Kinetic Energy and Gravitational Potential Energy We can rewrite Chapter 10 Energy Kinetic Energy and Gravitational Potential Energy We can rewrite

Kinetic Energy: We define K = ½ mV2 Unit of kinetic energy (Kg m2/s2) Joule Ex. For a mass 0.5 Kg, V = 4m/s, K = 4J Gravitational potential energy: • We define Ug=mgy • Unit of potential energy: Joule • Kinetic energy never be negative. • gravitational potential energy depends on the position.

Example 10.3 P275 Example 10.4 P276 Example 10.8 P283 Stop to think 10.1 P273 Stop to think 10.2 P275 Stop to think 10.3 P278 Stop to think 10.4 P280 Stop to think 10.5 P284 Stop to think 10.6 P292 Example 10.3 P275 Example 10.4 P276 Example 10.8 P283 Example 10.9 P286 Example 10.10 P291

Perfectly Inelastic collision

Elastic Collisions Perfectly elastic collision conserves both momentum and kinetic energy Momentum conservation Kinetic energy conservation

Perfectly elastic collision with ball 2 initially at rest Solve above equations, the solution is Question: If m1=m2, Vi1=V, m2 initially at rest, after collision what is Vf2, Vf1

Gravitational potential energy mgh Y or (h) depends on where you choose to put the origin of your coordinate system. But potential energy change ΔU is independent of the coordinate system

Energy Bar Chart

If we neglect air resistant or friction:

Quick think A small child slides down the four frictionless slides A-D. Each has the same height. Rank in order. From largest to smallest her speeds VA to VD at the bottom. VA = VB =VC =VD

Ex. 10.4 A ballistic pendulum A 10 g bullet is fired into a 1200g wood block hanging from a 150-cm-long string. The bullet embeds itself into the block, and block then swings out to an angle of 40o. What was the speed of the bullet? The momentum conservation equation Pi = Pf applied to the inelastic collision Then turning our attention to the swing The energy equation Kf + Ugf = Ki + Ugi We define y1 = 0 Get:

Three identical balls are thrown from the top of a building, all with the same initial speed the first is thrown horizontally, the second at some angle above the horizontal and third at some angle below the horizontal. Neglecting the air resistance, rank the speeds of the balls at the instant each hits the ground . Answer: All the three balls have the same speed at the moment they hit the ground. Since neglect the air resistance, total mechanical energies for each ball should be conserved. Ki+Ui= 1/2mvi2 +mgh Kf + Uf = 1/2mvf2 Ki+Ui = Kf +Uf Vf2= 2gh + vi2 does not matter the angle. Three balls take different times to reach the ground

Ex. 10.3 The speed of sled

A rebounding pendulum

Restoring forces and Hooke’s Law Displacement from equilibrium ∆s Hooke’s Law K is called the spring constant. It is spring character, unit:N/m

Measure spring constant k

Spring potential energy

Conservation of mechanical energy Mechanical energy E (mech) = K + U If there is no friction or other losses of mechanical energy then ΔE(mech)=0 This is the law of conservation of mechanical energy

Energy Diagrams Particle in free fall Energy Diagram is used to visualize motion.

A mass oscillating on a spring

More general energy diagram How to get kinetic energy from this diagram?