4 - The Figure below shows the potential energy for a particle that can move onl

Question

4 - The Figure below shows the potential energy for a particle that can move only along the x- axis under the influence of a conservative force. Here x is given in meters and U in joules, and we are considering the motion of a 1 kg object. We begin by releasing the object from the position x=2 m with a kinetic energy of 2 J. Where along the x-axis does the particle experience a force of the largest magnitude? What is the magnitude of this force? Over what range of x does the particle move? Where along the x-axis does the particle not experience a force (F-0) as it moves? What is its speed when it is at x-6m? What is the maximum speed the particle reaches while moving in this region? a) b) c) d) e)

Explanation / Answer

a) from x = 7 m to x = 8 m

because, F = -dU/dx

= -slope of U-x curve

from x = 7 m to x = 8m, slop is highest

b) from x = 0 to x = 8 m

c) from x = 6 m to x = 7 m

because, In this region F = -dU/dx = 0

d) total energy = U + KE

4 = 1 + KE

==> KE = 3 J

we know, KE = (1/2)*m*v^2

==> v = sqrt(2*KE/m)

= sqrt(2*3/1)

= 2.45 m/s

e) KEmax = 4 J

we know, KE_max = (1/2)*m*v_max^2

==> v_max = sqrt(2*KE_max/m)

= sqrt(2*4/1)

= 2.83 m/s

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