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

ssm 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 Frame

A non-inertial reference frame is one that is accelerating, causing apparent forces to be observed by an observer within that frame. In scenarios like an accelerating elevator, the effective weight (and therefore the normal force) of an object changes, which in turn affects the magnitude of the frictional force acting on it.

Kinetic Friction

Kinetic friction is the resistive force that opposes the relative sliding motion between two surfaces in contact. It is calculated using the coefficient of kinetic friction multiplied by the normal force, and its understanding is essential for analyzing the motion of sliding objects.

Newton's Second Law

Newton's Second Law relates the net force acting on an object to its mass and acceleration. This concept is crucial in understanding how external forces, including friction and inertial effects in non-inertial frames such as accelerating elevators, influence an object's motion.

Normal Force

The normal force is the perpendicular force exerted by a surface that supports the weight of an object resting on it. It plays a vital role in frictional force calculations since the magnitude of the frictional force is directly proportional to this quantity.

Transcript

00:01 We begin this question by setting up our reference frame and then applying newton's second law to the box.

00:06 So i will choose my reference frame as follows.

00:10 Everything that is pointing up is positive and everything that is pointing to the right is positive.

00:17 So as a consequence, everything that is pointing to the left will be negative and everything that is pointing downwards is also negative.

00:24 Now we proceed to apply newton's second law to that box.

00:28 So, let me call this vertical axis the y axis and this horizontal axis the x axis.

00:35 So now let us apply newton's second law to the vertical axis to the box.

00:42 So the net force that is acting on the box on the vertical axis is equals to the mass of the box times its acceleration in the vertical axis.

00:54 In that axis, there are two forces acting on the box.

00:57 The normal force that is pointing to the positive direction and the weight force that points to the negative direction.

01:05 And this is equal to the mass of the box times the acceleration of that box.

01:11 Now, note the following.

01:13 Note the following.

01:14 We can calculate the normal force as the mass of the box times the vertical acceleration of the box plus the weight of the box.

01:26 Now, remember that the frictional force, force that acts on the box, the absolute value of that frictional force is given by the kinetic frictional coefficient times the normal force.

01:41 Therefore, the frictional force is equal to the kinetic frictional coefficient times the mass of the box times the vertical acceleration of that box plus the weight of this box.

01:55 Putting in some values that the problem gives us, the frictional force is in general equals to 0 .36 times 6, which is the mass of the box, times the vertical acceleration of the elevator, plus the weight of the box.

02:13 Now, for the weight, remember that the weight is given by the mass times the acceleration of gravity, and the acceleration of gravity is approximately 9 .8 meters per second squared...

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