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! Physics 1710 Chapter 5: Laws of Motion—I v R

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

1′ Lecture Newton’s Laws of Motion are: Newton’s Laws of Motion are: Acceleration (or deceleration) occurs if and only if there is a net external force. Acceleration (or deceleration) occurs if and only if there is a net external force. a = F/m [Note this is a vector eqn.] 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. F 12 = - F 21 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. F 12 = - F 21 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. Weight is the force of gravity equal to g times the mass of the object. g =9.80 N/kg g =9.80 N/kg The force of friction is opposed to the motion of a body and proportional to the normal force. 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. Free body diagrams are sketches of all the forces acting on a body. Physics 1710 Chapter 5: Laws of Motion—I

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

Laws of Motion 1 st 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. Physics 1710 Chapter 5: Laws of Motion—I

First Law of Motion (implications) Equilibrium suggests ∑ F = 0. Equilibrium suggests ∑ F = 0. Force is a vector: [ F, not F] Force is a vector: [ F, not F] “Nature is conservative;” “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 An inertial frame of reference is one that is not accelerating. [ a 1 = a 2 ] that is not accelerating. [ a 1 = a 2 ] Physics 1710 Chapter 5: Laws of Motion—I

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

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

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

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

Balloon Drop v T = √[g‧m/γA] v T ∝ √m Physics 1710 Chapter 5: Laws of Motion—I

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

Physics 1710 Chapter 5 The Laws of Motion There are two kinds of mass ( assumed to be equivalent): gravitational mass: F g = g m inertial mass: a ∝ 1/m a 1 /a 2 = m 2 /m 1 Mass is an inherent property of matter, independent of the surroundings and the method used to measure it.

Physics 1710 Chapter 5 The Laws of Motion Summary Newton’s 1st Law of Motion is: 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.