PHYS 1111L - Introductory Physics Laboratory I

Laboratory Advanced Sheet
Newton's 2nd Law

1. Objectives. The objective of this laboratory is to measure the acceleration due to gravity by applying Newton's Second Law to the motion of an object on a frictionless inclined plane.

2. Theory.

a. General. Neglecting air resistance and friction, Newton's Second law predicts that an object released from rest on a inclined plane has an acceleration whose magnitude down the plane is given by

a_x = g sinq

where
g is the acceleration due to gravity,
q is the angle of the inclined plane with respect to the horizontal, and
x is chosen as the direction of motion down the plane.

b. Model. The acceleration due to gravity can be determined if the magnitude of the acceleration and the sine of the angle of the inclined plane are measured.

1) The magnitude of the acceleration down the plane can be calculated by making measurements of the speed of the object at two points and the displacement between the two points. One-dimensional, constant acceleration kinematics gives

v_x² = v_0x² + 2a_x(x - x₀)

where
v_x and v_0x are the final and initial speeds of the object along the x-direction, and
x - x₀ is the displacement between the two points at which the speeds are measured.

Thus the acceleration down the plane can be determined from

a_x = (v_x² - v_0x²)/[2(x - x₀)]

2) Measuring the speeds. The speeds are measured by dividing the length (L) of the object by the time (t) required for the object to pass a fixed point.

v = L/t

Two such measurements are made to determine the initial and final speeds.

3) Measuring the sine of the angle of inclination. The inclined plane's angle is determined by measuring the distance that a height that the incline drops (Dh) and the distance along the plane over which this drop occurs (Dd). The sine of the angle of inclination is then given by

sinq = Dh/Dd

4) Determining the acceleration due to gravity. Using the measured acceleration down the plane and the sine of the angle of inclination, the acceleration due to gravity can be determined from

g = a_x/sinq

c. Testing the model. The measured value of the acceleration due to gravity will be tested by comparison with the actual value of 9.81 m/s².

3. Apparatus and experimental procedures.

a. Equipment.

1) Air track with blower.

2) Cart for air track.

3) Two photogates with computer interface.

4) Meter stick

b. Experimental setup. The experimental setup is shown in Figure 1 (to be provided by the student).

c. Capabilities. To be provided by the student.

d. Procedures. Detailed instructions are provided in paragraph 4b below.

4. Requirements.

a. In the laboratory. Data tables are attached for your use.

1) Your instructor will introduce you to the equipment to be used in the experiment.

2) With the blower on, release the cart from rest from the top of the inclined plane. Using the photogates and computer, make ten (10) measurements of the time required for the cart to pass each photogate. Record the mean times for each photogate measurement.

3) Measure the length of the cart.

4) Make measurements to determine the distance between the two photogates.

5) Make measurements to determine the sine of the inclination angle of the air track.

b. After the laboratory. The items listed on below will be turned in at the beginning of the next laboratory period. A complete laboratory report is not required for this laboratory. Use a spreadsheet program to make your calculations.

Para 3. Apparatus and experimental procedures.

1) Provide a figure for the experimental setup (para 3b).

2) Describe the capabilities of the equipment used in the experiment (para 3c).

Para. 4. Data.

1) Data from your measurements.

2) The following calculations:

a) The initial and final speeds of the cart.

b) The displacement between the photogates.

c) The acceleration of the cart down the air track.

d) The sine of the inclination angle of the air track.

e) The acceleration due to gravity.

f) The percent discrepancy in your value of the acceleration due to gravity.

Para. 5. Results and Conclusions.

a. Results.

1) A statement providing the measured value of the magnitude of the acceleration due to gravity.

2) A statement providing the percent discrepancy in your results.

b. Conclusions.

1) Assess the precision and accuracy of your experiment.

2) Describe sources of random and systematic error in the experiment.

Annex A
Measurements

1. Times for cart to pass photogates.

2. Length of cart.

length (L): ________________________ m

3. Displacement measurements:

4. Sine of inclination angle measurements:

Last update: June 18, 2007