The figure showsthe force Fx exerted on a particle that moves along the x-axis. Draw a graph of the particle's potential energy as a function of position xfrom x=0m to x=1.1m . Let U be zero at x=0m .
We know P.E. u is given by
sorry, i forgot the minus sign before the integral. Lets include that in F(x)
where u(0)=0 (given)
∴
where for x<0.5, F(x)=4x and for x>0.5 F(x)=-4x+4
So, for x<=0.5, u=-2x2
for x>=0.5, u=[-2x2]x=0.5+[2x2-4x]xx=0.5=-0.5+2x2-4x-0.5+2
=2x2-4x+2
Now plot u (both eqns are parabolas) The plot will be continuous at x=0.5
How do I approach these questions?
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Learning Goal: To be able to interpret potential energy diagrams
and predict the corresponding motion of a particle. Potential
energy diagrams for a particle are useful in predicting the motion
of that particle. These diagrams allow one to determine the
direction of the force acting on the particle at any point, the
points of stable and unstable equilibrium, the particle's kinetic
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The figure below shows a plot of potential energy U
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involved.) In the graphs, the potential energies are
U1 = 15 J, U2 = 30 J, and
U3 = 40 J.
The figure below shows a plot of potential energy U versus position x of a 1.04 kg particle that can travel only along an x axis. (Nonconservative forces are...
The figure shows a plot of potential energy U versus
position x of a 0.280 kg particle that can travel only
along an x axis under the influence of a conservative
force. The graph has these values: UA
= 9.00 J, UC = 20.0 J and
UD = 24.0 J. The particle is released
at the point where U forms a “potential hill” of “height”
UB = 12.0 J, with kinetic energy 5.00
J. What is the speed of the...
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