Final answer:
To determine the child's mass, the work-energy principle is applied, and the formula W = mgd is used, yielding a mass of approximately 34.01 kilograms when lifting the child against gravity with a work of 250 J over a distance of 0.75 meters.
Step-by-step explanation:
To find the mass of the child lifted by the father, we can make use of the work-energy principle, which states that work done on an object is equal to the change in its kinetic energy. However, in this scenario, we are lifting the child at a constant speed, implying that all the work done by the father is used to overcome the gravitational pull.
The formula for work done (W) is given by:
Since the force exerted by the father is to lift the child against gravity, the force is equal to the weight (mg) of the child, where m is mass and g is the acceleration due to gravity (9.8 m/s²). We are given that the work done (W) is 250 J, and the distance (d) is 0.75 meters.
Using the formula for work:
W = mgd
Substituting the given values:
250 J = m × 9.8 m/s² × 0.75 m
Dividing both sides by (9.8 m/s² × 0.75 m):
m = 250 J / (9.8 m/s² × 0.75 m)
Calculating this gives us the mass:
m ≈ 34.01 kg
Thus, the mass of the child is approximately 34.01 kilograms.