Calculate the value for the acceleration due to gravity

Question

Experiment - Measurement of the Earth's Surface Gravity

Analysis

• For each of your trials, calculate the acceleration of the glider. Then find the mean and standard deviation of the accelerations.
• The acceleration due to gravity is split into components, with only part of it going to accelerating the glider down the air track. Using some geometry, you can show that the angle that the air track makes with the table is the same angle that is used to determine that portion of the acceleration due to gravity that goes to accelerating the cart down the air track. Draw a diagram of this in your report.
• The sine of the angle that the air track makes with the table is given by sin θ = h/L and the acceleration of the cart down the air track is a = g sin θ. Since both angles are the same, we find that

sin θ = a/g = h/L,

allowing us to solve for a the acceleration due to gravity

g = a L/h.

Calculate the value for the acceleration due to gravity.

• Find the uncertainty in your value of the acceleration due to gravity using

Δg = g √[(Δa/a)² + (Δh/h)² + (ΔL/L)²]

Use your values for mean and standard deviation for a, Δa, h, and Δh. For ΔL, use ±0.001 and the distance between the photogates for L. Report your values for the acceleration due to gravity as g + Δg. Does the range for your value contain the accepted value of 9.81 m/s²?

• Find the percent error between your experimental value and the accepted value of 9.81 m/s².