PHSX 211 10th Edition Lecture 21 Outline of Last 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? 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?Outline of Current Lecture Practice ProblemsI. A particle with the potential energy in an energy vs position graph is moving to the right at x=0 m with total energy E.a. At what value or values of x is the particles speed a maximum?b. At what value or values of x is the particle’s speed a minimum?c. At what value or values of x is the potential energy a maximum?d. Does this particle have a turning point in the range of x covered by the graph?II. For each pair of vectors, is the sign the dot product of the two vectors positive, negative,or zero?a. Two vectors that create an acute angle?b. Two vectors that create an obtuse angle?c. Two vectors that create a 90 degree angle?d. Two vectors that create a 180 degree angle?III. What is the angle between the vectors a and b?a. A = 3i – 2j + 4kb. B = -I + 5j – 2kThese 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. Force of 5 N being applied at a 30 degree angle up from the horizontal positive x-axis causes a 2kg crate to move 3 m across a frictionless surface, starting from rest. What is the final velocity of the crate?Current LecturePractice ProblemsI. A particle with the potential energy in an energy vs position graph is moving to the right at x=0 m with total energy E.a. At what value or values of x is the particles speed a maximum?i. Maximum speed at minimum points on the graphb. At what value or values of x is the particle’s speed a minimum?i. Minimum speed at maximum points on the graphc. At what value or values of x is the potential energy a maximum?i. Maximum potential energy at maximum points on the graphd. Does this particle have a turning point in the range of x covered by the graph?i. The particle will have a turning point if the potential energy is total energy or if the potential energy is 0.II. For each pair of vectors, is the sign the dot product of the two vectors positive, negative,or zero?a. Two vectors that create an acute angle?i.a ∙ b=‖a‖‖b‖cosθii.0 ≤θ ≤ 90 ;cosθ=negative numberb. Two vectors that create an obtuse angle?i.a ∙ b=‖a‖‖b‖cosθii.9 0 ≤θ ≤ 18 0 ; cosθ= positivenumberc. Two vectors that create a 90 degree angle?i.a ∙ b=‖a‖‖b‖cosθii.0 ≤θ ≤ 90 ;cosθ=negative numberd. Two vectors that create a 180 degree angle?i.a ∙ b=‖a‖‖b‖cosθii.9 0 ≤θ ≤ 18 0 ; cosθ= positivenumberIII. What is the angle between the vectors a and b?a. A = 3i – 2j + 4kb. B = -I + 5j – 2kc.a ∙ b=‖a‖‖b‖cosθd. Plugging in values into that equation we get that θ = 135 degreesIV. Force of 5 N being applied at a 30 degree angle up from the horizontal positive x-axis causes a 2kg crate to move 3 m across a frictionless surface, starting from rest. What is the final velocity of the crate?a. W=F*db. W= (5cos(30)) * (3)c. W = 13 N*m or Jd. W = ΔKE = KE final – KE initiale. W = 13 J, KE initial = 0f. 13 J = KE final = (1/2)mv2g. 13 J = (1/2)(2kg)v2h. V = 3.6