A model train with a mass of #3 kg# is moving along a track at #12 (cm)/s#. If the curvature of the track changes from a radius of #4 cm# to #8 cm#, by how much must the centripetal force applied by the tracks change?
The change in centripetal force is
Centripetal force is what
The tracks' respective radii are
additionally
The centripetal force's variance is
What are the centripetal forces?
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The centripetal force required for a train moving along a curved track is given by the formula: ( F_c = \frac{mv^2}{r} ), where ( m ) is the mass of the train, ( v ) is the velocity of the train, and ( r ) is the radius of the curvature of the track.
Initially, the radius of curvature is ( r_1 = 4 ) cm, and the velocity of the train is ( v = 12 ) cm/s. Substituting these values into the formula, we can calculate the initial centripetal force ( F_{c1} ).
( F_{c1} = \frac{(3, \text{kg}) \times (12 , \text{cm/s})^2}{4 , \text{cm}} )
After the curvature changes, the new radius of curvature is ( r_2 = 8 ) cm. To find the new centripetal force ( F_{c2} ), we use the same formula but with the new radius of curvature.
( F_{c2} = \frac{(3, \text{kg}) \times (12 , \text{cm/s})^2}{8 , \text{cm}} )
Finally, we can find the change in centripetal force by subtracting the initial centripetal force from the new centripetal force:
( \Delta F_c = F_{c2} - F_{c1} )
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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 satellite in a circular orbit 1250 kilometers above Earth makes one complete revolution every 110 minutes. What is its linear speed? (Assume that Earth is a sphere of radius 6400 kilometers.)

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