Determining Experimental Value for g Using Torricelli's Law
How can we calculate the experimental value for g using Torricelli's law?
Based on Torricelli's law, what does the graph between velocity (v) and √h look like? How can we use this data table to determine the experimental value for g?
Calculating Experimental Value for g Through Torricelli's Law
The graph between velocity (v) and √h is linear with a slope of √2g and an intercept of zero for Torricelli's law. To determine the experimental value for g using the provided data table, follow these steps:
Plot the graph with velocity (v) on the y-axis and the square root of height (√h) on the x-axis. Calculate the slope of the linear graph using the formula:
slope = Δv/Δ(√h)
To calculate the slope of the linear graph and the experimental value for g:
1. Calculate Δv and Δ(√h) using the given formulae:
Δv = v2 - v1
Δ(√h) = (√h2 - √h1)
2. Calculate slope using the values of Δv and Δ(√h) from the data table.
slope = Δv/Δ(√h)
3. Calculate the experimental value for g using the slope:
g experimental = (slope/√2)²
4. Determine the percent error by comparing the experimental value of g to the theoretical value of g.
Based on the data table provided, you can calculate the experimental value for g and the percent error.
Torricelli's law states that for a tall column of liquid with a small hole at the bottom, the water flows out with a velocity v= √2gh. By analyzing the data table mentioned, we can determine the experimental value for g through calculations based on Torricelli's law.
The linear graph between velocity (v) and √h will have a slope of √2g and an intercept of zero. To calculate the slope and experimental value for g, we follow the steps outlined above:
1. Plot the graph with the given data points
2. Calculate the slope of the linear graph using the formula slope = Δv/Δ(√h)
3. Determine the experimental value for g by applying the formula g experimental = (slope/√2)²
4. Calculate the percent error by comparing the experimental and theoretical values of g
Using the provided data and formulas, you can calculate the experimental value for g and evaluate the accuracy of the measurement through percent error.