A 20kg child slides down a long slide in a playground. She starts from rest at a height of 25m. When she is part way down the slide at a height of 10m, she is moving at 16m/s. Calculate the mechanical energy lost due to friction.
PEmax = mg*hmax - FE
PEmax = 20*9.8*25 - FE = (4900-FE) J.
KE + PE = 4900 - FE
0.5m*V^2 + mg*h = 4900-FE
10*16^2 + 196*10 = 4900-FE
2560 + 1960 = 4900-FE
4520 = 4900-FE
FE = 4900-4520 = 380 J. = Energy loss
due to friction.
To calculate the mechanical energy lost due to friction, we need to find the initial mechanical energy and the final mechanical energy of the child.
The mechanical energy of an object can be calculated using the formula:
Mechanical Energy = Potential Energy + Kinetic Energy
1. Determine the initial mechanical energy:
The initial potential energy of the child can be calculated using the formula:
Potential Energy = mass * gravity * height
where mass = 20kg, gravity = 9.8 m/s^2, and height = 25m.
So, the initial potential energy = 20kg * 9.8 m/s^2 * 25m
The initial kinetic energy of the child is zero because she starts from rest:
Initial Kinetic Energy = 0
Therefore, the initial mechanical energy = Potential Energy + Kinetic Energy
= (20kg * 9.8 m/s^2 * 25m) + 0
2. Determine the final mechanical energy:
The final potential energy can be calculated using the formula mentioned earlier:
Potential Energy = mass * gravity * height
where mass = 20kg, gravity = 9.8 m/s^2, and height = 10m.
So, the final potential energy = 20kg * 9.8 m/s^2 * 10m
The final kinetic energy can be calculated using the formula:
Kinetic Energy = 0.5 * mass * velocity^2
where mass = 20kg and velocity = 16m/s.
So, the final kinetic energy = 0.5 * 20kg * (16m/s)^2
Therefore, the final mechanical energy = Potential Energy + Kinetic Energy
= (20kg * 9.8 m/s^2 * 10m) + (0.5 * 20kg * (16m/s)^2)
3. Calculate the mechanical energy lost due to friction:
Mechanical Energy Lost = Initial Mechanical Energy - Final Mechanical Energy
Now, you can substitute the values and calculate the answer.