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.