Stekolnikova Daria Voronezh - 2 Problem 5 Falling ball Stekolnikova Daria Voronezh - 2

Condition of the problem An electronic balance (1) is connected to a PC (5) in order to record the time dependence of the measured weight. A light frame (4) is mounted on a tall beaker (2) filled with water. The frame has a holder (3) allowing controlled release of a small ball such that it falls into the water. The beaker is placed on the balance as depicted in the Figure. Investigate how the readings of the balance reflect the different phases of the motion of the ball.

Balance - device that measure weight. F T T T mg mg mg P = mg T = P = mg P = T = mg - F

Our setting Dynamometer Holder with the ball Ruler Beaker PC

Model Fixed on the foundation ball Vessel with water

Explanation of the process P – shows with which force the ball affects on the system T 𝑃= 𝐹 𝑔𝑟 𝐹 𝑔𝑟

𝐹 𝑔𝑟 𝑃=0

𝑃= 𝐹 𝑔𝑟 − 𝐹 𝑤𝑟 𝐹 𝑤𝑟 𝐹 𝑤𝑟 𝐹 𝑔𝑟

𝑃= 𝐹 𝑔𝑟 − 𝐹 𝐴 − 𝐹 𝑟𝑓 𝐹 𝑟𝑓 𝐹 𝐴 𝐹 𝑔𝑟

𝑃= 𝐹 𝑔𝑟 − 𝐹 𝐴 − 𝐹 𝑟𝑓 𝐹 𝑟𝑓 𝐹 𝐴 𝐹 𝑔𝑟

Hypothesis ∆𝑃∼∆𝑎

𝐹 𝑔𝑟 𝐹 𝑠𝑡 𝐹 𝑔𝑟 𝐹 𝑟𝑓 𝐹 𝐴 𝐹 =𝑚 𝑎 ∆𝑃=𝑚∆𝑎 ∆𝑎

Results ∆𝑃≈0,2𝑁

𝑚 𝑠𝑒𝑡 = 99,85 𝑔𝑟 𝑚 𝑏 = 31,15 𝑔𝑟 𝑚 𝑤 = 240 𝑔𝑟

𝑠= 0,137 𝑚

∆𝑡≈ 1 3 𝑠

𝑚 𝑏 ∙ 𝑣 𝑏 =( 𝑚 𝑏 + 𝑚 𝑠𝑒𝑡 + 𝑚 𝑤 )∙ 𝑣 𝑠𝑖𝑠 Calculations 𝑚 𝑏 ∙ 𝑣 𝑏 =( 𝑚 𝑏 + 𝑚 𝑠𝑒𝑡 + 𝑚 𝑤 )∙ 𝑣 𝑠𝑖𝑠 𝑠= 𝑣 𝑏 2 2𝑔 𝑚 𝑠𝑖𝑠 = 0,371 𝑘𝑔 𝑣 𝑏 = 2𝑔𝑠 𝑣 𝑏 =1,63 𝑚 𝑠

𝑣 𝑠𝑖𝑠 = 𝑚 𝑏 ∙ 𝑣 𝑏 𝑚 𝑠𝑖𝑠 𝑣 𝑠𝑖𝑠 =0,137 𝑚 𝑠 𝑎 𝑠𝑖𝑠 = 𝑣 𝑠𝑖𝑠 ∆𝑡 𝑎 𝑠𝑖𝑠 =0,416 𝑚 𝑠 2

∆𝑃=𝑚∆𝑎 ∆𝑃= 𝑚 𝑠𝑖𝑠 ∙ 𝑎 𝑠𝑖𝑠 ∆𝑃= 0,371 𝑘𝑔 ∙0,416 𝑚 𝑠 2 =𝟎,𝟏𝟓𝟒𝑵

Comparing results Experimental ∆𝑃=0,2𝑁 Theoretically ∆𝑃=0,15𝑁 Error: 0,05N – normal error for such experiments Our hypothesis was successfully confirmed!

During the traffic the weight of the whole system changes: Conclusion During the traffic the weight of the whole system changes: 1. 𝑡=𝑜 ⟶ 𝑃 0 = 𝑃 𝑠𝑖𝑠 + 𝑃 𝑏 2. 𝑇ℎ𝑒 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑓𝑎𝑙𝑙𝑖𝑛𝑔 ⟶ 𝑃 1 = 𝑃 𝑠𝑖𝑠 3. 𝑇ℎ𝑒 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑐𝑜𝑛𝑡𝑎𝑐𝑡 𝑤𝑖𝑡ℎ 𝑤𝑎𝑡𝑒𝑟⟶ 𝑃 2 = 𝑃 𝑠𝑖𝑠 +𝑚∆𝑎 4. 𝑇ℎ𝑒 𝑒𝑛𝑑⟶ 𝑃 3 = 𝑃 0

Thank you for your attention!