how do I convert force of gravity into horsepoweer?

Question

how much weight do I need pulled by gravity to obtain one horsepower

Answer 1

Note: The only answer above which gives a value for the mass uses the step 1HP = 250kg x 9.81m/s^2. This is an incorrect statement because the right-hand side of the equation is units of force kg m / s^2, and the left-hand side is units of horsepower = kg m^2 / m^3. Furthermore, the hinted at weight of 2452.5 Newtons would correspond to 2452.5/9.80 kg = 250 kg.

But the mass required is only = 15.6 kg, under a condition.

The condition is that we look at the power delivered in the first second of fall. When mass 15.6 kg starts to fall in gravity, in the first second of fall gravity delivers 750 Joules of energy to the mass (as kinetic energy), which makes 750 Watt in the first second = 1 horsepower HP, in the first second of fall.

As time continues, gravitational energy is converted into kinetic energy at a faster and faster rate. Hence the power increases in time. The formula is this:

P = m g^2 t

where the mass is dropped at time t = 0, and P is the power being drawn from gravity at any time t. This formula assumes no air friction or other friction, only gravitational force acts on the mass.

So if you want to wait a few seconds before measuring the power, you can observe 1 HP with a much smaller mass. So there is no definite answer to this problem.

Here is how to I get this mass:

As a mass falls through gravity energy is generated from the loss of graviational potential energy during the fall. (The object falls from a position of higher GPE to lower GPE). The energy generated goes into kinetic energy (and some could go into friction, against air, or pulleys, or a sliding surface, etc).

The power provided by gravity is the energy gained from gravity during the fall through distance h divided by the time it takes the mass to fall that distance.

Consider mass m falling by gravity through distance h in time t seconds. The energy generated is force x distance = mgh. The time for the fall is calculated by first writing the distance h

h = (average velocity) x (time of fall)
avg vel = (1/2)(final vel - initial vel) = (1/2)(g)(time of fall)
where g = acceleration due to gravity, 9.80 m/sec^2
h = (1/2) g t^2

So Power = (Energy gained in fall) / (time of fall) = mgh / t
P = m g (1/2) g t^2 / t = m g^2 t / 2
where Power is in Watts, mass is in kilograms, h is in meters, and g = 9.8 m/s^2.

Solve for mass:
m = 2 P / g^2 t

set time t = 1 second
m = 2 P / g^2 sec = 2*750 Watt / 9.8^2 m^2 sec^(-3)
m = 15.6 kg

Check units: W / m^2 sec^(-3) = kg m^2 s^(-3) / m^2 sec^(-3) = kg. Ok.

Another way to pose the problem is to ask what height must mass m fall through so that the energy received from gravitational potential energy divided by the time of fall = 750 Watts = 1 HP.

The answer is given by P = mgh/t, where t, the time for the fall, is calculated by first writing the distance h = (average velocity) x (time of fall) = (1/2) (v-final + v-initial) x time of fall = (1/2) x (gt - 0) x time = (1/2) g t^2, so t = sqrt(2 h /g).

P = m g h / sqrt(2 h /g) = m g^(3/2) h^(1/2) / sqrt(2)

h = 2 P^2 / ( m^2 g^3 )
so the required height decreases as mass m increases.

Again, there is no unique answer. You must choose h or m, then solve for the other. If you set P = 750 Watts, m=15.6 kg, then h = 4.91 m, the distance of fall in the first second.

Answer 2

Lifting 550 pounds the height of one foot in one second is one horsepower. Or if you obtain 750 watts from a horse you obstain also one Horsepower.Here you have energy conversion from one mechanical horsepower to an electrical horsepower. Or you could convert a Horse to Gravity power.So you could have 750 Newton meter per seconds of Gravity Power per horse.
So you have Gravity power in physics by conversion of energy into horse energy.

However ,in Relativity theory it is possible to convert energy into mass and mass into energy. So on that basis of the theory you can also convert energy into a horse which has mass. and you can convert a horse into energy.but the conversion takes time.

Answer 3

1kg(2.2lbs) x 9.81m/s = 9.81 N
1 HP = 550ft-lb/s
550lb/2.2lb = 250kg
Therefore 1HP = 250kg x 9.81m/s².
= 2,452.5 Newtons (weight) = 1 Horsepower.

(The above calculation is from my own interpretation of HP and Newtons. However, as 1lbf = 4.448N (conversion factor), then 550lbf = 550 x 4.448 = 2,446.4 Newtons...
....very close to the above).

(George S.... 550ft-lb/s means either 550lbs lifted 1 foot in 1 second or, 1 lb lifted 550 feet in 1 second. And as 550lbs = 250kg, I don't see where the problem is, as 250kg x gravity = Newtons.)

Answer 4

I don't know the answer, but to figure it out, you would formulate an equation that read like this:

mass (velocity/234)^3 = mass * velocity^2

mass would be x

velocity = 32 ft/sec^2 or 9.33 m/s^2 (gravitational pull)

solve for x

Answer 5

You cant. Only Chuck Norris can do that.