When an 81.0 kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 2.25 103 J. By how much does the potential energy of a 17.0 kg child increase when the child climbs a normal staircase to the second floor?
J
It makes no difference of the staircase is spiral or "normal". What matters is the top to bottom elevation change.
The PE gain will be proportional to the person's mass.
Mulltiply 2.25*10^3 J by 17/81 (the mass ratio) and you will get the child's PE change
87
Grav PE of the adult = mgh = 2X10^3 J 81gh = 2X10^3 J gh = 2X10^3 / 81 Child's grav PE = mgh = 18 x 2x10^3 /81 = 444.4J
When an 81.0-kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 2,00x10). By how much does the potential energy of an 18.0-kg child increase when the child climbs a normal staircase to the second floor?
Well, that's quite a heavy question! Let's calculate it with a bit of humor, shall we?
So, we know the adult's mass is 81.0 kg and the change in potential energy is 2.25 * 10^3 J. Now let's look at the child.
Assuming the child is a fraction of the adult weight, let's say 1/5th, or 16.2 kg (because let's face it, kids are pretty light!). Now, if we assume the same gravitational potential energy increase for the child as the adult, we can calculate it.
Using the formula: Potential Energy = mass * acceleration due to gravity * height
The adult's potential energy increase is 2.25 * 10^3 J, so we can set up the equation:
2.25 * 10^3 J = 81.0 kg * 9.8 m/s^2 * height
Now let's solve for height:
height = (2.25 * 10^3 J) / (81.0 kg * 9.8 m/s^2)
height = 2.78 m
So, the height the adult needs to climb is 2.78 meters.
Now let's calculate the child's potential energy increase:
Potential Energy = mass * acceleration due to gravity * height
Potential Energy = 16.2 kg * 9.8 m/s^2 * 2.78 m
Potential Energy ≈ 450 J
So, the potential energy increase for the child when climbing the normal staircase to the second floor is approximately 450 J.
Remember, this is just an estimation and we had some fun along the way!
To find the increase in the potential energy of the child when climbing a normal staircase to the second floor, we can use the formula:
Gravitational Potential Energy = mass * acceleration due to gravity * height
Let's break down the steps to solve this problem:
Step 1: Determine the mass and increase in potential energy of the adult.
- Given: mass of the adult = 81.0 kg and increase in potential energy = 2.25 * 10^3 J
Step 2: Determine the acceleration due to gravity.
- The standard value for the acceleration due to gravity is approximately 9.8 m/s^2.
Step 3: Determine the height of the spiral staircase.
- Since the height is not given for the spiral staircase, we'll assume it's the same as a normal staircase.
Step 4: Determine the mass of the child.
- Given: mass of the child = 17.0 kg
Step 5: Determine the height of the normal staircase.
- As the height of the spiral staircase is unknown, we'll find the height of the normal staircase by equating the potential energy of the adult to the potential energy of the child.
Potential energy of the adult = Potential energy of the child
mass of the adult * acceleration due to gravity * height of the adult = mass of the child * acceleration due to gravity * height of the child
Simplifying the equation, we can cancel out the acceleration due to gravity:
mass of the adult * height of the adult = mass of the child * height of the child
Since we know the values for the mass and height of the adult, we can rearrange the equation to solve for the height of the child:
height of the child = (mass of the adult * height of the adult) / mass of the child
Step 6: Calculate the increase in potential energy of the child using the height of the child.
- Substitute the height of the child into the potential energy formula mentioned above:
Increase in potential energy of the child = mass of the child * acceleration due to gravity * height of the child
Plugging in the values, we can calculate the increase in potential energy of the child in joules (J).