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Giải bài 4.11 trang 51 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Trên Hình 4.7 biểu diễn ba lực

🌠Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Trên Hình 4.7 biểu diễn ba lực \(\overrightarrow {{F_1}} ,\,\,\overrightarrow {{F_2}} ,\,\,\overrightarrow {{F_3}} \) cùng tác động vào một vị trí cân bằng \(A.\) Cho biết \(\left| {\overrightarrow {{F_1}} } \right| = 30N,\,\,\left| {\overrightarrow {{F_2}} } \right| = 40N.\) Tính cường độ của lực \(\overrightarrow {{F_3}} .\)

Phương pháp giải - Xem chi tiết

-  Chứng minh tứ giác \(ABEC\) là hình chữ nhật -  Áp dụng Py-ta-go để tính cạnh \(AE\): \(A{E^2} = A{B^2} + A{C^2}\) -  Do vật ở vị trí cân bằng nên \(\left| {\overrightarrow {{F_3}} } \right| = \left| {\overrightarrow F } \right| = AE\)

Lời giải chi tiết

Ta có: \(\widehat {BAC} = {90^ \circ }\)Nên tứ giác \(ABEC\) là hình chữ nhật\( \Rightarrow \) \(\left| {\overrightarrow F } \right| = AE = \sqrt {A{B^2} + A{C^2}}  = \sqrt {{{30}^2} + {{40}^2}}  = 50\,\,(N)\)Do vật ở vị trí cân bằng nên hai lực \(\overrightarrow F \) và \(\overrightarrow {{F_3}} \) có cùng cường độ và ngược chiều nhau\( \Rightarrow \) \(\left| {\overrightarrow {F{}_3} } \right| = \left| {\overrightarrow F } \right| = AD = 50\,\,(N)\)

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