When an 81.6 kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 2.14E+3 J. By how much does the potential energy of a 18.6 kg child increase when the child climbs a normal staircase to the second floor?

I know PE=mgh but I keep getting the wrong answer. please help. Thanks!

You should be good.

PE = mgh
so h = PE/mg = 2.14e3/(9.8*81.6) = 2.67
for child
PE = 1836*9.8*2.67 = 487.8 J

To calculate the gravitational potential energy (PE) of an object, you can use the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.

In this case, we are given the change in potential energy for the adult (2.14E+3 J) and the mass of the adult (81.6 kg). We need to find the change in potential energy for the child.

Let's assume the height of the staircase is the same for both the spiral staircase and the normal staircase. Therefore, the change in potential energy is directly proportional to the mass of the object.

First, we need to find the proportionality constant. We can set up a ratio using the given mass and change in potential energy for the adult:

(Change in PE of adult) / (Mass of adult) = (Change in PE of child) / (Mass of child)

2.14E+3 J / 81.6 kg = (Change in PE of child) / 18.6 kg

Now, solve for the change in potential energy of the child:

Change in PE of child = (2.14E+3 J / 81.6 kg) * 18.6 kg

Change in PE of child = 48.54 J

Therefore, the potential energy of the 18.6 kg child increases by 48.54 J when the child climbs a normal staircase to the second floor.