Final answer:
The work done to climb up the staircase is approximately 156.8 Joules.
Step-by-step explanation:
The work done to lift an object can be calculated by multiplying the force applied by the distance over which it is applied. In this case, the force required to lift the child up the staircase is equal to the weight of the child, which can be calculated as mass multiplied by acceleration due to gravity (W = m * g). The distance over which the force is applied is the height of the staircase. Plugging in the values, we have:
W = m * g * h
W = 20 kg * 9.8 m/s^2 * 0.8 m
W = 156.8 J
Therefore, the work done to climb up the staircase is approximately 156.8 Joules.