How Long Does It Take for a Box to Move Without Slipping on a Conveyor Belt?

AI Thread Summary
To determine how long it takes for a box to move without slipping on a conveyor belt moving at 2 m/s with a coefficient of friction of 0.4, the problem simplifies to analyzing the forces acting on the box. Initially, the box experiences kinetic friction as it is dropped onto the belt, which accelerates it sideways. The frictional force can be calculated using the equation F(friction) = N(normal reaction) x coefficient of friction. By applying Newton's laws, one can derive the motion equation for the box until it matches the belt's speed. Ultimately, the solution involves calculating the time required for the box to reach this speed without slipping.
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Homework Statement



a box is dropped onto a covoyer belt moving at 2 m\sec .if the coefficient of friction between the box &the belt is 0.4 ,how long before the box moves without slipping ?


Homework Equations


F(friction)=N(normal reaction) X coefficient of friction


The Attempt at a Solution



i have no ideas about solving the problem , :(
thnx for help
 
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Assume the box is slipping as it hits the belt, and doesn't bounce. Like, it's dropped from a very low height, almost touching the belt. So that simplifies the problem to where you just start out with the belt pushing the box's mass to the side via kinetic friction. What does the box do due to this sideways force? Write an equation for the motion of the box in this first part of its motion.
 

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