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 car) is moving with a high speed at the bottom of a hill (initial state) and gradually coasts to a stop as it moves up towards the top (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 car) is moving with a high speed at the bottom of a hill (initial state) and gradually coasts to a stop as it moves up towards the top (final state). Friction and air resistance influence the motion.
Solution
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The work-energy equation is given by:
W = ΔKE + ΔPE
Where: W is the work done, ΔKE is the change in kinetic energy, ΔPE is the change in potential energy.
In this case, the sledder starts with a high speed at the bottom of the hill and gradually comes to a stop at the top. This means that the kinetic energy at the start (KE_initial) is high and at the end (KE_final) is zero. Therefore, the change in kinetic energy (ΔKE) is KE_final - KE_initial = 0 - KE_initial = - KE_initial.
The sledder also moves from the bottom of the hill to the top, which means it gains potential energy. Therefore, the potential energy at the start (PE_initial) is low (we can consider it as zero for simplicity) and at the end (PE_final) is high. Therefore, the change in potential energy (ΔPE) is PE_final - PE_initial = PE_final - 0 = PE_final.
The work done (W) is the work done against friction and air resistance. Since these forces are opposing the motion of the sledder, the work done is negative.
Therefore, the work-energy equation simplifies to:
-W = - KE_initial + PE_final
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The corresponding work-energy bar chart would be:
a) Initial state: High bar for KE, low (or zero) bar for PE, no bar for W. b) Final state: No bar for KE, high bar for PE, negative bar for W (indicating work done against the motion).
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