Pushing a Block A hand pushes a 3 kg block along a table from point A to point C as shown in Fi

Step 1: The motion of the block as it moves from point A to point C can be described as follows:

Pushing a Block A hand pushes a 3 kg block along a table...

Pushing a Block A hand pushes a $3 \mathrm{~kg}$ block along a table from point $A$ to point $C$ as shown in Fig. $9-39 .$ The table has been prepared so that the left half of the table (from $A$ to $B$ ) is frictionless. The right half (from $B$ to $C$ ) has a nonzero coefficient of friction equal to $\mu^{k i n}$. The hand pushes the block from $A$ to $C$ using a constant force of $5 \mathrm{~N}$. The block starts off at rest at point $A$ and comes to a stop when it reaches point $C .$ The distance from $A$ to $B$ is $\frac{1}{2}$ meter and the distance from $B$ to $C$ is also $\frac{1}{2}$ meter. (a) Describe in words the motion of the block as it moves from $\bar{A}$ to $C$. (b) Draw a free-body diagram for the block when it is at point $P$. (c) What is the direction of the acceleration of the block at point $P ?$ If it is 0 ,state that explicitly. Explain your reasoning. (d) Does the magnitude of the acceleration increase, decrease, or remain the same as the block moves from $B$ to $C$ ? Explain your reasoning. (e) What is the net work done on the object as it moves from $A$ to $B$ ? From $B$ to $C$ ? (f) Calculate the coefficient of friction $\mu^{\text {kin }}$.

Transcript

00:01 Hello, for this problem you're considering a block being pushed.

00:05 I'm going to draw a picture of at least how i understand the problem.

00:10 So we have point a, point b, and point c, where from a to b is frictionless, and from b to c there is friction.

00:21 So i'll draw that as a rough surface.

00:24 Our block starts at a and is pushed with a force.

00:31 And eventually comes to rest at point c.

00:36 And lastly, this distance here is x.

00:40 And some of the information that we're given is that the mass of the block is by, or sorry, three kilograms, not five.

00:52 The magnitude of the force is five newtons.

00:56 And x is one half of a meter.

01:01 Okay, so for part a, you're asked to describe the acceleration of the block, or i guess describe the motion of the block as it moves from a to c.

01:18 And so i think that it's helpful to think about acceleration there.

01:21 So it's going to be accelerating the entire time, but as it moves from a to b, because there is a net force being applied, it will accelerate and speed up.

01:42 And the net force has to be in the negative direction, causing a negative acceleration, and causing the block to slow down as it moves right from b to c.

02:04 Okay.

02:05 For part b, we are told to draw a free body diagram at point p.

02:12 Now, i don't actually know where point p is because i can't see the figure, but i can draw a free body diagram.

02:21 For both sides.

02:23 So if point p is between a and b, then the only forces acting on our block will be the gravitational force with a magnitude mg directed downward, the normal force with a magnitude of n directed upwards, which will be in balance, and a net force f to the right due to the applied force of the hand pushing the block.

02:53 If instead point p is somewhere between b and c, then we need to start with these three forces, but there will also be a friction force.

03:09 And specifically, because the block is slowing down, we know that the friction force must have a larger magnitude than the applied force.

03:20 For part c, you're asked what the direction of the acceleration is.

03:28 At point p, again, i don't know where point p is, but if it's between a and b, because we know the object is speeding up and it's moving to the right, then acceleration has to be to the right or positive.

03:43 If it's between b and c, because we know the block is slowing down, but it's moving to the right.

03:49 Acceleration has to be opposite.

03:50 It's motion to cause it to slow down.

03:53 So acceleration must be to the left or negative if it, if point p is between b and c.

04:05 Excuse me.

04:07 I guess if point p is right at location b, i'll point out that acceleration will be zero because it has to obviously flip from being positive to negative and that you would have the applied force and the friction force, but they would be in balance, but that would be just for a split second at point b as the motion is changing.

04:34 Anyway, for part d, you are asked if the magnitude of the acceleration increases, decreases, or remains the same as the block is moving from b to c.

04:52 So i wasn't sure if it meant the acceleration from the first section of the motion to the second section of the motion or the acceleration as the block itself moves from b to c.

05:09 As the block is moving between b and c, if we're excluding points b and points c, because we know that we just talked about how the acceleration for a split second there would go to zero.

05:22 As it switched from positive to negative at b, and then for c, it's going to go to zero when the object comes to a stop.

05:33 And i guess this also depends on how you're thinking about it.

05:36 So i'm thinking about it as the object is continually moving, so its acceleration is not going to just suddenly switch if you were to plot the acceleration.

05:49 So i'm just going to do that here versus position...

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