Question

There is a bell at the top of a tower with a mass of 20kg. If it had 8829 J of gravitational potential energy, estimate how many floors the tower has.

Answer 1

10 floors

Step-by-step explanation:

We are told that a bell of mass 20 kg is atop a tower and has 8829 J of gravitational energy. The question asks us to estimate the number of floors the tower has.

To do this, we must first calculate how high above the ground the bell is. We can do that using the formula for gravitational potential energy:

`\boxed{g.p.e = mgh}`,

where:

• g.p.e = gravitational potential energy (8829 J)

• m = mass of object (20 kg)

• g = acceleration due to gravity (approximately 10 m/s²)

• h = height of object above ground (? m).

Using the above information and formula, we can solve for h:

g.p.e =
`20 * 10 * h = 8829`

⇒
`200 h = 8829`

⇒
`h = (8829)/(200)`

⇒
`h = \bf 44.145 \ m`

Therefore the bell is 44.145 m above the ground, which means that the height of the tower is also 44.145 m.

One floor of a building can be estimated to be around 4.3 m, therefore the number of floors the tower has is:

44.145 ÷ 4.3

≈ 10

Therefore there are 10 floors in the tower.