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Ugo [173]
3 years ago
14

Which dog has the most kinetic energy?

Physics
2 answers:
Nadya [2.5K]3 years ago
5 0

A. A dog of mass 14kg running with the speed of 3m/s

Furkat [3]3 years ago
3 0

Nobody actually needs to know how much kinetic energy any of these dogs has.  

The purpose of this question is to help you discover whether you know <em>how </em>to calculate kinetic energy, and then to give you some practice at <em>doing it</em>.

You have to calculate the kinetic energy of each dog, and then review your results to see which dog has the most.

The whole secret behind working this problem is the formula for the kinetic energy of any object:

<em>Kinetic Energy = (1/2) · (mass) · (speed)²</em>

The little ² next to 'speed' means 'squared' or 'multiplied by itself'.

(speed)² means (speed · speed) .

So, in order to calculate how much kinetic energy an object has, here's what you do:

-- Take the object's speed.  Multiply the speed by itself.

-- Take that number and multiply it by the object's mass.

-- Take that number and throw away half of it.

So now here we go:

Dog A:  KE = (1/2) (14 kg) (2 m/s)² = 28 Joules

Dog B:  KE = (1/2) (14 kg) (3 m/s)² = 63 Joules

Dog C:  KE = (1/2) (11 kg) (5 m/s)² = 137.5 Joules

Dog D:  KE = (1/2) 12 kg) (4 m/s)² = 96 Joules

==> <em>Dog C</em> has more kinetic energy than any of the other 3 dogs.

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From the question we are told that

   The force exerted by the wind is  F_{sail} =  (330 ) \ N \ north

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Now Force is mathematically represented as

      F =  ma

Now the acceleration towards the north is mathematically represented as

      a_n  =  \frac{F_{sail}}{m_b}

substituting values

       a_n  =  \frac{330 }{260}

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Now the acceleration towards the east is mathematically represented as

       a_e = \frac{F_{keel}}{m_b }

substituting values

      a_e = \frac{210}{260}

      a_e =0.808 \ m/s^2

The resultant acceleration is  

      a_r =  \sqrt{a_e^2 + a_n^2}

substituting values

     a_r =  \sqrt{(0.808)^2 + (1.269)^2}

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The direction with reference from the north is evaluated as

Apply SOHCAHTOA

        tan \theta =  \frac{a_e}{a_n}

       \theta = tan ^{-1} [\frac{a_e}{a_n } ]

substituting values

     \theta = tan ^{-1} [\frac{0.808}{1.269 } ]

    \theta = tan ^{-1} [0.636 ]

   \theta =  32.5 6^o

     

   

       

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