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Announcements

Announcements. CAPA Set #9 due Friday at 10 pm This week in Section: Lab #3 – Momentum Reading – Chapter 7 on Momentum. Clicker Question. Room Frequency BA. Two paths lead to the top of a big hill. Path #1 is steep and direct and Path #2 is twice as long but less steep.

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Announcements

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  1. Announcements • CAPA Set #9 due Friday at 10 pm • This week in Section: Lab #3 – Momentum • Reading – Chapter 7 on Momentum

  2. Clicker Question Room Frequency BA Two paths lead to the top of a big hill. Path #1 is steep and direct and Path #2 is twice as long but less steep. Both are rough paths and you push a box up each. How much more potential energy is gained if you take the longer path? A) none B) twice as much C) four times as much D) half as much 2d d h h #1 #2 φ θ

  3. Clicker Question Room Frequency BA Consider the same two paths as in the previous problem. Is the amount of work done the same along each path? A) Yes B) No, more work is done on the steeper path. C) No, more work is done on the longer path. D) Probably not, but the details are needed to know which is larger. 2d d h h #2 #1 φ θ

  4. Springs Spring in “relaxed” position exerts no force Force Compressed spring pushes back Stretched spring pulls back Force Hooke’s “Law” k = “spring constant” units = N/m x = displacement of spring Force = -kx Large k = stiff spring Small k = floppy spring

  5. Stored Energy in Springs Compressed spring has elastic potential energy Stretched spring also has elastic potential energy =Fspring x d If no change in any other energy, then DPE = Wext However Fspring = -kx changes as we stretch the spring Use average Fspring = -½ kx PE = ½ kx2 Elastic potential energy:

  6. Clicker Question Room Frequency BA A force of magnitude F stretches a spring through a displacement x. The force is then increased so that displacement is doubled. What is the magnitude of force needed to double the displacement and what will be the effect on the potential energy of doubling displacement? Force doubles, PE doubles. Force doubles, PE quadruples. Force quadruples, PE doubles. Force doubles, PE halves. Force quadruples, PE quarters. F = -kx, PE = ½kx2

  7. Clicker Question Room Frequency BA Which of the following types of potential energy can be negative? Gravitational Potential Energy Elastic Potential Energy Both of the above Neither of the above PEgravity = mgy

  8. A block of mass m is released from rest at height H on a frictionless ramp. It strikes a spring with spring constant kat the end of the ramp. How far will the spring compress (i.e. x)? 0 0 KEi + PEi + Wfrict + Wexternal= KEf + PEf 0 + mgH + 0 + 0 = 0 + (0 + ½ kx2) gravitational elastic

  9. Elastic Potential Energy – Does Not Have to Look Like a Spring

  10. What is Power?

  11. Power is a rate of energy per time Units are Joules / second = Watts The average power can be written in terms of the force and the average velocity:

  12. Raise a box of mass 2 kg at constant velocity by a height of 6 meters over a time interval of 2 seconds. How much energy is required to do the work? 6m Wext = DPE = mgh since DKE=0 Wext = 2 kg x 9.8 m/s x 6 m = 117 Joules 2 kg Also Wext = Fext x d  Fext = 117J/6m = 19.6 N How much power is required to do the work in that amount of time? Power = Wext / time = 117 J / 2 s = 59 Watts Also Power = Fext v = 19.6 N x (6m/2s) = 59 Watts

  13. Clicker Question Room Frequency BA A kiloWatt-hour is a unit of energy (Power x time). 1 kW-hour = 3.6 x 106 Joules The average household in the USA uses 2.7 billion Joules of electrical energy each month. Approximately how many 100 Watt lightbulbs would need to be left on all the time to amount to that energy consumption? xx 1 lightbulb 10 lightbulbs 100 lightbulbs 1000 lightbulbs 10,000 lightbulbs Energy = Power x time = (10 x 100 W) x (30x24x60x60 s) ≈ 2.6 x 109 Joules

  14. Collisions Before the collision: v2i v1i m1 m2 After the collision: v1f v2f m1 m2 v1f = final velocity of mass 1 v2f = final velocity of mass 2 These collisions should obey Newton’s Laws

  15. Elastic Collision Totalkinetic energy remains constant during the collision KE is conserved or ΔKE = 0 No energy converted to thermal or potential energy

  16. Demonstration Macroscopic objects never have perfectly elastic collisions but it’s often a good approximation. Inelastic Collision: KE is not constant; some is converted to another kind of energy; typically heat or deformation. Totally Inelastic Collision: KE is not conserved, and the objects stick together after collision.

  17. New Conserved Quantity Momentum Kind of like kinetic energy (associated with motion). However, not in units of Joules (instead kg m/s) and so not an energy. In addition to total energy being conserved in every collision, the total momentum vector is also conserved! Conservation of Momentum (in one-dimension)

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