PHSX 211 10th Edition Lecture 22 Outline of Last 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 – 2kIV. 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?Outline of Current Lecture Practice ProblemsI. If you have a force F(x) = 3x2 + 2, find the work done by F as a particle goes from x=0 m to x=2 m.II. The force in the previous problem acts on a particle of mass 4 kg. The particle’s speed at x = o m is 1.5 m/s. What is the particle’s speed at x = 2m?III. A particle moves in a vertical plane along a closed path, starting at A and eventually returning to its starting point. How much work is done on the particle by gravity? Explain.IV. If the force on a particle at some point in space is zero, must its potential energy also be zero at that point?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.V. If the potential energy of a particle at some point in a space is zero, must the force on it also be zero at that point? VI. How do we find the Force acting on an object if given a Potential vs Distance graph?Current LecturePractice ProblemsI. If you have a force F(x) = 3x2 + 2, find the work done by F as a particle goes from x=0 m to x=2 m.a.∫xixfFd (x)b.∫02(3 x 2+2)c.x3+2 xd. ((2)3+2(2)e. W = 12 JII. The force in the previous problem acts on a particle of mass 4 kg. The particle’s speed at x = o m is 1.5 m/s. What is the particle’s speed at x = 2m?a. W = 12 J = ΔKE = (1/5)mvi2 – (1/2)mvf2b. 12 = (1/5)(4)(1.5)2 – (1/2)(4)vf2c. Vf = 2.9 m/sIII. A particle moves in a vertical plane along a closed path, starting at A and eventually returning to its starting point. How much work is done on the particle by gravity? Explain.a. Gravity is a conservative force and thus does not depend on the path taken by the particle. W = F * d, and the total displacement is zero, which means the work done by gravity is also zero.IV. If the force on a particle at some point in space is zero, must its potential energy also be zero at that point?a. No. For example, a particle moving at a nonzero height vertically at constant velocity it has no acceleration, thus the force is zero, but it still has potential energy because it has a nonzero height with gravity acting on it.V. If the potential energy of a particle at some point in a space is zero, must the force on it also be zero at that point? a. No. For example, a particle moving at height zero and is accelerating has a potential energy of zero but still has a nonzero force acting on it.VI. How do we find the Force acting on an object if given a Potential Energy vs Distance graph?a.F=−(dudx)b.U=∫Fd (x)c. According to these equations the force at a certain distance x, would be equivalent to the negative of the slope of the Potential Energy vs Distance at that distance