(b) Find the change in potential energy and change in kinetic energy as the part

Question

(b) Find the change in potential energy and change in kinetic energy as the particle moves from x = 1.00 m to x = 3.20 m. (Use A, B, and x as appropriate.)

The ball launcher in a pinball machine has a spring that has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If the spring is initially compressed 5.50 cm, find the launching speed of a 100 g ball after the plunger is released and fully extended. Friction and the mass of the plunger are negligible.
m/s

Explanation / Answer

F = -Ax + Bx^5 N
Potential Energy = - Integral F.dx
U = - Integral (-Ax + Bx^5).dx
U = Ax^2/ 2 - Bx^6/ 6

Uintial = A*1.0^2/ 2 - B(1.0)^6/ 6
Uintial = A/2 - B/6

Ufinal = A*3.2^2/ 2 - B*3.2^6/ 6
Ufinal = A * 10.24/2 - B*1074/6

U = Ufinal - UInitial
U =   A * 10.24/2 - B*1074/6 - A/2 + B/6
U = 4.62 A - 178.8 B
Change in Potential Emergy, U = 4.62 A - 178.8 B J

Change in Kinetic Emergy KE = 178.8 B - 4.62 A J

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