Objective
This experiment will determine the force of kinetic friction using Newton's 2^nd Law of Motion by measuring the acceleration of an object moving on a horizontal force. The force pulling the car is provided by the force of gravity on small masses attached to it by a string. When these masses are small compared to the mass of the car, friction plays a role in the experiment. The idea is that when the mass is released, it falls to the floor (due to the force of gravity) and accelerates the car.

Equipment

Procedure

1. The mass of the car, M₁, is 364gm and so its weight is 0.364kg * 9.8m/s² (remember, weight should be expressed in Newtons).
2. There is a single photogate that you can move around. As soon as the applet loads, setup the photogate for the first run by placing it at the x_{a (initial)} = 20cm (s = 0.200m) mark. This ensures the first measurement is far enough in front of the car's starting position to allow it to be moving before the wing gets to the gate (so that it's influenced by kinetic friction instead of static friction).
3. Once the photogate is setup at the 20cm mark, press the Start button. This will record your first measurement (i.e., note the time t_{a (initial)}).
4. Now press the Record Data button. Move the photogate forward by 5cm so that x_{a (final)} = 25cm (i.e., set it at the s = 0.250m mark).
5. Press the Start button again to record the next measurement (i.e., note the time t_{a (final)}).
6. Next, press Record Data again and then move the photogate to the x_{b (initial)} = 60cm mark (s = 0.600m).
7. Press the Start button to record the time t_{b (initial)}.
8. Finally, press the Record Data button again, move the car forward by 5cm to the x_{b (final)} = 65cm mark (s = 0.650m), and press the Start button to record your final measurement time measurement (i.e., the time t_{b (final)}).
9. This first experiment used a mass of 20gm (0.02kg) to accelerate the car. The value of acceleration is measured by finding the time (t_ab) that the car takes to travel the distance (D_ab = 40cm) between the gates and by measuring the velocity through each gate (v_a and v_b).
   
   v_a = 0.05m / Δt_asec and v_b = 0.05m / Δt_bsec (remember, Δt_a and Δt_b are the times through each of the gates).
   
   

                         vb - va
       Acceleration a = ----------     where Δtab = tb (final) - ta (final)
                           Δtab
       

   v_avg = ½ (v_a + v_b) and v_avg = D_ab / Δt_ab , where D_ab = x_{b (final)} - x_{a (final)}
10. To find the frictional force, F_fr, we note that the net force (that's acting to move the car) is just the difference between the pulling force (due to the hanging mass, m₂) and the force of friction (holding the car back):

        Fnet = mnetanet = Fpulling - Ffriction
        Fnet = mnetanet = m2g - Ffr
        rearranging → Ffr = m2g - mnetanet
        

    But for the total system, Newton's 2^nd Law says: F_net = [total_mass] x [acceleration] = (M₁ + m₂) a
    
    → F_fr = m₂g - (M₁ + m₂) a
    
    
    
    References: 1, 2, 3
11. Record the data in the first column of the table below. Now repeat this experiment for masses m₂ of 50gm and 70gm.
12. Finally, increase the mass of the car, M₁, to 410gm and repeat the experiment for each of the three masses.
13. Plot the results on a graph of F_fr vs. m₂. Label the axes and choose a scale to fit the data.

Questions

1. At what point is friction present?
2. What is the effect on F_fr of adding mass to the car?
3. What would you expect to find a good value for F_fr if the pulling mass (m₂) was much larger than the mass of the car?

Notes

1. The unit of Force is the Newton: N = kg * m / s² (Note: be sure to convert all your mass measurements from grams to kilograms) and Weight = m * g, where g is the acceleration due to gravity: g = 9.8 m/s²
2. Remember, when you change the masses of either the car or the hanging mass, you have to press the Reset button TWICE (once to activate the text boxes and once again to actually record the changes)
3. Collect the Data (Item #'s 1-8 in the spreadsheet below) first and then go on to do the calculations to determine the F_fr
4. x is just the x position (it's sometimes referred to by the letter "s" and is also often called the "distance")
5. Reference to Prof. Fendt's Original version (which was derived further into the version here)

#	Physical Values	Car Mass = 364-gm			Car Mass = 410-gm
		20-gm mass	50-gm mass	70-gm mass	20-gm mass	50-gm mass	70-gm mass
1	xa (initial) [m]	0.200m	0.200m	0.200m	0.200m	0.200m	0.200m
2	ta (initial) [s]
3	xa (final) [m]	0.250m	0.250m	0.250m	0.250m	0.250m	0.250m
4	ta (final) [s]
5	xb (initial) [m]	0.600m	0.600m	0.600m	0.600m	0.600m	0.600m
6	tb (initial) [s]
7	xb (final) [m]	0.650m	0.650m	0.650m	0.650m	0.650m	0.650m
8	tb (final) [s]
9	Δta = ta (final) - ta (initial) [s]
10	va = 0.05m / Δtasec [m/s]
11	Δtb = tb (final) - tb (initial) [s]
12	vb = 0.05m / Δtbsec [m/s]
13	Δtab = tb (final) - ta (final) [s]
14	a = (vb - va)/Δtab [m/s2]
15	Ffr = m2g - (m1 + m2)a [N]

Graph of F_fr vs. m₂