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Transcript
12/12/2011 Brick Problem Energy How would you do this problem? Phy 121 Types of Energy • Kinetic Energy K= An object is moving • Gravitational Potential Energy An object is at some elevation • Spring Potential Energy A spring is compressed or stretched. Work 1 2 mv 2 U g = mgh U g = mgy Us = An 18.0 kg load of bricks is pulled at constant speed by a rope inclined at 20.0° above the horizontal. It moves 20.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. What is the Tension in the rope? 1 2 kx 2 Calculating Work Done • Find Work by Tension force of 20 N at 30º when the sled moves to the right 10 m. Tll • Work causes the energy of a system to change. Work = Fll ⋅ displacement • Definition: Component of F parallel to the displacement times the displacement Parallel Calculating Work Done • Find Work by Weight force of 300 N when the sled moves to the right 10 m. Wll=0 W = (T cos 30°) • ∆x W = (20 N) cos 30°(10 m) Work = (Wll ) • ∆x W = 17.3 N(10 m) W = 173 Nm Work = (0 N )(10 m ) W = 173 J Work = (mg ll ) • ∆x Work = 0 J Figure 5.6, p.92 1 12/12/2011 Springs ∆x Fspring Energy-Bar Charts ∆x and F are opposite direction • Identify Initial and Final Situations (+ 0 -) • Is there work done? Fspring = −kx Us = 1 2 kx 2 ∆x – Draw Coordinate, ∆x & Force vectors – (+ 0 -)? Energy Type Initial +, 0, - Between Final +, 0, - K U grav ∆x NA U spring Work Energy-Bar Charts Ug Usp W K Ug NA Brick Problem • Physics Principles • Identify initial & final situations • Identify types of energy • Is work done? • Draw Energy-bar Chart • Write Work-Energy Equation • List other information • Solve • Evaluate • Draw Energy Bar Charts • Write the Work-Energy Equation K NA Usp An 18.0 kg load of bricks is pulled at constant speed by a rope inclined at 20.0° above the horizontal. It moves 20.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. What is the Tension in the rope? Brick Problem Brick Problem An 18.0 kg load of bricks is pulled at constant speed by a rope inclined at 20.0°above the horizontal . It moves 20.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. What is the Tension in the rope? An 18.0 kg load of bricks is pulled at constant speed by a rope inclined at 20.0°above the horizontal . It moves 20.0 m on a horizontal surface. The coefficient of kinetic between the sledge and surface is 0.500. What is the Tension in the rope? Wbyrope = Fbyrope _ parallel • ∆x Wbyfriction = Fbyfriction _ parallel • ∆x Wbyrope = Tx • ∆x Wbyrope = + • + Ty + Tx Wbyfriction = f x • ∆x Wbyfriction = − • + + 2 12/12/2011 Brick Problem Brick Problem An 18.0 kg load of bricks is pulled at by a rope inclined at 20.0°above the horizontal. It moves 20. 0 m on . The coefficient of kinetic friction between the sledge and surface is 0.500. What is the Tension in the rope? An 18.0 kg load of bricks is pulled at by a rope inclined at 20.0°above the horizontal. It moves 20. 0 m on . The coefficient of kinetic friction between the sledge and surface is 0.500. What is the Tension in the rope? K K Ug Usp Wby Wby friction rope K Ug Ug Usp Usp Wby Wby friction rope K Ug Usp K i − W friction + Wrope = K f Brick Problem Brick Problem An 18.0 kg load of bricks is pulled at by a rope inclined at 20.0°above the horizontal. It moves 20.0 m on . • Evaluate by checking the FBD – So what size are the forces to make Constant Speed? – Does this make sense with your answers to the question? An 18.0 kg load of bricks is pulled at by a rope inclined at 20.0°above the horizontal. It moves 20. 0 m on . The coefficient of kinetic friction between the sledge and surface is 0.500. What is the Tension in the rope? K i − W friction + Wrope = K f N 1 2 Ty + − f∆x + Tx ∆x = 0 Tx Tx ∆x = f∆x W Brick Problem An 18.0 kg load of bricks is pulled at by a rope inclined at 20.0°above the horizontal. It moves 20. 0 m on . The coefficient of kinetic friction between the sledge and surface is 0.500. What is the Tension in the rope? ∑F y Brick Problem • Evaluate: How many ways can we do this? – Compare to a known value = ma n −W = 0 n =W f = µn mv 2 − f∆x + Tx ∆x = 12 mv 2 • How do you find known values? – Check signs with MD – Check forces with FBD – Unit Analysis • Did you really check? An 18.0 kg load of bricks is pulled at constant speed by a rope inclined at 20.0° above the horizontal. It moves 20.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. What is the Tension in the rope? T=94N 3 12/12/2011 Physics Principles Motion • MDs • Kinematic Equations Energy Forces • Work • Work Energy Equation • FBDs • Newton’s Laws Skier Problem • Physics Principle: Forces • FBD • Newton’s 2nd Law • Solve • Evaluate A skier starts from rest at the top of a hill that is inclined 10.5°with respect to the horizontal. The hillside is 200 m long, and the coefficient of friction between snow and skis is 0.075 0. At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. How far does the skier glide along the horizontal portion of the snow before coming to rest? Is It TRUE? •Alfa Romeo Spider Road Test Data •W=2645 lb •Power rated at 115 hp •Ref: Road & Truck , March 1984 t (s) 0 3.6 11.7 18.3 21.6 v(mph) 0 30 60 74 80 Skier Problem • Physics Principle: Energy A skier starts from rest at the top of a hill that is inclined • Identify initial & final 10.5°with respect to the situations • Identify types of energy horizontal. The hillside is 200 m long, and the coefficient of • Is work done? friction between snow and skis • Draw Energy-bar Chart is 0.075 0. At the bottom of the • Write Work-Energy hill, the snow is level and the Equation coefficient of friction is • List other information unchanged. How far does the • Solve skier glide along the horizontal • Evaluate portion of the snow before coming to rest? Power • Rate of Change of Position • Rate of Change of Velocity • Rate of Use or Transfer of Energy v= ∆x ∆t a= ∆v ∆t P= ∆U ∆t Challenges • Find the spring constant for the low setting on the projectile motion cannon. • Estimate the spring constant for one of your car’s suspension springs. • Look up what you pay for your electricity. How much is 8 hours of running up and down stairs worth? Want to change jobs? • How much energy could be generated when 1 kg of water falls over a 100 m water fall. 4