Physics 1710 Chapter 5: Laws of Motion—I

1. 0 Physics 1710 Chapter 5: Laws of Motion—I v Quiz: What lateral acceleration does a pilot experience who is flying a jet at 350 m/s in a 1.00 km banked turn? a = v 2/R a = (350. m/s) 2 /1000. m = 122. m/s/s = 12 g. Wow! R

2. 0 Physics 1710 Chapter 5: Laws of Motion—I Isaac Newton (1642 –1727) Published Principia 1687 At age 45

3. 0 Physics 1710 Chapter 5: Laws of Motion—I • Acceleration (or deceleration) occurs if and only if there is a net external force. 1′ Lecture Newton’s Laws of Motion are: • a = F/m[Note this is a vector eqn.] • The force exerted by a first object on a second is always equal and opposite the the force exerted by the second on the first. F12= - F21

4. 0 Physics 1710 Chapter 5: Laws of Motion—I 1′ Lecture –continued (30″ more) Weight is the force of gravity equal to g times the mass of the object. g =9.80 N/kg The force of friction is opposed to the motion of a body and proportional to the normal force. Free body diagrams are sketches of all the forces acting on a body.

5. 0 Physics 1710 Chapter 5: Laws of Motion—I Aristotle (384-322 BC) Wrote Physica Thought that force causes motion. i.e. F → v Error: v ≠ 0, but F =0

6. 0 Physics 1710 Chapter 5: Laws of Motion—I Laws of Motion 1st Law: An acceleration is caused by a net external force. Subtleties: No net force ⇆ no acceleration. Acceleration is the secret to understanding motion. Cf. Aristotle.

7. 0 Physics 1710 Chapter 5: Laws of Motion—I First Law of Motion (implications) Equilibrium suggests ∑ F = 0. Force is a vector: [ F, not F] “Nature is conservative;” inertia is the tendency to resist a change in the status quo. [ Φ \ Ω \ Δ] An inertial frame of reference is one that is not accelerating. [ a1 = a2]

8. 0 Physics 1710 Chapter 5: Laws of Motion—I Balloon Drop

9. 0 Physics 1710Chapter 5 The Laws of Motion Terminal Velocity Weight is the force due to gravity Fg = g‧m; g =9.80 N/kg Air resistance depends on the wind velocity Fv≈ - γA v 2 Total ∑ F = Fg+ Fv = 0 ∑ F = gm – γAvT2 = 0 vT = √[g‧m/ γA] Implications?

10. 0 Physics 1710 Chapter 5: Laws of Motion—I Terminal Velocity

11. 0 Physics 1710 Chapter 5: Laws of Motion—I At Terminal Velocity Free Fall

12. 0 Physics 1710 Chapter 5: Laws of Motion—I Balloon Drop vT = √[g‧m/γA] vT∝ √m

13. 0 Physics 1710 Chapter 5: Laws of Motion—I Terminal Velocity Weight is the force due to gravity vT = √[g‧m/kA] Heavy (i.e. massive) objects fall faster than lighter ones. For example g‧m > 100 kA →vT > 10 m/s, a hard fall. A parachute slows you down. kA > g‧m/100 →vT < 10 m/s, not too bad

14. 0 Physics 1710 Chapter 5: Laws of Motion—I Why does a projectile follow a parabolic trajectory? There is only a Force acting in the vertical (downward) direction. Therefore, the is only a downward acceleration.

15. 0 Physics 1710 Chapter 5: Laws of Motion—I Concept Test: A spaceship in deep space is moving side- wise initially when it fires it’s impulse engine, producing a constant thrust. Sketch the trajectory of the spacecraft.

16. 0 Physics 1710 Chapter 5: Laws of Motion—I Concept Test: A spaceship in deep space is moving side- wise initially when it fires it’s impulse engine, producing a constant thrust. Sketch the trajectory of the spacecraft. It then turns off its engine; what happens then?

17. Physics 1710Chapter 5 The Laws of Motion There are two kinds of mass ( assumed to be equivalent): gravitational mass: Fg = g m inertial mass: a ∝ 1/m a1 /a2 = m2 /m1 Mass is an inherent property of matter, independent of the surroundings and the method used to measure it.

18. Physics 1710Chapter 5 The Laws of Motion Summary Newton’s 1st Law of Motion is: A body at rest will remain at rest and a body in motion will remain in the same state of motion unless acted upon by an external unbalanced force. That is:force causes acceleration.