A model train, with a mass of #3# #kg#, is moving on a circular track with a radius of #3# #m#. If the train's kinetic energy changes from #18# #J# to #0# #J#, by how much will the centripetal force applied by the tracks change by?
The centripetal force is given by
Thus, the centripetal force is as follows:
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The change in kinetic energy can be calculated using the formula ΔKE = KE_final - KE_initial. ΔKE = 0 J - 18 J = -18 J. The centripetal force can be calculated using the formula F_c = (mv^2)/r, where m is the mass, v is the velocity, and r is the radius. Initial velocity can be calculated using the kinetic energy formula KE = 0.5 * m * v^2 rearranged to v = √(2 * KE / m) = √(2 * 18 J / 3 kg) = √12 m/s. Initial centripetal force can be calculated as F_c_initial = (3 kg * (√12 m/s)^2) / 3 m = 4 N. Final centripetal force can be calculated as F_c_final = (3 kg * 0 m/s^2) / 3 m = 0 N. The change in centripetal force is the difference between the initial and final centripetal forces: ΔF_c = F_c_final - F_c_initial = 0 N - 4 N = -4 N. Therefore, the centripetal force applied by the tracks will change by -4 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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