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Giải bài 4.70 trang 71 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Một ô tô có khối lượng 2,5 tấn chạy từ chân lên đỉnh một con dốc thẳng

ꦯTổng 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

Một ô tô có khối lượng 2,5 tấn chạy từ chân lên đỉnh một con dốc thẳng. Tính công của trọng lực tác động lên xe, biết dốc dài 50 m và nghiêng \({15^ \circ }\) so với phương nằm ngang (trong tính toán, lấy gia tốc trọng trường bằng 10 \(m/{s^2}.\)

Lời giải chi tiết

Đổi 2,5 tấn = 2500 kgTrọng lực của ô tô có độ lớn bằng \(\left| {\overrightarrow P } \right| = 2500.10 = 25000\) (N).Trọng lực \(\overrightarrow P \) của ô tô hợp với hướng dời \(\overrightarrow {MN} \) một góc \(\alpha  = {15^ \circ } + {90^ \circ } = {150^ \circ }\)Trọng lực \(\overrightarrow P \) được phân tích thành hai lực \(\overrightarrow {{P_1}} \) và \(\overrightarrow {{P_2}} \): \(\overrightarrow P  = \overrightarrow {{P_1}}  + \overrightarrow {{P_2}} \) với \(\overrightarrow {{P_1}} \) có phương vuông góc với mặt dốc, \(\overrightarrow {{P_2}} \) có phương song song với mặt dốc.Công của trọng lực tác động lên xe là:\(A = \overrightarrow P .\overrightarrow {MN}  = P.MN.\cos {105^ \circ } \approx  - 323524\) (J)
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