the second weighs 10
pounds. He drops the lighter sphere and it
falls to the ground.
• What is the speed of the sphere when it
impacts the ground?
• How long did it take for the sphere to hit the
ground?
• Josh now drops the second and heavier
sphere.
• How fast is it going when it impacts the
ground?
• Is this faster than the lighter sphere?
• How long does it take to hit the ground?
• Is this less time than the lighter sphere?
• Explain your answers.
• A pitcher for the Boston Red Sox visits the
campus at Dartmouth. He is asked to throw a
baseball straight up as fast as he can.
• The ball is clocked leaving the pitchers hand at
60 mph and at a height of 8 ft.
• What is the force on the ball as it travels
upwards?
• What is the acceleration of the ball as it
travels upwards?
• At what height will the ball stop going up and
begin to fall downward?
• How fast will the ball be traveling when it
changes direction?
• How long did it take for the ball to reverse
direction?
• How fast will the ball be going when it hits the
ground?