21.7 kg child descends a slide 3.5 m high and reaches the bottom with a speed of 2.2 m/s How many joules of thermal energy are created due to friction as a kid slides down a slide?
692.6
Well, well, well, looks like we have a little daredevil on our hands! The joules of thermal energy created due to friction as the child slides down the slide can be calculated using the work-energy principle. We have the mass of the child (21.7 kg) and the height of the slide (3.5 m), so we can determine the change in potential energy. Since we know the final speed of the child (2.2 m/s), we can also determine the change in kinetic energy. The difference between the initial potential energy and the final kinetic energy would give us the work done by friction, which we could convert to thermal energy. Unfortunately, without the coefficient of friction or any other relevant information, it's impossible to calculate the exact amount of joules of thermal energy created. So, my friend, it seems we'll have to leave this one unanswered. But hey, at least we can appreciate the awesome ride the child had, right? Wheeee! 🎢
To calculate the amount of thermal energy created due to friction as the child slides down the slide, we first need to determine the change in potential energy and kinetic energy.
1. Let's calculate the potential energy (PE) at the top of the slide using the formula:
PE = mass × gravitational acceleration × height
Given:
mass (m) = 21.7 kg
gravitational acceleration (g) = 9.8 m/s²
height (h) = 3.5 m
PE = 21.7 kg × 9.8 m/s² × 3.5 m
PE = 752.47 J
2. Next, we need to calculate the kinetic energy (KE) at the bottom of the slide using the formula:
KE = 0.5 × mass × velocity²
Given:
mass (m) = 21.7 kg
velocity (v) = 2.2 m/s
KE = 0.5 × 21.7 kg × (2.2 m/s)²
KE = 54.098 J
3. Finally, we can calculate the thermal energy (TE) created due to friction by subtracting the initial potential energy from the final kinetic energy:
TE = KE - PE
TE = 54.098 J - 752.47 J
TE ≈ -698.37 J
The negative sign indicates that thermal energy is dissipated or lost due to friction. Therefore, approximately 698.37 joules of thermal energy are created due to friction as the child slides down the slide.
Subtract the kinetic energy at the bottom from the potential energy loss. The remainder becomes frictional heat.
Potential energy loss:
M g H = 21.7*9.81*3.5 = 745.1 J
Kinetic energy at bottom of slide:
= (1/2) M v^2 = 52.5 J