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?

Answer 1

The change in centripetal force is #=0.54N#

Centripetal force is what

#vecF_C=(mv^2)/r*vecr#
The mass is of the train #m=3kg#
The velocity of the train is #v=0.12ms^-1#

The tracks' respective radii are

#r_1=0.04m#

additionally

#r_2=0.08m#

The centripetal force's variance is

#DeltaF=F_2-F_1#

What are the centripetal forces?

#||F_1||=3*0.12^2/0.04=1.08N#
#||F_2||=3*0.12^2/0.08=0.54N#
#DeltaF=F_1-F_2=1.08-0.54=0.54N#
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Answer 2

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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Answer from HIX Tutor

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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