Question

For the 10cm position on the ruler, I got a distance of 10.795 cm of the movement of the gauge. I'm struggling to find the force of friction (f) from that to find the coefficient of kinetic friction.

1. From the 10-cm position on the ruler, let the steel bearing ball roll into the kinetic energ gauge positioned at the bottom of the ruler. 2. Measure the distance along the flat surface that the gauge moves before stopping. We recommend using your tape measure to do this, rather than moving your ruler and re- positioning it each time. 3. Note answers to all of the following questions for your lab report: What forces caused it to stop? What happened to the kinetic energy of the ball at the bottom of the ruler? 4. Place the ball at the 20-cm and the 30-cm positions and again measure the distance the gauge moves after the ball enters it. For your lab report: Plot the distance the gauge moves versus the initial steel ball position on the ruler. Is this relationship linear? 5. With some simple assumptions, you can use these data to find the coefficient of kinetic friction Mx of the gauge on the table: The force of friction f on the gauge is: f = ukN The normal force Nis just the weight of the gauge plus the ball. The normal force and force of gravity do no work because they are perpendicular to the displacement of the gauge, which moves horizontally. The work done by friction is - fd th е What value did you find for fix? 6. Report all of your answers to 1-5 to your group. Discuss the results of your experiments. Note: A steel ball has a mass of approximately 28.4 grams (.0284 kg). You may use this value, or if you have access to a small scale, you can weigh the ball for a more accurate value. You can either neglect the weight of the gauge or, alternatively, weigh the gauge and ball together for a more accurate value for their total weight. Note in your lab report which for datamininethembin tof the holland ME 0 envi

Answer 1

1. First of all, place the ruler inclined at height by placing book or something at one end. Position (with your hand) the steel ball at 10 cm on the ruler. Place gauge at the bottom of the ruler.
2. Now, roll (by leaving free) the ball from its position. It will collide with gauge smoothly and sticks to together. Then both moves some distance.
3. Measure that distance $\Delta x$ from another meter stick ot ruler.
4. Repeat steps 1 to 3 for ball position 15 cm, 20 cm, 25 cm, and 30 cm.
5. Make a table in the spreadsheet as below from all the experimental trials:

Trial 1 х X 2 3 Initial position of ball x (m) Distance d (m) 10 15 20 25 30 х 4 х 5 х

1. In spreadsheet, graph the scatter plot as initial position of the ball on Y-axis and distance moved by ball and gauge together on the X-axix. Now draw linear best-fit line in the scatter graph.
2. The linear best-fit line will be staight line.

The linear best line is given as:

y = pr + b

(1) 9 + pd = r.

The slope of the linear best-fit line is $p={rise}/{run}$ .

The Y-intercept of the linear best-fit line is .

Now, we know that distance is expressed in terms of work done by ball and gauge together
6+9
and friction force :

$W_{b+g}=-fd$

Similarly, the position distance is expressed in terms of work done:

Now, positive work done is by steel ball $W_{b}$ due to gravity is equal to negative work done by ball and gauge together
6+9
.

$\therefore W_{b}=W_{b+g}$

Therefore, the work done
6+9
by ball and gauge is given as:

$W=-\mu_{k} mgd\ (\because f=\mu_{k}N=\mu_{k}mg)$

Here is the total weight of the ball and gauge together.

The assumption is done that work done by steel ball alone is equal to the work done by it.

$\therefore W_{b}=W_{b+g}=-\mu_{k} mgd\ ---(2)$

Therefore, equating equation (1) and (2) give the slope of the linear best-fit line is equal to term $\mu_{k} mg$ :

$\therefore p=\mu_{k} mg$

${\color{Blue} \therefore \mu_{k}= \frac{p}{mg}}$

Therefore, coefficient of the friction can be calculated from the slope of the linear best-fit line, total weight of the ball and gauge, and gravitational acceleration.