A model train with a mass of #3 kg# is moving along a track at #16 (cm)/s#. If the curvature of the track changes from a radius of #12 cm# to #32 cm#, by how much must the centripetal force applied by the tracks change?
The change in centripetal force is
Centripetal force is what
The centripetal force fluctuation is
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To find the change in centripetal force, we can use the formula:
ΔF = m * Δv^2 / r
Where: ΔF = Change in centripetal force m = Mass of the train (3 kg) Δv = Change in velocity (final velocity - initial velocity) r = Radius of curvature (final radius - initial radius)
Calculating Δv: Initial velocity (v1) = 16 cm/s Final velocity (v2) = 16 cm/s (since speed is constant)
Δv = v2^2 - v1^2
Calculating Δv^2: Δv^2 = (v2^2 - v1^2)^2
Substitute the values into the formula and solve for ΔF:
ΔF = 3 * ((16^2 - 16^2)^2) / (32 - 12)
ΔF = 0
Therefore, the change in centripetal force applied by the tracks is 0.
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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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