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To experimentally verify Newton’s Second Law, a relation between force, mass, and acceleration

A computer with Internet connection, a calculator (The built-in calculator of the computer may be used.), paper, and pencil

"A nonzero net force ΣF acting on mass M generates an acceleration a in that mass such that ΣF = Ma."

In verifying this formula, we may write it as (ΣF / M) = a. In the course of experiment, we can show that if the ratio of the net force, ΣF, to the total mass being moved M_total or M+m is kept constant, the acceleration remains constant as well.

In Fig.1, assuming no friction, the hanging mass m can cause motion for both m and M. The force of gravity on m is F = mg. This force has to move a total mass of m + M. In the absence of friction, F = mg is the only force affecting motion. In this case mg is ΣF.

Using Newton's 2nd Law:

ΣF = (Mass)(Accel) , we may write:

mg = (m + M) a or,

a = mg / (m + M)

Fig. 1

In Fig. 2, assume friction is present for M only because it has to slide on the top of the horizontal table. Since N = w in magnitude, we may write or N = Mg.

The force of kinetic friction is F_k = μ N , or F_k = μ Mg. Here the net force, ΣF, causing motion is mg - μ Mg. The total mass to be moved is m+M. This makes the acceleration a = ( mg - μ Mg ) / ( m+M ).

Using Newton's 2nd Law:

ΣF = (Mass)(Accel) , we may write:

mg - μ Mg = (m + M) a or,

a = (mg - μ Mg ) / (m + M)

Fig. 2

Click on the following link: http://www.walter-fendt.de/ph14e/n2law.htm . Note that masses in the applet are in (grams). For ease of calculation, suppose they are given in kilograms (kg) and ignore the grams. This is not going to affect the results.

For the first 9 trials, set the coefficient of friction μ to zero. To change the numbers each time, the applet must be in the "Reset" mode. Follow the values for M given in the Table below. Run the applet for the values given in the first row. In the first row, both M and m are given. Calculate the "Measured a" based on these values. Also, record the "Accepted a" from the applet. Find the % error using the %error formula you used in the previous experiments.

For rows 2 through 9, in each row, use the given M and keep running the experiment for different values of m that you choose until you get the same acceleration as you got for the first row. The applet calculates the accepted value of acceleration for you, each time. That can be observed and used each time, to make sure the acceleration is kept constant. Note that the accelerations you calculate from a = ( mg - μ Mg ) / ( m+M ) and record under the column "Measured a", must turn out to be the same or very close, each time. In each row, you should find m (experimentally) such that the resulting acceleration is the same as before. Once you find the experimental value of m in a row, use it to calculate the measured value of a as in Column 7. Of course, both ΣF and Total mass (Columns 5 and 6) must be calculated before Column 7.

Include the given coefficients of kinetic friction in the experiment and calculations. Follow the same procedure as applied to Part A.

Trial	M	m	μ_k	ΣF = mg - μMg	Total mass M + m	Measured a = ΣF/(M+m)	Accepted a = 2s /t²	% error
Part A	(kg)	(kg)		( N )	(kg)	( m/s² )	( m/s² )
1	100.0	4.00	0
2	150.0		0
3	200.0		0
4	250.0		0
5	300.0		0
6	350.0		0
6	400.0		0
8	450.0		0
9	500.0		0

Part B
1	100.0	11.73	0.080
2	150.0		0.080
3	200.0		0.080
4	250.0		0.100
5	300.0		0.100
6	350.0		0.100
7	400.0		0.160
8	450.0		0.160
9	500.0		0.160

Calculation(s):

Show a sample calculation.

State your conclusions of the experiment with reference to the values obtained in columns 5, 6, 7, 8, and 9 of the above Table.