The figure shows the potential energy of a 350g particle as it moves along the x

Question

The figure shows the potential energy of a 350g particle as it moves along the x-axis. Suppose the particle's mechanical energy is 12J.

http://session.masteringphysics.com/problemAsset/1070475/3/10.P59.jpg

A - Where are the particles turning points? (x=)
B - What is the particles speed at x = 2m?
C - What is the particles maximum speed?
D - At what position(s) does this occur?
E - Write a description of the motion of the particle as it moves from the left turning point to the right turning point.
F - Suppose the particle's energy is lowered to 4.0 . Describe the possible motions.

I need these answers for hw, but also need to be able to figure it out on the test. Thanks in advance

Explanation / Answer

The mass of the particle m = 350g = 0.35kg
The mechanical potential energy E = 12J

(a) From the given graph the turning point are at distance
1m and 7m
at these point the potential energy changes with respect to the mechanical energy

(b) The potential energy at x = 2m is U = 8J
then the kinetic energy K = 12 - 8 = 4J
k = 1/2 mv^2
then speed
v = (2K/m) = (2*4/0.35)

                   = 4.78 m/s

(c) The maximum speed is given by

        the total energy E = K = 1/2 mvmax^2

therefore the maximum speed

         vmax = (2K/m) = (2*12/0.35)

                                 = 8.3m/s

(d) the maximum speed we get when the potential becomes zero

so it happened at x = 4m   U = 0J

(e)
The initial potential energy is completed converted to kinetic energy and there after it regains its potential after the next turning point.

(f)

If the energy E = 4J then, at, x = 2m it has U = 8J of potential energy which is impossible.

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