Force and Acceleration - Newton's Second Law

Objective:

- To observe the relationship between force and acceleration and to test the hypothesis that the force is equal to the mass times the acceleration.

Equipment:

- Track with cart, accessory weights
- Smart pulley timer
- Table clamp
- Triple beam balance
- Slotted weights, one 10 g, and three 20 g

Physical principles:

A net force, *F*, applied to an object with a mass, *M*, will
cause the mass to accelerate with an acceleration, *a*. Newton's law
of motion asserts that the net force is directly proportional to the acceleration
produced. The proportionality constant is denoted by the inertial mass,
*M*. In equation form, this law can be written as

When an object with a mass *M*, on a smooth horizontal surface,
is connected by a string over a pulley to another mass *m*, a tension
is created in the string. This tension is the force that accelerates the
object on the surface. From the free body diagram shown in figure 1, it
can be deduced that the total force acting on the mass is the tension in
the string minus the force of gravity. Assuming that the mass of the hanging
weight is *m*, and its acceleration is *a*, the following equation
can be written. The acceleration of gravity is symbolized by *g*.

Equation (1) can be solved for tension to yield the following equality.

Since the tension is constant in the string, the object on the surface and the mass hanging on the string have the same acceleration. Thus, Newton's law of motion for the object on the surface is

Connect a string to the paper clip or wire loop on the front of the
cart and place it over the pulley at the end of the track. Make a loop
on the other end of the string and slip a 10 g slotted weight into it.
The length of the string should keep the mass about 5 cm above the floor
when the cart is at the track bumper. Following the procedure below, obtain
the value of the acceleration.

Figure 3Smart Pulley. |
Figure 4 Cart on the air track. |

Plug in the smart pulley on the screen by clicking on the digital plug icon, dragging it over digital channel 1 and selecting smart pulley (linear). Click on OK.

Click on the recording options button, set periodic samples to 10,000 Hz, and click on OK.

Make a graph of velocity versus time by clicking on the graph icon, dragging it over the smart pulley icon, selecting velocity, and clicking on OK.

Start statistics by clicking on the button in the graph window, then click on the button in the new window annd select curve fit and then linear fit.

Position the cart so that the small slotted weight is just below the smart pulley.

Release the cart, click on the REC button, when click on Stop just before it reaches the end of the track.

Record the value of the slope (a2) from the statistics section of the
graph window in the column entitled *a* in Table 1. This value represents
the acceleration of the cart system. Take a series of seven (7) more measurements
each time increasing the mass at the end of the string by 10 g. Be sure
to delete the previous run between measurements by clicking on Run #1,
pressing the delete key on the keyboard and clicking on OK. Record the
acceleration for each mass in Table 1.

In your conclusions you should:

Discuss the percent error that you calculated for both graphs.

Interpret the value of the Correlation Coefficient.

Examine how the presence of constant frictional force would affect the results of the experiment.

Speculate on the origin(s) of error.

Mention what you learned in this experiment.

Include any additional comments that you think are essential.

M

Table 1 Cart without additional mass data

m | a | g-a | T |

10g | |||

20g | |||

30g | |||

40g | |||

50g | |||

60g | |||

70g | |||

80g |

Slope of the Tension vs. Acceleration line = __________________

%Err = _________________

**Table 2** Cart with two blocks data

m | a | g-a | T |

10g | |||

20g | |||

30g | |||

40g | |||

50g | |||

60g | |||

70g | |||

80g |

Slope of the Tension vs. Acceleration line = __________________

%Err = _________________