Test Review: Examples Chapters on the test: - momentum - energy/work - oscillations Physics 1D03 - Lecture 34

Practice Question Momentum: Pg 262 # 10,15,19,20,29a,31,51 Energy: Pg 298 # 3,5,9,15,23,25,29ab,33 Pg 332 # 2,3,7,15,29,31,39 SHM: Pg 438 # 3,5,9,15,23,25, 43d, 47 # 65 - extra, for fun, not on test Physics 1D03 - Lecture 34

Momentum Remember, momentum is always conserved, but energy not. draw a picture of Before and After, and write down the momentum equation for impulse, remember, J=Δp=FΔt=area under a F-t graph Physics 1D03 - Lecture 34

Example Initially at rest, a block explodes into two pieces of equal mass. How would the velocities of the two pieces compare ? Initially at rest in space, your arm, 1/20 of the mass of your body, falls off and moves away with seed v. How would the velocity of the rest of your body compare, and in what direction would it move ? Physics 1D03 - Lecture 34

how does this change if the collision is elastic ? Example A block of mass m moving with speed v=3m/s hits a block of mass 4m at rest and sticks to it. What will their speed after the collision be ? how does this change if the collision is elastic ? Physics 1D03 - Lecture 34

what is the change of momentum ? what is the impulse ? Example A ball falls down with velocity 10m/s, hits the ground and bounces back with the same speed. what is the change of momentum ? what is the impulse ? if the collision lasts 0.1s, what was the average force ? if the force looks like below, what was the max force ? F t Physics 1D03 - Lecture 34

Energy Energy is conserved, but sometimes it gets converted into a form that is difficult to quantify, like heat or sound Remember kinetic and potential energy equations: 1/2mv2 and mgh (h depends on your point of reference). Physics 1D03 - Lecture 34

Example you walk up some stairs and end up 5m higher than when you started. If your mass is 75kg, how much work was done by gravity? you walk across a horizontal surface for 5m. How much work was done by gravity ? Physics 1D03 - Lecture 34

how much energy is in the system? Example A 100g bullet is shot into a 10kg block connected to a spring with k=10N/m on a surface with μ=0.1 with velocity of 100m/s. How far would the block compress? how much energy is in the system? Physics 1D03 - Lecture 34

SHM Simple Harmonic Motion is governed by the equation: x(t)=Acos(ωt+φ) where ω comes from the equation of motion: a(t)=-ω2x(t) A is the amplitude of your motion and φ is the phase factor, or where you start. Physics 1D03 - Lecture 34

Springs and Pendulum Newton’s 2nd Law: Physics 1D03 - Lecture 34

Energy Since we know the total energy of a SHM, we can calculate the or displacement velocity at any point in time: ETot=1/2kA2 = K+U = 1/2mv2 + 1/2kx2 So, if x=0, all E is in kinetic, and v is at max if x=A, all E is in potential, and v is zero Physics 1D03 - Lecture 34

Example What is the total energy of a mass/spring system with k=20N/m and m=0.1kg if the amplitude of the motion is 2.0cm and the maximum velocity vmax=0.28m/s ? does it take more time for the mass to move from equilibrium to A/2, or from A/2 to A ? Physics 1D03 - Lecture 34

If the mass starts at θ=30o, what is its angular position at t=4s ? Example A mass of 1.0kg is swinging on a string connected to the ceiling of a building with a period of 10s. What is the height of the building ? If the mass starts at θ=30o, what is its angular position at t=4s ? Physics 1D03 - Lecture 34