A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #5 m#. If the train's kinetic energy changes from #9 j# to #45 j#, by how much will the centripetal force applied by the tracks change by?
The change in centripetal force is
The centripetal force is
The kinetic energy is
The variation of kinetic energy is
The variation of centripetal force is
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To find the change in centripetal force, we first need to calculate the initial and final velocities of the train using the kinetic energy formula:
Initial kinetic energy (KE1) = 9 J Final kinetic energy (KE2) = 45 J
KE1 = (1/2) * mass * initial velocity^2 9 = (1/2) * 3 * initial velocity^2 Initial velocity = √(9 * 2 / 3) = √6 m/s
KE2 = (1/2) * mass * final velocity^2 45 = (1/2) * 3 * final velocity^2 Final velocity = √(45 * 2 / 3) = √30 m/s
Now, we can use the centripetal force formula to find the initial and final centripetal forces:
Initial centripetal force (F1) = (mass * initial velocity^2) / radius F1 = (3 * (√6)^2) / 5 = (3 * 6) / 5 = 18/5 N
Final centripetal force (F2) = (mass * final velocity^2) / radius F2 = (3 * (√30)^2) / 5 = (3 * 30) / 5 = 90/5 N
The change in centripetal force is: ΔF = F2 - F1 ΔF = (90/5) - (18/5) = 72/5 N
So, the centripetal force applied by the tracks changes by 72/5 N.
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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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