A 22.1 kg child descends a slide 3.4 m high and reaches the bottom with a speed of 2.4 m/s. How much thermal energy due to friction was generated in this process? I'm sure where to even start this problem
To find the amount of thermal energy generated due to friction, we need to determine the initial potential energy at the top of the slide, and then subtract the final kinetic energy at the bottom of the slide to account for the loss.
Here's how you can approach this problem:
1. Determine the potential energy at the top of the slide:
The potential energy (PE) of an object is given by the formula PE = mgh, where:
- m is the mass of the object (22.1 kg),
- g is the acceleration due to gravity (9.8 m/s²), and
- h is the height of the slide (3.4 m).
Therefore, the potential energy at the top of the slide is:
PE = (22.1 kg) * (9.8 m/s²) * (3.4 m)
2. Determine the kinetic energy at the bottom of the slide:
The kinetic energy (KE) of an object is given by the formula KE = (1/2)mv², where:
- m is the mass of the object (22.1 kg), and
- v is the velocity of the object at the bottom of the slide (2.4 m/s).
Therefore, the kinetic energy at the bottom of the slide is:
KE = (1/2) * (22.1 kg) * (2.4 m/s)²
3. Calculate the thermal energy due to friction:
The thermal energy due to friction can be found by subtracting the final kinetic energy from the initial potential energy:
Thermal energy = PE - KE
Now, you can substitute the values in the appropriate equations and find the thermal energy due to friction.