To investigate inertia and newton’s 2nd law of motion

Course code

Students name

Date

To investigate inertia and newton’s 2nd law of motion

Objectives

To determine the relationship between force and acceleration for a cart mass with different masses.

Determine the variation in acceleration with an increase in force applied for a cart mass with different masses.

Apparatus

Quantity Equipment Part number

1 Compact cart mass ME-6755

2 Motion Sensor PS-2103A

3 Force sensor PS-2189

4 Dynamics system ME-6955

5 Balance SE-8723

Theory

Newton’s second law of motion defines the concept of force and the principle of inertia. When a force is applied on a body at rest, it results to a change in its existing state. And when the force is applied on a moving body with uniform velocity, it would result to an acceleration of the body.

Newton Second Law of motion states that, “the rate of change of momentum is proportional to the imposed force and goes in the direction of the force.”

This relationship can be expressed mathematically as;

F=MaWhere F – force

M – the mass

a – acceleration

Setup

The setup was set as shown in the figure below.

The motion sensor was connected to the interface and attached to the track. The alignment knob was attached to the side of the motion sensor so that it pointed parallel to the track. The switch on the top of the motion sensor was set to cart.

The force sensor was connected to the interface.

The long thumbscrew was used to attach the force sensor to the cart. The Cart/Force assembly was placed on the track.

Procedure

The cart was placed about 30cm from the motion sensor and the monitor was clicked.

The cart was moved about 30cm from the motion sensor and then back.

The cart was shaken back and forth the motion sensor would measure the acceleration of the cart and the force applied was also recorded. In order to make the cart oscillate, push and pull was applied on the force sensor hook.

The push and pull force were maintained in the direction of the motion, not in a sideways direction or up or down.

The zero button was pressed to tare the force sensor.

The cart was placed 40cm from the motion sensor, the cart was made to oscillate about 10cm by pushing and pulling on the force sensor hook. The oscillation was maintained at one oscillation per second.

When the cart was oscillating, 5 seconds of data was recorded. The graph of force vs acceleration was recorded.

The graph obtained was not a straight line but a line of best fit was obtained.

The physical property of the force and acceleration curve was obtained and its units obtained.

The graph obtained showed that the force was directly proportional to the acceleration.

Some runs of data were taken. The cart was shaken as fast as possible trying to maintain the cart wheel on tracks on the groove.

Several runs were taken with different people shaking the cart. The values were taken in a table.

One or two masses were added to the cart and the experiment was done again

Data and observations

The monitor display of the position and the velocity were obtained from the monitor as shown.

1828800top

Table representing values of slope with cart empty and slope with extra mass.

Slope with cart empty(kg) Slope with extra mass(kg)

1 0.378 0.956

2 0.393 0.938

3 0.376 0.950

4 0.381 0.940

5 0.385 0.936

6 0.397 0.952

7 0.391 0.942

8 0.380 0.955

9 0.382 0.960

10 0.391 0.977

11 0.395 0.944

12 0.382 0.950

13 0.372 0.951

Data analysis and calculations

Slope with cart empty(kg) Slope with extra mass(kg)

1 0.378 0.956

2 0.393 0.938

3 0.376 0.950

4 0.381 0.940

5 0.385 0.936

6 0.397 0.952

7 0.391 0.942

8 0.380 0.955

9 0.382 0.960

10 0.391 0.977

11 0.395 0.944

12 0.382 0.950

13 0.372 0.951

Mean 0.385 0.950

Std.dev0.00784 0.0109

The standard deviation of the slope with cart empty was obtained as shown

466725247650s2 = Σ (xi – x̄)2

N – 1

476250257175= (0.378 – 0.38484615384615)2 + … + (0.372 – 0.38484615384615)2

13 – 1

447675248285= 0.00073769230769231

12

= 6.1474358974359E-5

s = √6.1474358974359E-5

= 0.0078405585881593

The standard deviation of the cart with extra mass was obtained as shown

-47625228600Σ(xi – x̄)2

N – 1

-57150191135(0.956 – 0.95007692307692)2 + … + (0.951 – 0.95007692307692)2

13 – 1

38099219710000.0014349230769231

12

=  √0.00011957692307692

=  0.010935123368162

A graph of force against acceleration of the cart mass

The graph above is a representation of the force against the acceleration of the cart mass.

The equation related to the graph is given as

f=ma+bWhere F represented the force applied on the force sensor

m- the mass of the body

a – the acceleration of the body

b – represents the damping coefficient

Given the values above, the slope of the line is

0.385+/ 0.00784

From the results obtained above, there exists a slight variation from the values obtained with the experimentally expected values. This can be attributed to the different magnitudes of the forces applied on the cart mass. However, the results obtained depict the relationship of force and acceleration which is a representation of Newton’s second law of motion

Conclusion

The relationship between force and acceleration for a cart mass with different masses was found to be directly proportional. Thus, an increase in mass lead to an increase in the force. The source of error in the experiment could come from the instruments used. The certainty of the results largely depends on the accuracy of the precision of the apparatus. These errors could come in the measurements when the time, length and the mass of the variables are measured. This error can be limited by doing multiple experiments and getting the average of the results. In doing similar experiments the use of stopwatches to measure the acceleration time within a given distance is encouraged while motion sensors can be used when plotting the graph of velocity against time.