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Giải bài 22 trang 54 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Thời gian T (s) để con lắc trên đồng hồ quả lắc thực hiện được một dao động (thời gian giữa hai tiếng “tích tắc” liên tiếp) gọi là chu kì con lắc và được tính bởi công thức (T = 2pi sqrt {frac{l}{g}} ), trong đó l (m) là chiều dài của dây, g = 9,8 m/s2. a) Tính chu kì của con lắc khi chiều dài của dây là l = 0,5 m (kết quả làm tròn đến hàng phần nghìn của giây). b) Chiều dài của dây phải bằng bao nhiêu thì con lắc có chu kì T = 2 s (kết quả làm tròn đến hàng phần nghìn của mét)? c) Nếu c

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Thời gian T (s) để con lắc trên đồng hồ quả lắc thực hiện được một dao động (thời gian giữa hai tiếng “tích tắc” liên tiếp) gọi là chu kì con lắc và được tính bởi công thức \(T = 2\pi \sqrt {\frac{l}{g}} \), trong đó l (m) là chiều dài của dây, g = 9,8 m/s2.

a) Tính chu kì của con lắc khi chiều dài của dây là l = 0,5 m (kết quả làm tròn đến hàng phần nghìn 𒊎của giây)ꦦ.

b) Chiều dài của dây phải bằng bao nhiêu thì con lắc có chu kì T = 2 s (kết quả làm tròn đến hàng phần nghìn của mét)? c) Nếu chiều dài của dây tăng lên gấp 2 lần thì chu kì của con lắc thay đổi như thế nào?

Phương pháp giải - Xem chi tiết

Đọc kĩ dữ kiện đề bài để tính toán. Dựa vào: \(\frac{{\sqrt a }}{{\sqrt b }} = \frac{{\sqrt a .\sqrt b }}{{{{\left( {\sqrt b } \right)}^2}}} = \frac{{\sqrt {ab} }}{b}(a \ge 0,b > 0)\) \(\sqrt {\frac{a}{b}}  = \sqrt {\frac{{ab}}{{{b^2}}}}  = \frac{{\sqrt {ab} }}{b}(a \ge 0,b > 0)\)

Lời giải chi tiết

a) \(T = 2\pi \sqrt {\frac{l}{g}}  = 2\pi \sqrt {\frac{{0,5}}{{9,8}}}  \approx 1,419(s)\)

b) Nếu chiều dài của dây là l1 = 2l thì con lắc có chu kì là

\({T_1} = 2\pi \sqrt {\frac{{{l_1}}}{g}}  = 2\pi \sqrt {\frac{{2l}}{g}} .\sqrt 2  = T\sqrt 2 \). Suy ra nếu chiều dài của dây tăng lên gấp hai lần thì chu kì của con lắc tăng lên gấp \(\sqrt 2 \) lần.

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