This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Welcome back Dàññý — missed you this week. The image shows an experiment involving a simple pendulum. The table provides data for the length of the pendulum (l) and the time taken for 20 swings. The period T and T^2 values are also partially filled. First, let's complete the table for T(s) and T^2(s^2). The period T is the time for one swing. Since the mean time is for 20 swings, T = Mean t20. Then, T^2 is the square of the period. Here's the completed table: | l (cm) | l (m) | t_1 (s) | t_2 (s) | Mean t (s) | T (s) = Mean t/20 | T^2 (s^2) | | :------- | :------ | :-------- | :-------- | :----------- | :-------------------- | :------------ | | 100 | 1.00 | 40.33 | 40.06 | 40.19 | 2.0095 | 4.038 | | 90 | 0.90 | 38.00 | 38.10 | 38.05 | 1.9025 | 3.620 | | 80 | 0.80 | 36.00 | 36.10 | 36.05 | 1.8025 | 3.249 | | 70 | 0.70 | 34.00 | 33.90 | 33.95 | 1.6975 | 2.881 | | 60 | 0.60 | 31.00 | 31.00 | 31.00 | 1.5500 | 2.403 | | 50 | 0.50 | 29.00 | 28.60 | 28.80 | 1.4400 | 2.074 | a) Plot a graph T^2(s^2) against l in meters. This step requires plotting on graph paper, which cannot be done here. However, I can provide the data points for plotting. The points to plot are (l, T^2): (1.00, 4.038) (0.90, 3.620) (0.80, 3.249) (0.70, 2.881) (0.60, 2.403) (0.50, 2.074) b) Find the slope of the graph. The formula for the period of a simple pendulum is T = 2((l)/(g)). Squaring both sides gives T^2 = 4^2 (l)/(g). This equation is in the form y = mx, where y = T^2, x = l, and the slope m = (4^2)/(g). To find the slope, we can use two points from the calculated data. Let's use the first and last points for better accuracy. Point 1: (l_1, T_1^2) = (1.00 m, 4.038 s^2) Point 2: (l_2, T_2^2) = (0.50 m, 2.074 s^2) Step 1: Calculate the slope m. m = (T_1^2 - T_2^2)/(l_1 - l_2) m = 4.038 s^2 - 2.074 s^21.00 m - 0.50 m m = 1.964 s^20.50 m m = 3.928 s^2/m The slope of the graph is 3.928 s^2/m. c) Calculate the value of g. From the relationship m = (4^2)/(g), we can find g. Step 1: Rearrange the formula to solve for g. g = (4^2)/(m) Step 2: Substitute the value of the slope m. g = (4 × (3.14159)^2)/(3.928 s)^2/m g = (4 × 9.8696)/(3.928 s)^2/m g = (39.4784)/(3.928 s)^2/m g = 10.050 m/s^2 The value of g is 10.05 m/s^2. Send me the next one 📸