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A 500 kg horse can provide a steady output power of 750 W (that is, 1 horsepower) when pulling a load; how about a 38 kg sled dog? Data shows that a 38 kg dog can pull a sled that requires a pulling force of 60 N at a steady 2.2 m/s.

1. What is the specific power for the dog and the horse?
2. What is the minimum number of dogs needed to provide the same power as one horse?

Respuesta :

boffeemadrid

Answer:

1.5 W/kg, 3.47 W/kg

6 dogs

Explanation:

[tex]m_d[/tex] = Mass of dog = 38 kg

[tex]v_d[/tex] = Pulling speed of dog = 2.2 m/s

[tex]F_d[/tex] = Force on sled = 60 N

[tex]P_h[/tex] = Power of horse = 750 W

[tex]m_h[/tex] = Mass of horse = 500 kg

Power is given by

[tex]P_d=F_dv_d\\\Rightarrow P_d=60\times 2.2\\\Rightarrow P_d=132\ W[/tex]

Specific power is given by

[tex]P_{sh}=\frac{P_h}{m_h}\\\Rightarrow P_{sh}=\frac{750}{500}\\\Rightarrow P_{sh}=1.5\ W/kg[/tex]

Specific power of horse is 1.5 W/kg

[tex]P_{sd}=\frac{P_d}{m_d}\\\Rightarrow P_{sd}=\frac{132}{38}\\\Rightarrow P_{sh}=3.47\ W/kg[/tex]

Specific power of dog is 3.47 W/kg

We have the relation

[tex]nP_d=P_h\\\Rightarrow n=\frac{P_h}{P_d}\\\Rightarrow n=\frac{750}{132}=5.68\ dogs\approx 6\ dogs[/tex]

The number of dogs is 6

onyebuchinnaji

(1) The specific power of the horse is 1.5 W/kg and the specific power of the dog is 3.5 W/kg.

(2) The minimum number of dogs needed to provide the same power as one horse is 6 dogs.

Specific power of the horse

The specific power of the horse is calculated as follows;

Cp = P/m

Cp = 750/500

Cp = 1.5 W/kg

Specific power of the horse

The specific power of the dog is calculated as follows;

Cp = P/m

Cp = (Fv)/m
Cp = (60 x 2.2)/38

Cp = 3.5 W/kg

Minimum number of dogs required to provide same power as horse

n(Fv) = 750

n = (750)/(60 x 2.2)

n = 6 dogs

Learn more about instantaneous power here: https://brainly.com/question/8893970

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