Question

A student pushes a box with mass M. The student exerts a constant horizontal force Fpush on the table. At first, The box rolls on tiny rollers and the friction force Ff is negligible compared to F. As the box moves to the right, it eventually begins to slide over slick pavement, Where the magnitude of the friction force is non-negligible, but less than Fpush, then on normal pavement where the magnitude of the friction force is equal to the student's push, then finally on rough pavement where the magnitude of the friction force is greater than the student's push.

i. Given the scenario described, will the box accelerate? If so, in what direction? If not, why not? Explain.

ii. Draw a graph of the box's velocity vs time. SInce No values (numbers) for F or M have been provided, the axes will have arbitrary units, so you should focus on the qualitative freatures of the plot.

iii. Draw a graph of the box's acceleration vs Time.

Answer 1

(i)

Table: There is no frictional force hence lock will accelerate with acceleration a₁

Slick pavement: The frictional force is small. Block will accelerate with acceleration a₂. (a₂ < a₁)

Normal pavement: The firction force is equal to F_push. Acceleration a₃ of the block will be zero. It will move with constant velocity.

(ii)

(iii)

Rough pavement: Friction force is greater than F_push. Now the acceleration a₄ will be -ve. The block will decelerate and its velocity starts to decrease.

(ii)