Problem: shows the potential energy of a 500 g particle as it moves along the x-axis. Suppose the particles mechanical energy is 12 J.Where are the particles turning points?What is the particles speed when it is at x = 4.0 m?What is the particles maximum speed?At what position or positions does this occur?Suppose the particle’s energy is lowered to 4.0 J. Can the particle ever be at x = 2.0 m? Suppose the particle’s energy is lowered to 4.0 J. Can the particle ever be at x = 4.0 m?

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Problem Details

The figure shows the potential energy of a particle moving along the x-axis. The energy is measured in joules. There is a linear vertical potential barrier at x equal to 1 meter. For x from 1 to 4 meters the energy linearly increases from 2 to 8 joules. For x from 4 to 6 meters the energy linearly decreases to 0. For x from 6 to 8 meters the energy linearly increases to 12 joules and keeps growing for further distances. shows the potential energy of a 500 g particle as it moves along the x-axis. Suppose the particles mechanical energy is 12 J.

Where are the particles turning points?

What is the particles speed when it is at x = 4.0 m?

What is the particles maximum speed?

At what position or positions does this occur?

Suppose the particle’s energy is lowered to 4.0 J. Can the particle ever be at x = 2.0 m?

Suppose the particle’s energy is lowered to 4.0 J. Can the particle ever be at x = 4.0 m?

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