A carton of mass is placed on a motorised conveyor belt moving horizontally toward…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A carton of mass

12\,\text{kg}

is placed on a motorised conveyor belt moving horizontally toward the right. Besides the belt’s steady driving force

P

, the carton experiences an opposing air drag of

10\,\text{N}

. The coefficient of kinetic friction between the carton and the belt surface is

0.30

. Take

g = 9.8\,\text{m/s}^2

. (a) Derive an expression, in terms of

P

, for the horizontal acceleration of the carton while it is being driven to the right. (b) The carton must accelerate at

2.0\,\text{m/s}^2

toward the right. Calculate the value of

P

that should be set on the belt to meet this requirement. (c) If the belt is instead adjusted so that

P = 90\,\text{N}

and the carton starts from rest, determine the distance travelled by the carton in the first

4.0\,\text{s}