The amount of energy needed to power a 0.10-kW bulb for one minute would be just sufficient to lift a 1.0-kg object through a vertical distance of
To find the amount of energy needed to lift a 1.0-kg object through a vertical distance, we can use the formula for gravitational potential energy:
Potential Energy (PE) = m * g * h
where:
m = mass of the object (1.0 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = vertical distance (unknown)
Since we want to find the height (h) that corresponds to the amount of energy needed to power a 0.10-kW bulb for one minute, we need to convert the power to energy.
Power is the rate at which energy is consumed or produced. It is measured in watts (W), where 1 watt is equal to 1 joule per second (J/s).
Energy (E) = Power (P) * Time (t)
Given:
Power of the bulb (P) = 0.10 kW
Time (t) = 1 minute = 60 seconds
First, we need to convert the power from kilowatts to watts:
0.10 kW = 0.10 * 1000 W = 100 W
Now, we can find the energy consumed by the bulb:
E = P * t = 100 W * 60 s = 6000 J
Substituting this value into the equation for potential energy:
6000 J = 1.0 kg * 9.8 m/s^2 * h
Solving for h:
h = 6000 J / (1.0 kg * 9.8 m/s^2)
h ≈ 612.24 meters
Therefore, the vertical distance required to use the same amount of energy needed to power a 0.10-kW bulb for one minute would be approximately 612.24 meters.