what is the answer for these 3 questions ? A particle of mass m = 1.0 kg moves a

Question

what is the answer for these 3 questions ?

A particle of mass m = 1.0 kg moves along the x axis without friction through a region in which its potential energy U(x) varies as shown in the Figure. when the particle is at x = 7.0 m, its velocity is 2.550 m/s. What is the magnitude of the force that acts on the particle at this position? The particle will move back and forth in a limited region along the x axis. What is the smallest value of x which the particle ever has? A proposed space station consists of a large circular disk with the living quarters on the rim of circular ring, 50.0m in diameter. What speed should the rim of the ring have, so that the occupants feet that they have the same weight as they do on Earth?

Explanation / Answer

parta)

F = -dU/dx = (-14.5+4.5) / (10-2) = 1.25 N

partb) to find U at 7

slope at 7

(U + 4.5)/(-14.5+4.5) = (7-2)/(10-2)

U = -10.75

total enrgy at 7 = KE + PE = (0.5*1*2.5*2.5)-10.75 = -7.625

if total energy = Umax

(-7.625+4.5) / (-14.5+4.5) = (x-2)/(10-2)

x = 4.5 m <--------------answer

a = v^2/r = g

v = sqrt(gr)

v = sqrt(9.8*25)

v = 15.65 m/s

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