Applied Physics Experiment 4

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

### Procedure:

Place the cart on the track and level the track so that the cart does not accelerate in either direction. With a table clamp, position the smart pulley (see figure 3) at the aisle end of the track. Measure and record the mass of the cart, Mcart . Measure and add the masses of the two blocks to the mass of the cart. Record the total mass, Mtotal.

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 3 Smart Pulley. Figure 4 Cart on the air track.
Run Science Workshop.

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.

### Analysis of Data:

Complete column 3 of both tables by calculating the values for g-a. For the value of g use the accepted value of 9.81 m/s2. Compute the values for T by using equation (3). Plot a graph of tension T vs. acceleration a using Mathcad. Use the slope() function of Mathcad to compute the slope of the best fitting line. Use the corr() function to find the closeness of the fit. As equation (4) predicts, this slope should be very close to the mass of the cart (Mcart) in the case of Table 1. In the case of Table 2 the slope should be very close to the total mass (Mtotal). Calculate the percent error for both cases by using

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.

### Recording data:

Mcart = __________________ Mtotal = Mcart + Mblocks = _______________________

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 = _________________