A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #3 m#. If the train's kinetic energy changes from #8 j# to #48 j#, by how much will the centripetal force applied by the tracks change by?
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To find the change in centripetal force applied by the tracks, use the relationship between kinetic energy and centripetal force.
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Calculate the initial and final centripetal forces: Initial centripetal force = initial kinetic energy / (radius of the circular track) Final centripetal force = final kinetic energy / (radius of the circular track)
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Find the difference between the final and initial centripetal forces.
Given:
- Mass of the train (m) = 4 kg
- Radius of the circular track (r) = 3 m
- Initial kinetic energy (KE_initial) = 8 J
- Final kinetic energy (KE_final) = 48 J
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Initial centripetal force = 8 J / 3 m = 2.67 N Final centripetal force = 48 J / 3 m = 16 N
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Change in centripetal force = Final centripetal force - Initial centripetal force = 16 N - 2.67 N ≈ 13.33 N
So, the centripetal force applied by the tracks will change by approximately 13.33 Newtons.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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- A model train with a mass of #3 kg# is moving along a track at #8 (cm)/s#. If the curvature of the track changes from a radius of #4 cm# to #18 cm#, by how much must the centripetal force applied by the tracks change?
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