PHSX 211 10th Edition Lecture 20 Outline of Last Lecture Practice ProblemsI. What is the initial and final gravitational potential energy of a 1 kg ball that starts at 1 m above the ground and ends at 2 m above the ground?II. A roller coaster car rolls down a frictionless track, reaching speed vf at the bottom. If youwant the car to go twice as fast as the bottom, by what factor must you increase the height of the track? Does your answer depend on whether the track is straight or not?III. A car is going 15 m/s when it runs out of gas at the bottom of a 10 m high hill. Can it coast to the top of the hill? Assume friction is negligible.IV. Three balls of equal mass are fired with equal speeds from the same height above the ground. Rank the speeds as they hit the ground.V. A block of mass 100 kg slides from rest down a frictionless incline. Find the speed at the bottom using:a. Energy methodsb. Newton’s laws force methodsOutline of Current Lecture Practice ProblemsI. Use energy methods to find the speed of the 2 kg block just before it hits the floor. Assume the system starts from rest and the table and pulley are frictionless.II. Can a Tension vs. Length graph for a spring have a positive slope?III. Describe the energy transfers as the mass oscillates up and down on a spring hanging from the ceiling. At what points in the motion are the different types of energy are a maximum? These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.IV. A spring gun shoots out a plastic ball at speed v. The spring is then compressed twice thedistance it was on the first shot.a. How does this affect the velocity?b. How does this affect the spring potential energy?Current LecturePractice ProblemsI. Use energy methods to find the speed of the 2 kg block just before it hits the floor. Assume the system starts from rest 1.5 m above the ground and the table and pulley are frictionless.a. (1/2)mv2 + mgy = (1/2)mv2 + mgyb. The initial velocity is 0 m/s and the final height is 0 m so:c. mgy = (1/2)mv2 d. (2kg)(9.8m/s)(1.5m) = (1/2)(5kg)v2e. V=3.43 m/sII. Can a Tension vs. Length graph for a spring have a positive slope?a. Yesb. A positive slope represents a spring being stretched and negative slope represents a spring being compressed.III. Describe the energy transfers as the mass oscillates up and down on a spring hanging from the ceiling. At what points in the motion are the different types of energy are a maximum? a. There are 3 types of energy:1. Kinetic Energyi. The kinetic energy is 0 m/s at the top and bottom of its oscillating, but is at a maximum in the middle.2. Gravitation Potential Energyi. Ug = mghii. The gravitation potential energy is a maximum only at the top because its height is greater.3. Spring Potential Energyi. Us = (1/2)kx23 kg2 kgii. The spring potential energy is only a maximum at the bottom because it is stretched more at the bottomIV. A spring gun shoots out a plastic ball at speed v. The spring is then compressed twice thedistance it was on the first shot.a. How does this affect the velocity?1. (1/2)mv2 = (1/2)kx22. Only looking at what is being affected: v, x:i. V2=x2ii. Doubling the distance would then:iii. V2=(2x)2iv. Simplifying:v. V=2xvi. Increase by a factor of 2b. How does this affect the spring potential engergy?1. (1/2)mv2 = (1/2)kx22. Only looking at what is being affected: Us, x:i. Us = x2ii. Doubling the distance would then:iii. Us =(2x)2iv. Simplifying:v. Us =4x2vi. Increase by a factor of