TO INVESTIGATE THE RELATIONSHIP BETWEEN FORCE AND ACCELERATION

COURSE CODE

STUDENTS NAME

DATE

Contents

TOC o “1-3” h z u Objectives of the study PAGEREF _Toc23488808 h 3Apparatus PAGEREF _Toc23488809 h 3Theory PAGEREF _Toc23488810 h 4Setup PAGEREF _Toc23488811 h 4Procedure PAGEREF _Toc23488812 h 6Analysis PAGEREF _Toc23488813 h 6Conclusion PAGEREF _Toc23488814 h 11

To Investigate The Relationship Between Force And Acceleration.

Objectives of the studyTo 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.

ApparatusQuantity Equipment Part number

1 Compact cart mass ME-6755

1 Motion Sensor PS-2103A

1 Force sensor PS-2189

1 Dynamics system ME-6955

1 Balance SE-8723

1 Braided spring SE-8050

1 Mass and hanger set ME-8979

1 Compact Cart mass ME-6755

1 Pulley (part of the CI 6691) ME-9448B

Theory

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. This exhibits the principle of Newton’s second law of motion. This law states that, “the rate of change of momentum is proportional to the imposed force and goes in the direction of the force.”

SetupThe 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.

The pulley was connected to the upper set of holes. The pulley was clamped to the end of the track and placed at the end of the track.

The adjustable feet was placed on both ends of the track to make the track level. A spirit level could be used in this case.

A loop was tied to the end of a one meter string. A mass was hanged on the hanger of the loop. 15g was added to the hanger and a total of 20g. A loop was tied to the other end and it was attached to a force sensor. The mass was hanged over the pulley.

The string was levelled by adjusting the pulley

ProcedureThe string was removed from the force sensor hook and the zero button pressed on the force sensor. The string was then replaced.

The cart was pulled backwards as far as possible without allowing the mass hanger to contact the pulley. The record button was clicked and the cart released.

The force sensor cord was restricted so as not to impede the motion of the cart. This was done by holding the cord at least 30cm above the cart and hand kept directly above the cart as it moves so that the cord did not push or pull the cart.

The STOP button was clicked after the cart stroke the end point. When noise spikes were seen in the velocity data, the angle of the motion sensor was adjusted and all objects moved away from the track.

When a good run was obtained, the data summary was obtained in the left tool palette.

10g was added to the cart and the procedure above was repeated.

The process was repeated for 40g ,50g and 60g

AnalysisThe run select tool was clicked in the graph and 10 g selected.

The statistics tool on the graph was turned on displaying the mean value on the graph. The selection tool was used to restrict the range in which the average value is restricted.

The force values were recorded in the table.

The procedure was repeated for the other values.

F(N)

1 2 3 4 The run select tool was clicked and 10g selected.

A linear curve was selected and the selection tool used to restrict the range.

Acceleration was recorded in the table below.

a (m/s2)

1 2 3 4 The procedure was repeated for the other values.

The graph shows the table values of the applied force and resulting acceleration.

A linear curve fit was selected and the slope determined.

Results and observations

The data was recorded in the tables below.

Force values

F(N)

1 -0.189

2 -0.370

3 -0.453

4 -0.537

A graph of force against time was plotted below.

The acceleration values

a(m/s2)

1 0.481

2 0.837

3 1.170

4 1.240

A graph of acceleration against time was recorded below

From the results, a relationship between the applied force and acceleration was obtained.

F=maWhere F – force

M – the mass

a – acceleration

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.