Final answer:
To accelerate an 8 kg mass at 5 m/s² with 14 N of friction, a total force of 54 N is required, which is the sum of the frictional force and the force needed for the desired acceleration.
Step-by-step explanation:
To calculate the force required to accelerate an 8 kg mass at 5 m/s² in the presence of 14 N of friction, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m × a). However, we must take into account the frictional force that opposes the motion.
The force needed to overcome friction is already given as 14 N. Besides this force, we must apply additional force to achieve the desired acceleration. Therefore, the total force (F_total) that needs to be applied is the sum of the force required to overcome friction and the force needed to accelerate the object:
F_total = F_friction + F_acceleration
Where the force required for acceleration (F_acceleration) can be calculated using the formula:
F_acceleration = m × a
Substituting the given values:
F_acceleration = 8 kg × 5 m/s² = 40 N
Now, we add the force needed to overcome friction:
F_total = 14 N + 40 N = 54 N
Therefore, a force of 54 N is required to accelerate the mass at the given rate, taking the frictional force into account.