A hockey puck slides without friction along a frozen lake toward an ice ramp and plateau as shown. The speed of the puck is 4m/s and the height of the plateau is 1m. Will the puck make it all the way up the ramp? A: Yes B: No C: Need more information h = 1m v =4m/s

Energy Gravitational Potential Energy PE g Kinetic Energy KE Spring Potential Energy PE s

Spring force displacement x 0 ΔxΔx F2F 2Δx2Δx

Hooke’s law force displacement x 0ΔxΔx2Δx2Δx F2F-F 2Δx2Δx ΔxΔx -Δx-Δx -Δx-Δx Δx is proportional to F F ext = k Δx –F Spring Constant F spring = - k Δx Restoring Force

Spring force displacement x 0 Hooke’s law F = k Δx k1k1 k2k2 k 1 > k 2 1/k 1 1/k 2

How to measure? Typical values Units

Spring Energy force displacement F = k Δx δxδx F Work Done by a Varying Force x 0 ΔxΔx F2F 2Δx2Δx Area = F×δx Area = Work! PE sf – PE si = Work W = ½ kx 2

Spring Energy force displacement F = k Δx δxδx F Work Done by a Varying Force x 0 ΔxΔx F2F 2Δx2Δx Area = F×δx Area = Work! PE sf – PE si = Work W = ½ kx 2

0 + - Before After KE i PE gi PE si KE f PE gf PE sf W 1. Define a system 2. Define the initial and final states 3. Draw an Energy Bar Chart (Work?!) 4. Write the Energy-Work Formula ΔE = W k V-? ΔxΔx No Friction m ½ kx 2 = ½ mv 2

0 + - Before After KE i PE gi PE si KE f PE gf PE sf W 1. Define a system 2. Define the initial and final states 3. Draw an Energy Bar Chart (Work?!) 4. Write the Energy-Work Formula ΔE = W k H max ? V-? No Friction ½ kx 2 = ½ mv 2 +mgh

1. Define a system 2. Define the initial and final states 3. Draw an Energy Bar Chart (Work?!) 4. Write the Energy-Work Formula ΔE = W k H max ? ΔxΔx Friction: μ s and μ k θ Before After KE i PE gi PE si KE f PE gf PE sf W

Homework Due Monday Chapters 5.4, Read 5.6 Power!!! # 20, 35, 39, 53, 59

Quiz A ball is dropped from a tower and attains a speed v at the bottom. To achieve a speed 2v at the bottom, how many times as high must the new tower be?