1) A force parallel to the x -axis acts on a particle moving along the x -axis.

Question

1) A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces a potential energy U(x) given by U(x)=? x4where ?=1.10J/m4 .

What is the force when the particle is at position x = -0.790m ?

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2) A 350kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop shown in the accompanying figure.(Figure 1)

part a) How fast is this roller coaster moving at point B?

part b) How hard does it press against the track at point B?

1) A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces a potential energy U(x) given by U(x)=? x4where ?=1.10J/m4 . What is the force when the particle is at position x = -0.790m ? ........................................................... 2) A 350kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop shown in the accompanying figure.(Figure 1) part a) How fast is this roller coaster moving at point B? part b) How hard does it press against the track at point B?

Explanation / Answer

U = a x4

Force = -dU/dx = - 4a x3= -4 * 1.10 * -0.7903

=   2.17 N (in the positive x direction)

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v = sqrt ( 2 g h )

h = 25 - 12 m = 13 m

v = sqrt( 2 * 9.8 * 13 ) = 15.962 m /s at point B

N + mg = mv2 / r

N = mv2 / r - mg

N = m ( v2 / r - g )

r = 12 /2 = 6 m

N = 350 ( 15.9622 / 6 - 9.8 )

N = 11433.3 N = 11.4 kN

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