Hướng dẫn giải Vận dụng 3 (Trang 22 SGK Vật lý 10, Bộ Chân trời sáng tạo)

Bảng 3.4 thể hiện kết quả đo khối lượng của một túi trái cây bằng cân đồng hồ. Em hãy xác định sai số tuyệt đối ứng với từng lần đo, sai số tuyệt đối và sai số tương đối của phép đo. Biết sai số dụng cụ là 0,1 kg. <img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/16062022/bai-1-trand-32-toan-lop-10-tap-1-feGnXN.png" /> Sai số tuyệt đối của phép đo: <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x394;</mi><mi>m</mi><mo>=</mo><mover accent="true"><mrow><mi>&#x394;</mi><mi>m</mi></mrow><mo>&#xAF;</mo></mover><mo>+</mo><mi>&#x394;</mi><msub><mi>m</mi><mrow><mi>d</mi><mi>c</mi></mrow></msub><mo>=</mo><mo>?</mo></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Δ</mi><mi>m</mi><mo>=</mo><menclose notation="top"><mi>Δ</mi><mi>m</mi></menclose><mo>+</mo><mi>Δ</mi><msub><mi>m</mi><mrow><mi>d</mi><mi>c</mi></mrow></msub><mo>=</mo><mo>?</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo></mo></math> Sai số tương đối của phép đo: <span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x3B4;</mi><mi>m</mi><mo>=</mo><mfrac><mrow><mi>&#x394;</mi><mi>m</mi></mrow><mover accent="true"><mi>m</mi><mo>&#xAF;</mo></mover></mfrac><mn>.100</mn><mi>%</mi><mo>=</mo><mo>?</mo></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>δ</mi><mi>m</mi><mo>=</mo><mfrac><mrow><mi>Δ</mi><mi>m</mi></mrow><menclose notation="top"><mi>m</mi></menclose></mfrac><mo>.</mo><mn>100</mn><mo>%</mo><mo>=</mo><mo>?</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo></mo></math> Kết quả phép đo: <span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mover accent="true"><mi>m</mi><mo>&#xAF;</mo></mover><mo>&#xB1;</mo><mi>&#x394;</mi><mi>m</mi></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><menclose notation="top"><mi>m</mi></menclose><mo>±</mo><mi>Δ</mi><mi>m</mi></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mi></mi></math> Lời giải: <table style="border-collapse: collapse; width: 100%;" border="1"> <tbody> <tr> <td style="width: 37.2745%;"> Lần đo </td> <td style="width: 35.4709%;"> m (kg) </td> <td style="width: 27.2545%;">  (kg) </td> </tr> <tr> <td style="width: 37.2745%;"> 1 </td> <td style="width: 35.4709%;"> 4,2 </td> <td style="width: 27.2545%;"> 0,1 </td> </tr> <tr> <td style="width: 37.2745%;"> 2 </td> <td style="width: 35.4709%;"> 4,4 </td> <td style="width: 27.2545%;"> 0,1 </td> </tr> <tr> <td style="width: 37.2745%;"> 3 </td> <td style="width: 35.4709%;"> 4,4 </td> <td style="width: 27.2545%;"> 0,1 </td> </tr> <tr> <td style="width: 37.2745%;"> 4 </td> <td style="width: 35.4709%;"> 4,2 </td> <td style="width: 27.2545%;"> 0,1 </td> </tr> </tbody> </table> Giá trị trung bình: <math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>m</mi></menclose><mo>=</mo><mfrac><mrow><msub><mi>m</mi><mn>1</mn></msub><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub><mo>+</mo><msub><mi>m</mi><mn>3</mn></msub><mo>+</mo><msub><mi>m</mi><mn>4</mn></msub></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>,</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>+</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>+</mo><mn>4</mn><mo>,</mo><mn>2</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mn>4</mn><mo>,</mo><mn>3</mn><mi>k</mi><mi>g</mi></math> Sai số tuyệt đối ứng với mỗi lần đo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Δ</mi><msub><mi>m</mi><mn>1</mn></msub><mo>=</mo><mfenced open="|" close="|"><mrow><menclose notation="top"><mi>m</mi></menclose><mo>−</mo><msub><mi>m</mi><mn>1</mn></msub></mrow></mfenced><mo>=</mo><mfenced open="|" close="|"><mrow><mn>4</mn><mo>,</mo><mn>3</mn><mo>−</mo><mn>4</mn><mo>,</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo> </mo><mi>k</mi><mi>g</mi><mspace linebreak="newline"/><mi>Δ</mi><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><mfenced open="|" close="|"><mrow><menclose notation="top"><mi>m</mi></menclose><mo>−</mo><msub><mi>m</mi><mn>2</mn></msub></mrow></mfenced><mo>=</mo><mfenced open="|" close="|"><mrow><mn>4</mn><mo>,</mo><mn>3</mn><mo>−</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo> </mo><mi>k</mi><mi>g</mi><mspace linebreak="newline"/><mi>Δ</mi><msub><mi>m</mi><mn>3</mn></msub><mo>=</mo><mfenced open="|" close="|"><mrow><menclose notation="top"><mi>m</mi></menclose><mo>−</mo><msub><mi>m</mi><mn>3</mn></msub></mrow></mfenced><mo>=</mo><mfenced open="|" close="|"><mrow><mn>4</mn><mo>,</mo><mn>3</mn><mo>−</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo> </mo><mi>k</mi><mi>g</mi><mspace linebreak="newline"/><mi>Δ</mi><msub><mi>m</mi><mn>4</mn></msub><mo>=</mo><mfenced open="|" close="|"><mrow><menclose notation="top"><mi>m</mi></menclose><mo>−</mo><msub><mi>m</mi><mn>4</mn></msub></mrow></mfenced><mo>=</mo><mfenced open="|" close="|"><mrow><mn>4</mn><mo>,</mo><mn>3</mn><mo>−</mo><mn>4</mn><mo>,</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo> </mo><mi>k</mi><mi>g</mi></math> Sai số tuyệt đối trung bình của n lần đo: <math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>Δ</mi><mi>m</mi></menclose><mo> </mo><mo>=</mo><mfrac><mrow><mo> </mo><mi>Δ</mi><msub><mi>m</mi><mn>1</mn></msub><mo>+</mo><mi>Δ</mi><msub><mi>m</mi><mn>2</mn></msub><mo>+</mo><mi>Δ</mi><msub><mi>m</mi><mn>3</mn></msub><mo>+</mo><mi>Δ</mi><msub><mi>m</mi><mn>4</mn></msub></mrow><mn>4</mn></mfrac><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>,</mo><mn>1</mn><mi>k</mi><mi>g</mi></math> Sai số tuyệt đối của phép đo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Δ</mi><mi>m</mi><mo>=</mo><menclose notation="top"><mi>Δ</mi><mi>m</mi></menclose><mo>+</mo><mi>Δ</mi><msub><mi>m</mi><mrow><mi>d</mi><mi>c</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>+</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>=</mo><mn>0</mn><mo>,</mo><mn>2</mn></math> Sai số tương đối của phép đo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>δ</mi><mi>m</mi><mo>=</mo><mfrac><mrow><mi>Δ</mi><mi>m</mi></mrow><menclose notation="top"><mi>m</mi></menclose></mfrac><mo>.</mo><mn>100</mn><mo>%</mo><mo>=</mo><mfrac><mrow><mn>0</mn><mo>,</mo><mn>2</mn></mrow><mrow><mn>4</mn><mo>,</mo><mn>3</mn></mrow></mfrac><mo>.</mo><mn>100</mn><mo>%</mo><mo>=</mo><mn>4</mn><mo>,</mo><mn>65</mn><mo>%</mo></math> Kết quả phép đo: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><menclose notation="top"><mi>m</mi></menclose><mo>+</mo><mi>Δ</mi><mi>m</mi><mo>=</mo><mn>4</mn><mo>,</mo><mn>3</mn><mo> </mo><mo>±</mo><mo> </mo><mn>0</mn><mo>,</mo><mn>2</mn><mi>k</mi><mi>g</mi></math>

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