At what height is an object that weighs 490 N if it gravitational potential energy is 4900 N-m?
Divide the PE gain (4900 N-m) by the weight.
To find the height at which an object weighs 490 N and has a gravitational potential energy of 4900 N-m, we can use the formula for gravitational potential energy:
Gravitational Potential Energy (GPE) = mass x gravity x height
In this case, the weight (490 N) can be equated to the gravitational potential energy:
Weight = GPE
We can rearrange the formula to find the height:
Height = GPE / (mass x gravity)
Given that the weight is equal to the gravitational potential energy, the mass is given by the weight divided by gravity:
mass = weight / gravity
Now we can substitute the values into the formula:
mass = 490 N / 9.8 m/s² = 50 kg (rounded to two decimal places)
Height = 4900 N-m / (50 kg x 9.8 m/s²) = 10 m
Therefore, the object is at a height of 10 meters.
To find the height of an object when its gravitational potential energy is known, we can use the formula for gravitational potential energy:
Gravitational Potential Energy = mgh
Where:
m is the mass of the object
g is the acceleration due to gravity (9.8 m/s^2 on Earth)
h is the height of the object
In this case, we are given that the gravitational potential energy is 4900 N-m and the weight (force due to gravity) of the object is 490 N. Since weight is equal to mass multiplied by the acceleration due to gravity (W = mg), we can find the mass of the object:
m = W / g
m = 490 N / 9.8 m/s^2
m = 50 kg
Now we can rearrange the formula for gravitational potential energy to solve for the height:
h = Gravitational Potential Energy / (mg)
h = 4900 N-m / (50 kg × 9.8 m/s^2)
By plugging in the values:
h = 10 m
Therefore, the object is at a height of 10 meters.