Final answer:
The correct option is (b) μs = 0.267, P > F. This is because, on an incline, the pulling force P must overcome both the force of static friction F and a portion of the gravitational force to prevent slipping and maintain a steady speed.
Step-by-step explanation:
The student is asking about the minimum coefficient of static friction required to roll a drum up a 15° incline without slipping, and the corresponding values of the force applied to the drum (P) and the friction force (F). To determine the coefficient of static friction (μs), we must consider the forces acting on the drum parallel and perpendicular to the incline.
The force needed to roll the drum up the incline at a steady speed implies that the net force in the direction of the incline must be zero. This condition means that the force of friction must balance out the component of the weight of the drum acting down the slope. The friction force is the force that prevents the drum from slipping and is equal to the product of the coefficient of static friction and the normal force (N), which is perpendicular to the incline.
From the information provided in various related concepts, we know that static friction responds to the applied forces and can take on values from zero up to its maximum, which is μsN. When the drum is being rolled up at a steady speed, the frictional force is at its maximum, which implies that F = μsN. Since there is no acceleration, the pulling force (P) must equal the frictional force (F).
Given the options provided and understanding the physics behind rolling without slipping on an incline, we can deduce that the correct answer is option (b) μs = 0.267, P > F, as the pulling force must overcome not only friction but also the component of gravitational force acting down the slope to maintain steady speed.