A 21.0 kg child descends a slide 3.4 m high and reaches the bottom with a speed of 2.0 m/s.
How much thermal energy due to friction was generated in this process?
Initial PE = Final KE + frictionallosses
mgh=1/2 m vf^2 + losses
solve for losses.
To calculate the thermal energy due to friction generated in this process, we need to use the following equation:
Thermal energy = force of friction × distance
The force of friction can be calculated using the equation:
Force of friction = mass × acceleration
First, let's calculate the force of friction using the formula above:
Force of friction = mass × acceleration
We know the mass of the child is 21.0 kg, and the child descends the slide with a speed of 2.0 m/s. To calculate acceleration, we can use the following kinematic equation:
vf^2 = vi^2 + 2aΔd
Where:
vf = final velocity (2.0 m/s in this case)
vi = initial velocity (0 m/s as the child starts from rest)
a = acceleration
Δd = distance (3.4 m in this case)
Let's rearrange the equation to solve for acceleration:
a = (vf^2 - vi^2) / (2Δd)
Substituting the given values:
a = (2.0^2 - 0^2) / (2 × 3.4)
a = 4 / 6.8
a = 0.588 m/s^2
Now we can calculate the force of friction:
Force of friction = mass × acceleration
Force of friction = 21.0 kg × 0.588 m/s^2
Force of friction = 12.348 N
Next, we need to calculate the distance traveled:
Distance = 3.4 m
Now we can calculate the thermal energy:
Thermal energy = force of friction × distance
Thermal energy = 12.348 N × 3.4 m
Thermal energy = 41.9652 J (rounded to four decimal places)
Therefore, the thermal energy due to friction generated in this process is approximately 41.9652 Joules.