You are conducting an experiment in which a metal bar of...

You are conducting an experiment in which a metal bar of length 6.00 cm and mass 0.200 kg slides without friction on two parallel metal rails ($\textbf{Fig. P29.67}$). A resistor with resistance $R =$ 0.800 $\Omega$ is connected across one end of the rails so that the bar, rails, and resistor form a complete conducting path. The resistances of the rails and of the bar are much less than $R$ and can be ignored. The entire apparatus is in a uniform magnetic field $\overrightarrow{B}$ that is directed into the plane of the figure. You give the bar an initial velocity $v =$ 20.0 cm/s to the right and then release it, so that the only force on the bar then is the force exerted by the magnetic field. Using high-speed photography, you measure the magnitude of the acceleration of the bar as a function of its speed. Your results are given in the table: (a) Plot the data as $a$ graph of a versus $v$. Explain why the data points plotted this way lie close to a straight line, and determine the slope of the best-fit straight line for the data. (b) Use your graph from part (a) to calculate the magnitude $B$ of the magnetic field. (c) While the bar is moving, which end of the resistor, $a$ or $b$, is at higher potential? (d) How many seconds does it take the speed of the bar to decrease from 20.0 cm/s to 10.0 cm/s?

You are conducting an experiment in which a metal bar of length 6.00 cm and mass 0.200 kg slides without friction on two parallel metal rails ($\textbf{Fig. P29.67}$). A resistor with resistance $R =$ 0.800 $\Omega$ is connected across one end of the rails so that the bar, rails, and resistor form a complete conducting path. The resistances of the rails and of the bar are much less than $R$ and can be ignored. The entire apparatus is in a uniform magnetic field $\overrightarrow{B}$ that is directed into the plane of the figure. You give the bar an initial velocity $v =$ 20.0 cm/s to the right and then release it, so that the only force on the bar then is the force exerted by the magnetic field. Using high-speed photography, you measure the magnitude of the acceleration of the bar as a function of its speed. Your results are given in the table:

(a) Plot the data as $a$ graph of a versus $v$. Explain why the data points plotted this way lie close to a straight line, and determine the slope of the best-fit straight line for the data. (b) Use your graph from part (a) to calculate the magnitude $B$ of the magnetic field. (c) While the bar is moving, which end of the resistor, $a$ or $b$, is at higher potential? (d) How many seconds does it take the speed of the bar to decrease from 20.0 cm/s to 10.0 cm/s?

Transcript

00:03 Okay, so in this problem, we have an experimental setup here.

00:07 It has a resistor connected to some bars with a metal bar freely moved to complete the circuit.

00:13 It's a 6 centimeters long.

00:16 And it's moving on a speed v equals 20 centimeters per second.

00:22 Here's a resistant r, where r is 0 .8 oms.

00:28 The mass of our rod is 0 .2 kilograms.

00:33 And we put this whole thing in a magnetic field that is into the page of the strength.

00:42 We don't know.

00:45 Okay.

00:47 So they give us this chart here, this table of a's and v's.

00:55 So for a's we have 6 .2, 4 .9, 4 .3, 3 .1, and 2 .10, 12, 14, 6 .2, 4 .3, 3 .1, and 2 .10, 12, 14.

01:12 Okay, so it wants us to plot these.

01:15 So let's draw up a plot here and we want to plot as a versus v.

01:20 So a versus v.

01:22 I'm going to make mine pretty big u .s.

01:26 Here.

01:29 Do these by fives and these by twos.

01:37 So now let's find our first one.

01:39 Our first one is at 8.

01:42 8 and 2 .5.

01:46 10 and 3 .1.

01:49 12 and 3 .7, 14 and 4 .3, 16 and 4 .9, and 20 and 6 .2.

02:06 So we look like we have a pretty linear relationship here.

02:10 So for part a, we want to plot it, and then we want to find what the average slope is here.

02:20 So the average slope we can do as the total rise overrun.

02:25 And this is given as 3 .7, that's the max a minus the min a over 12, which is the max v minus the min v.

02:35 And we see that this is 0 .308.

02:39 So that's our slope, which means we have a relationship that looks like, a equals 0 .308 times v.

02:48 This kind of looks like it with some possible y intercept, but this is a slope relationship, which is what we're really care about.

02:57 So now for part b we want to see if we can figure out what b is because that's what we want to know.

03:06 So we got to figure out a relationship between a and v that involves b.

03:12 Okay.

03:13 So to start this, we know the emotional emf is given as bvl.

03:18 And that means the current induced with that motional emf is vbl over r.

03:26 And we also know that the force from that kind of is given as i, l, b.

03:34 So if we put all this together, we see this becomes v, b squared, l squared over r.

03:42 And that is our force...

Please give Ace some feedback