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For the situation described: (1) Simplify the work-energy equation to its proper form. (2) Then identify the letter of the corresponding work-energy bar chart.A sledder (or a roller coaster car) begins from rest on the top of a hill (initial state) and slides to the bottom of the hill (final state). Friction and air resistance influence the motion.

Question

For the situation described: (1) Simplify the work-energy equation to its proper form. (2) Then identify the letter of the corresponding work-energy bar chart.A sledder (or a roller coaster car) begins from rest on the top of a hill (initial state) and slides to the bottom of the hill (final state). Friction and air resistance influence the motion.

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Solution

  1. The work-energy equation is given by:

W = ΔKE + ΔPE

where W is the work done, ΔKE is the change in kinetic energy, and ΔPE is the change in potential energy.

In this case, the sledder starts from rest at the top of the hill and ends at the bottom. This means that the initial kinetic energy (KE_initial) is zero and the final potential energy (PE_final) is also zero. Therefore, the equation simplifies to:

W = KE_final - PE_initial

  1. The work-energy bar chart for this situation would be as follows:
  • The initial bar (at the top of the hill) would have a high potential energy (PE_initial) and no kinetic energy (KE_initial = 0).
  • The final bar (at the bottom of the hill) would have a high kinetic energy (KE_final) and no potential energy (PE_final = 0).
  • The work done (W) would be negative, indicating that energy has been lost due to friction and air resistance.

So, the corresponding letter for the work-energy bar chart would be 'D'.

This problem has been solved

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