Final answer:
Physics principles such as work, energy, and friction are applied to calculate the speed of a baby being pulled across the floor after a certain distance. The work by the pulling force and the work against friction must be considered, leading to the use of the work-energy theorem to find the final speed.
Step-by-step explanation:
The subject of the question is Physics, specifically involving concepts of energy, work, and friction relevant to high school coursework. The problem requires the use of work and energy principles to determine the speed of Susan's baby brother Paul after he is pulled for a certain distance.
To solve for Paul's speed after being pulled 2.60 m, one must consider the work done by Susan and the work done against friction, calculate the net work done on Paul, and then use the work-energy principle to find his final speed. Additionally, remember to include the component of the tension force that actually does work in the direction of motion.
Work done by Susan (Ws) is calculated by multiplying the tension in the rope (T) by the distance (d) and the cosine of the angle (θ), which accounts for the vertical component of the tension that doesn't contribute to the work:
Ws = T × d × cos(θ)
Work done against friction (Wf) is calculated using the coefficient of friction (μ), the normal force (N), which is the weight of Paul minus the vertical component of the tension, and the distance (d):
Wf = -μ × (N) × d
The net work done on Paul (Wnet) is the sum of Ws and Wf:
Wnet = Ws + Wf
Finally, use the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy (Kf - Ki, where Ki is the initial kinetic energy and is 0 since Paul starts from rest):
Wnet = ½ m × v2 - 0
Solving for v yields Paul's final speed: