Final answer:
The coefficient of kinetic friction between the calculus book and the floor is calculated using the work-energy principle and is found to be approximately 0.88.
Step-by-step explanation:
To find the coefficient of kinetic friction between the calculus book and the floor, we need to consider the forces acting on the book along the horizontal surface and apply Newton's second law of motion. The forces acting on the book include the applied force from the broom, 24 N, and the force of kinetic friction opposing the book's motion. The book starts from rest, so the initial velocity u is 0 m/s. After being pushed the speed v is 1.2 m/s over a distance d of 0.75 m. Using the work-energy principle, the work done by the applied force and the frictional force equals the change in kinetic energy of the book.
The change in kinetic energy (KE) can be calculated by:
KE = (1/2)mv2 - (1/2)mu2
With the mass m of the book being 2.5 kg, the change in kinetic energy is:
KE = (1/2)(2.5 kg)(1.2 m/s)2 - (1/2)(2.5 kg)(0 m/s)2 = 1.8 J
The work done by the applied force is:
Work = Force × Distance = 24 N × 0.75 m = 18 J
The work done against frictional force is whatever work is left over:
Workfriction = Workapplied - KE = 18 J - 1.8 J = 16.2 J
The force of friction is hence the work of friction divided by the distance:
Ffriction = Workfriction / d = 16.2 J / 0.75 m = 21.6 N
The coefficient of kinetic friction μ is defined as the force of friction divided by the normal force (which for horizontal surfaces is the weight of the object). Thus,
μ = Ffriction / (mg) = 21.6 N / (2.5 kg × 9.81 m/s2) = 0.88
Therefore, the coefficient of kinetic friction between the book and the floor is approximately 0.88.