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I was wondering if you can calculate horsepower given this information:

Distance traveled: 180 Meters

Weight of object: 1582 KG

Speed at the 180 meters: 93 KPH

Thanks,

Steven

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- Thread starter Cadbury204
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- #1

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I was wondering if you can calculate horsepower given this information:

Distance traveled: 180 Meters

Weight of object: 1582 KG

Speed at the 180 meters: 93 KPH

Thanks,

Steven

- #2

russ_watters

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No, you can't. You need to know the force.

- #3

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- #4

rcgldr

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Define:

a = acceleration

v = velocity

x = distance

c = constant

f = force

m = mass

p = power

Assuming constant power, lossless continuously variable transmission:

a = c / v

f = m a = m c / v

p = f v = (m c / v) v = m c

a = dv/dt = c/v

v dv = c dt

1/2 v^{2} = c t

v = (2 c)^{1/2} t^{1/2}

a = c / ((2 c)^{1/2} t^{1/2})

v = (2 c)^{1/2} t^{1/2}

x = 2/3 (2 c)^{1/2} t^{3/2}

x = 180 m

v = 93 kph = 25.833333 m / s

using equation for v:

25.833333 = (2 c)^{1/2} t^{1/2}

t = (25.833333)^{2} / (2 c)

t = 333.68055 / c

using equation for x

180 = 2/3 (2 c)^{1/2} (333.68055 / c)^{3/2}

180 = 2/3 (2)^{1/2} (333.68055)^{3/2} (c / c^{3})^{1/2}

180 = 2/3 (2)^{1/2} (333.68055)^{3/2} / c

c = 2/3 (2)^{1/2} (333.68055)^{3/2} / 180

c = 31.926226

p = m c = 1582 * 31.926226 = 50507.29 watts = 67.7314 hp

check

t = 333.68055 / c = 10.451613

v = (2 c)^{1/2} t^{1/2}

v = (2 * 31.926226)^{1/2} 10.451613^{1/2}

v = 25.833333

x = 2/3 (2 c)^{1/2} t^{3/2}

x = 2/3 (2 * 31.926226)^{1/2} 10.451613^{3/2}

x = 180.00000

I've never encountered this type of problem before, so it was a discovery process for me, perhaps someone could check my math?

a = acceleration

v = velocity

x = distance

c = constant

f = force

m = mass

p = power

Assuming constant power, lossless continuously variable transmission:

a = c / v

f = m a = m c / v

p = f v = (m c / v) v = m c

a = dv/dt = c/v

v dv = c dt

1/2 v

v = (2 c)

a = c / ((2 c)

v = (2 c)

x = 2/3 (2 c)

x = 180 m

v = 93 kph = 25.833333 m / s

using equation for v:

25.833333 = (2 c)

t = (25.833333)

t = 333.68055 / c

using equation for x

180 = 2/3 (2 c)

180 = 2/3 (2)

180 = 2/3 (2)

c = 2/3 (2)

c = 31.926226

p = m c = 1582 * 31.926226 = 50507.29 watts = 67.7314 hp

check

t = 333.68055 / c = 10.451613

v = (2 c)

v = (2 * 31.926226)

v = 25.833333

x = 2/3 (2 c)

x = 2/3 (2 * 31.926226)

x = 180.00000

I've never encountered this type of problem before, so it was a discovery process for me, perhaps someone could check my math?

Last edited:

- #5

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Use the equation of motion v^2 = u^2 + 2as and rearrange for a. Assume initial speed is 0, s=180m and v=25.8m/s

This gives an acceleration of 1.849m/s^2

Now F=ma with m=1582kg gives a force of 2925N

Work done = force x distance = 2925 x 180 = 526500J

Power = Work done/time = 526500/13.95 = 37742W (Time here is calculated using v = u +at)

Since 1 horsepower = 745.7 watts

Power = 37742/745.7 = 50.6 Horsepower.

The only incorrect assumption I can see is that you're not starting from rest, but I think the question suggests this.

- #6

rcgldr

Homework Helper

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This formula assumes constant acceleration and constant force, so the power is increasing linearly with speed. My assumption was that the original post was asking for the constant power required to accelerate to speed for a given distance, similar to an estimate of power given time to distance or speed achieve in a distance, in a drag race for a given weight vehicle. The constant power is also the minimum power. Constant acceleration requires double the power at the end of the run, or force x speed => 101.2 horse power.v = u +at

Last edited:

- #7

Pythagorean

Gold Member

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- #8

rcgldr

Homework Helper

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Not that creative on my part, do a web search for "horsepower estimator" and you'll find a lot of hits that based on 1/4 mile speed or time and weight, which is the approach I took, determine power given speed and distance from a standing start and weight of vehicle, although I simplified this assuming unlimited traction, and constant power. Examples of power estimators:Well as long as we're all being creative here

http://www.dragtimes.com/horsepower-et-trap-speed-calculator.php

http://www.dsm.org/tools/calchp.htm

- #9

Pythagorean

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Not that creative on my part, do a web search for "horsepower estimator" and you'll find a lot of hits that based on 1/4 mile speed or time and weight, which is the approach I took, determine power given speed and distance from a standing start and weight of vehicle, although I simplified this assuming unlimited traction, and constant power. Examples of power estimators:

http://www.dragtimes.com/horsepower-et-trap-speed-calculator.php

http://www.dsm.org/tools/calchp.htm

Well, I didn't mean it as an insult!

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