1. Motion

2. 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.

3. 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.

4. dv = a dt ∫dv = ∫adt If a = constant v = v o + at Where v o is the velocity at t=0.

5. v = v o + at The definition of velocity is v = Δ x/Δ t = dx/dt dx/dt = v dx = v dt ∫dx = ∫v dt x = x o + v o t + (1/2) at 2

6. v = dx/dt v/a = (dx/dt) / (dv/dt) v/a = dx/dv vdv = adx ∫vdv = ∫adx v 2 = (v o ) 2 + 2a(x – x o )

7. 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?

8. 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.

9. 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?

10. 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?