Minimum Acceleration Calculation for Slab with Block on Top
What is the minimum magnitude of the slab's acceleration when a horizontal force of 50 N is applied to accelerate the slab?
Given data:
Horizontal force = 50 N
Mass of the slab = 10 kg
Block mass = 5 kg on top of the slab
Coeficient of friction is not known
What would be the minimum acceleration of the slab when the block might slip?
Answer:
When there is no slipping, the coefficient of friction is maximum. In this case, the acceleration of the slab would be:
aslab = F / (mslab + mblock)
aslab = 50 / (10 + 5)
aslab = 3.33 m/s2
When slipping occurs and the coefficient of friction is not known, the acceleration of the slab would be:
aslab = F / mslab
aslab = 50 / 5
aslab = 10 m/s2
When a horizontal force of 50 N is applied to a 10 kg slab that is initially stationary on a frictionless floor with a 5 kg block on top, two scenarios are considered based on the possibility of slipping between the slab and the block.
First, assuming there is no slipping, the maximum coefficient of friction allows for an acceleration of 3.33 m/s2. This calculation takes into account the combined mass of the slab and the block on top.
On the other hand, when slipping occurs, and the coefficient of friction is not known, the acceleration of the slab increases to 10 m/s2. This higher acceleration is a result of the reduced effective mass due to the slipping motion.
In conclusion, the minimum acceleration of the slab is determined by considering both scenarios with and without slipping, showcasing the influence of friction on the motion of the system.