Question

Over 630 m in height, the Burj Khalifa is the world's tallest skyscraper. What is the change ∆Uᵣₐᵥ in the gravitational potential energy of a $20 gold coin (33.5 g) when it is carried from ground level to a floor of the Burj Khalifa that is 550 m high? Neglect any slight variations in the acceleration due to gravity.

∆Uᵣₐᵥ=____.

Answer 1

The change in gravitational potential energy (ΔUᵣᵉᵖ) of a $20 gold coin (33.5 g) carried to a height of 550 m in the Burj Khalifa is 181.45725 joules, calculated using the formula for gravitational potential energy.

Step-by-step explanation:

To calculate the change in gravitational potential energy (ΔUᵣᵉᵖ) of a $20 gold coin (weighing 33.5 g) when it is carried to a height of 550 m in the Burj Khalifa, we use the formula ΔUᵣᵉᵖ = mgh, where 'm' is the mass in kilograms, 'g' is the acceleration due to gravity (9.81 m/s²), and 'h' is the change in height.

Firstly, convert the mass of the gold coin from grams to kilograms by dividing by 1000: m = 33.5 g / 1000 = 0.0335 kg.

Using the known values:

• mass (m) = 0.0335 kg
• acceleration due to gravity (g) = 9.81 m/s²
• change in height (h) = 550 m

Now, plug the values into the formula:

ΔUᵣᵉᵖ = (0.0335 kg)(9.81 m/s²)(550 m) = 181.45725 J (joules)

Therefore, the change in gravitational potential energy of the gold coin is 181.45725 joules when carried to 550 m high inside the Burj Khalifa.