To determine the total force necessary to accelerate the system, we need to consider both the applied force and the force of friction acting against the motion.
First, let's calculate the force of friction (F_friction) using the equation:
F_friction = coefficient of friction * normal force
The normal force (F_normal) is the force exerted by the surface perpendicular to the direction of motion and is equal to the weight of the system in this case. The weight (F_weight) is given by:
F_weight = mass * acceleration due to gravity
Given that the mass of the system is 30 lb and the acceleration due to gravity is approximately 32.2 f/s², we can calculate the weight:
F_weight = 30 lb * 32.2 f/s²
Next, we can calculate the force of friction:
F_friction = 0.25 * F_weight
Now, we can calculate the total force (F_total) required to accelerate the system:
F_total = mass * acceleration + F_friction
Given that the acceleration is 15 f/s², we can substitute the values into the equation:
F_total = 30 lb * 15 f/s² + 0.25 * F_weight
Now we have all the information needed to compute the total force. Let's calculate it:
F_weight = 30 lb * 32.2 f/s² = 966 lb·f F_friction = 0.25 * 966 lb·f = 241.5 lb·f F_total = 30 lb * 15 f/s² + 241.5 lb·f = 724.5 lb·f
Therefore, the total force necessary to accelerate the system at 15 f/s² on a rough surface with a coefficient of friction of 0.25 is 724.5 pound-force (lb·f).