Quiz 5 Rubrics on the website

Physics 7B - ABLecture 9May 29Detailed Relation of Force to Motion Recap Newtonian Model, Circular MotionSimple Harmonic Motion

Quiz 3 Re-evaluation Request Due TODAY Quiz 4 Due June 5 (next Thursday)Quiz 5 & 6 Due June 9 at the time of Final Quiz 5 Rubrics on the website TODAY Quiz 6 (Last Quiz!!!)

11 days till…

11 days till… 7B Final June 9 Mon 1- 3pm • Practice Final as well as Quiz problems from Fri lecture sections are on the course website (solutions will be posted on Tuesday, June 3) • Next Week, June 5 is Last lecture • will focus on Final Review = Practice Final Problems • Come prepared! • Review session schedule (June 5 - 8) will be on the course web site next week.

Final format 6 ~ 8 questions (most likely…) Quantitative and qualitative questions Questions are on any material throughout the quarter. Chapter 5 Fluids, Circuits, Transport, Capacitor/Exponential Chapter 6 Vectors/Force (Galilean Space-Time Model) Chapter 7 Momentum/Force, Angular Momentum/Torque Chapter 8 Newtonian Model, SHM To do science, one must practise!But make sure your practice is useful...... available resources : Quiz problems from this quarter, Quiz problems from lecture section C/D , Practice Final Problems.

Recap Detailed Relation of Force to Motion Which takes longer to hit the ground: a bullet shot horizontally or a bullet dropped from the same height? A) The dropped bullet hits the ground firstB) The fired bullet hits the ground firstC) It depends on the mass of the bulletD) They both hit the ground at the same time

Recap Detailed Relation of Force to Motion Some relevant questions to ask:What is the vertical component of the initial velocity in two cases? Are they different? How is the force diagram look like in two cases?What is the vertical component of acceleration (while the bullet is moving toward the ground)? A) The dropped bullet hits the ground firstB) The fired bullet hits the ground firstC) It depends on the mass of the bulletD) They both hit the ground at the same time

Recap Detailed Relation of Force to Motion A rider in a “barrel of fun” is shown to the right. The rider finds herself stuck with her back to the wall. Which diagram below correctly shows the forces acting on her? Rotating at constant speed

Recap Detailed Relation of Force to Motion Consider two carts of masses M and 2M, at rest on a frictionless track. If you push one cart for 3s and then the other for the same length of time, exerting equal force on each, the momentum of the light cart is: Four times Twice Equal to One-half One quarter The momentum of the heavy cart 2M M

Recap Detailed Relation of Force to Motion Consider two carts of masses M and 2M, at rest on a frictionless track. If you push one cart for 3s and then the other for the same length of time, exerting equal force on each, the momentum of the light cart is: Four times Twice Equal to One-half One quarter The momentum of the heavy cart 2M M Impulseext = ∆ p = Fave.ext x ∆ t

A person spins a tennis ball on a string in a horizontal circle. At the point indicated in the figure, the ball is given a sharp blow in the forward direction. This causes a change in the angular momentum L in the Recap Detailed Relation of Force to Motion x direction y direction z direction

A person spins a tennis ball on a string in a horizontal circle. At the point indicated in the figure, the ball is given a sharp blow in the forward direction. This causes a change in the angular momentum L in the Recap Detailed Relation of Force to Motion ∆L  (torque exerted by the blow) x direction y direction z direction Net Angular Impulseext = ∆ L = ave.ext x ∆ t

Recap Detailed Relation of Force to Motion An asteroid is traveling to the right through deep space at a constant velocity. The path of the asteroid is shown to the right. Suddenly, it is hit fairly hard by a comet that comes flying in from above and then bounces off. So the asteroid feels a downward force, which acts only for a very short time. Which path in the picture is the most reasonable for the asteroid to follow after the impact?

Recap Detailed Relation of Force to Motion An asteroid is traveling to the right through deep space at a constant velocity. The path of the asteroid is shown to the right. Suddenly, it is hit fairly hard by a comet that comes flying in from above and then bounces off. So the asteroid feels a C downward force, which acts only for a very short time. Which path in the picture is the most reasonable for the asteroid to follow after the impact?

Recap Detailed Relation of Force to Motion An asteroid is traveling to the right through deep space at a constant velocity. Suddenly, a giant rocket engine which is attached to the asteroid is fired upward so that there is a constant downward force on the asteroid. Rocket engine starts here Which path in the picture is the most reasonable for the asteroid to follow after the impact?

Recap Detailed Relation of Force to Motion An asteroid is traveling to the right through deep space at a constant velocity. Suddenly, a giant rocket engine which is attached to the asteroid is fired upward so that there is a constant downward force on the asteroid. Rocket engine starts here B Which path in the picture is the most reasonable for the asteroid to follow after the impact?

Recap Detailed Relation of Force to Motion The moon does not crash into the Earth because: It is not accelerating too much It is not accelerating toward the Earth It is accelerating away from the Earth More than one of the above Earth

A lot of things oscillate (periodically) Atoms in Liquids and Solids Tuning fork Detailed Relation of Force to Motion

Simple harmonic motion: is simply a type of motion which follows a repetitive pattern caused by a restoring force ∑F = – k x Force is zero at equilibrium. For many systems, the net force takes this form near equilibrium, provided equilibrium is stable Particle in a bowl equilibrium equilibrium “Stable” means the net force pushes back to equilibrium equilibrium

Not all systems are “stable” We don’t find many unstable systems, as any small “bump” has already disrupted them equilibrium SHM not applicable tipping point tipping point Most realistic systems have SHM like behaviour close to equilibrium, but behave in very different ways if they get a large push. equilibrium new equilibrium • The environment • The stock market • etc. SHM applicable for small oscillations near (stable) equilibrium.

Simple harmonic motion: SHM means that: ∑F = – k x The nice thing about SHM is we can solve it! From Newton’s Second Law, ∑F = – k x = ma From the definition of a, ∑F = – k x = ma = m d2x/dt2 This means, a(t) =d2x(t)/dt2 =– (k/m) x(t) Math Question What kind of function x(t) is a function whose second derivcative is proportional to the negative of the original function?

Simple harmonic motion: SHM means that: ∑F = – k x The nice thing about SHM is we can solve it! From Newton’s Second Law, ∑F = – k x = ma From the definition of a, ∑F = – k x = ma = m d2x/dt2 This means, a(t) =d2x(t)/dt2 =– (k/m) x(t)=– (constant) x(t) Math Question What kind of function x(t) is a function whose second derivcative is proportional to the negative of the original function? Answer: Sine function! Where T = 2√m/k, A and  depend on the initial condition,e.g. how far you pull the spring before letting it go.

Simple harmonic motion: ∑F = – k x Position of the object with above restoring force exerted on it is SHM, i.e. x(t) T A is the amplitude A is the phase constant responsible for the offset at t = 0 time T is the period: time it takes for one cycle (crest to crest, or trough to trough) A T The motion is identical one period later at any point.

k: spring constant is the phase constant m: mass T: is the period f : frequency Explaining the parameters in SHM: Ais the amplitude responsible for the offset at t = 0 Set by what you do to the system Set by what the systemis made of.  A may change, but Tmust remain the same.  The same setup with a different starting push always have the same periods

Shown to the right are two systems undergoing SHM. The vertical position represents displacement and the horizontal axis represents time. How are the two systems different? A) They have different periods B) They have different amplitudes C) They have different phase constants D) Only two of the above E) a, b and c correct

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Quiz 5 Rubrics on the website