## Frictional Force on a Box in an Elevator### Problem StatementA 6.44-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.271. Determine the kinetic frictional force that acts on the box when the elevator is:- (a) Stationary- (b) Accelerating upward with an acceleration whose magnitude is 1.37 m/s²- (c) Accelerating downward with an acceleration whose magnitude is 1.37 m/s²### Solution ApproachLet's start by recalling that the force of kinetic friction (\(f_k\)) is given by the equation:\[ f_k = \mu_k \cdot N \]where:- \( \mu_k \) is the coefficient of kinetic friction.- \( N \) is the normal force exerted by the surface on the object.When the elevator is moving, the normal force \(N\) can be affected by the additional pseudo-forces due to elevator's acceleration.1. **Stationary Elevator:** The normal force \(N\) is simply the weight of the box: \[ N = m \cdot g \] where \( m \) is the mass of the box and \( g \) is the acceleration due to gravity. 2. **Elevator Accelerating Upward:** The normal force \(N\) increases because of the additional force due to the elevator accelerating upward. \[ N = m \cdot (g + a) \] where \( a \) is the upward acceleration of the elevator. 3. **Elevator Accelerating Downward:** The normal force \(N\) decreases due to the opposing force from the downward acceleration. \[ N = m \cdot (g - a) \] where \( a \) is the downward acceleration of the elevator.### Numerical Solutions(a) For a stationary elevator:- Enter the correct number and units in the corresponding fields for part (a).(b) For an elevator accelerating upward:- Enter the correct number and units in the corresponding fields for part (b).(c) For an elevator accelerating downward:- Enter the correct number and units in the corresponding fields for part (c).Once all values are calculated, submit your answers.### Additional Resources- eTextbook and Media are

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A 6.44-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.271. Determine the kinetic frictional force that acts on the box when the elevator is (a) stationary, (b) accelerating upward with a acceleration whose magnitude is 1.37 m/s², and (c) accelerating downward with an acceleration whose magnitude is 1.37 m/s². (a) Number (b) Number (c) Number M i i Units N Units N Units N

A 6.44-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.271. Determine the kinetic frictional force that acts on the box when the elevator is (a) stationary, (b) accelerating upward with a acceleration whose magnitude is 1.37 m/s², and (c) accelerating downward with an acceleration whose magnitude is 1.37 m/s². (a) Number (b) Number (c) Number M i i Units N Units N Units N

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter6: Applications Of Newton’s Laws Of Motion

Section: Chapter Questions

Problem 44PQ

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