A 6.00-kg box is sliding across the horizontal floor of an...

A 6.00-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.360. 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 $1.20 \mathrm{m} / \mathrm{s}^{2}$, and $(\mathrm{c})$ accelerating downward with an acceleration whose magnitude is $1.20 \mathrm{m} / \mathrm{s}^{2}$.

Key Concepts

Non-inertial Reference Frames

A non-inertial reference frame is one that is accelerating, meaning that objects within it experience apparent forces, such as an increased or decreased effective gravitational force. Recognizing and analyzing these additional forces is essential to correctly apply Newton’s laws of motion in environments like an accelerating elevator.

Kinetic Friction

Kinetic friction is the resistive force that opposes the relative motion between two sliding surfaces. It is calculated as the product of the coefficient of kinetic friction and the normal force (f_k = ?_k * N). Understanding this concept allows one to determine how frictional forces change in different scenarios, especially when the normal force is altered by external accelerations.

Normal Force in Accelerating Frames

The normal force is typically the force exerted by a surface perpendicular to an object in contact with it. In an accelerating frame, such as an elevator moving upward or downward, the normal force differs from the gravitational force alone because the acceleration effectively increases or decreases the force experienced by the object. This concept is crucial when evaluating friction in non-stationary systems.

Newton’s Second Law

Newton’s Second Law relates the net force acting on an object to its mass and acceleration (F = ma). In problems involving accelerating systems like an elevator, it is used to analyze how additional acceleration affects the forces on an object, particularly when calculating the normal force acting on the object.

Transcript

00:01 So in this problem, you have a box that weighs 6 kilograms that's moving inside of an elevator.

00:07 We're given the coefficient of kinetic friction of the floor has 0 .36, and we want to calculate the friction of force for three different scenarios.

00:18 The first being if the elevator isn't moving, the second, if the elevator is moving up, and finally for the third part, if the elevator is moving down.

00:27 So to solve this problem, we first need to know the equation for the frictional force.

00:32 And in this case, there's movement, so it's the kinetic friction that we're calculating, and that's equal to the coefficient of kinetic friction times the normal force.

00:43 So since we're given the coefficient of kinetic friction, what we need to solve for is a normal force.

00:51 And to do that, we need to draw a free body diagram of the box so that we can see the forces involved in the object so that we can find the normal force and then plug it into our equation for the friction of force.

01:06 So for part a, the elevator isn't moving, so there's zero acceleration.

01:14 Again, the equation for kinetic friction is the coefficient of kinetic friction times the normal force.

01:21 So drawing a free body diagram of the box, we have the weight of the box pushing down and the floor is going to exert a force on the object in the opposite direction of the weight called the normal force.

01:38 Let's say moving up is positive.

01:41 So when we use newton's second law, which is some of the forces f equals a normal force is pointing up that's positive minus the weight equals mass time acceleration but again there's no movement.

01:57 Movement in the elevator.

01:59 So acceleration is zero, so this equals zero.

02:02 So now we can solve for the normal force.

02:06 We have f of n equals w the weight, and the equation for weight is mass times gravity.

02:14 So now we can plug that in to our equation for the frictional force.

02:19 So we have the coefficient of kinetic friction 0 .36 times the mass of the object, 6 times gravity, 9 .8.

02:33 So we get for part a, the frictional force is 21 .17 newtons...

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