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A 1.0 kg toy car is released at the top of a frictionless track on the left and rolls off of the track from its right side ramp. The car starts at a height of 0.80 m, goes through a 0.50 m diameter loop, and exits the ramp at a height of

a) 0.25 m.
b) 0.80 m
c) 0.50 m
d) 0.25 m
What is the change in the car's gravitational potential energy from A to B? Round answer to two significant digits.

User Achu
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Final answer:

The change in the toy car's gravitational potential energy is calculated using the formula PE = mgh for both the initial and final heights, and then finding the difference. The final answer depends on the final height the car reaches at point B, which was given as options a, b, and c in the question.

Step-by-step explanation:

To calculate the change in the toy car's gravitational potential energy from point A to point B, we use the potential energy formula, PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (9.81 m/s²), and h is the height above the reference point. Initially, the toy car is at 0.80 m and moves to a new height, which could be 0.25 m, 0.80 m, or 0.50 m as per the given options. We need to compare the initial and final gravitational potential energy to find the change (ΔPE).

If, for example, option (a) were correct, the final height would be 0.25 m, so the change in potential energy from 0.80 m to 0.25 m would be ΔPE = PE_final - PE_initial = mgh_final - mgh_initial. Plugging in the numbers ΔPE = (1 kg)(9.81 m/s²)(0.25 m) - (1 kg)(9.81 m/s²)(0.80 m) = 2.4525 J - 7.848 J = -5.3955 J. We usually round this to two significant digits, resulting in ΔPE ≈ -5.4 J, indicating a decrease in potential energy as the car descends.

The same steps would be taken if evaluating options (b) and (c) with their corresponding final heights, to find the changes in potential energy for those scenarios.

User Parag Diwan
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