Leonardo da Vinci and the resolution of forces. Leonardo (1452-1519) asked himself how the weight of a body, supported by two strings of different length, is apportioned between the two strings. Three forces arc acting at the point D: the tensions F → and F → 2 in the strings and the weight W → . Leonardo believed that ‖ F → 1 ‖ ‖ F → 2 ‖ = E A ¯ E B ¯ . Was he right? (Source: Les Manuscrits de Leonard de Vinci, published by Ravaisson-Mollien, Paris, 1890.) Hint: Resolve F → 1 into a horizontal and a vertical component; do the same for F → 2 . Since the system is at rest, the equation F → 1 + F → 2 + W → = 0 → holds. Express the ratios ‖ F → 1 ‖ ‖ F → 2 ‖ and E A ¯ E B ¯ in terms of α and β using trigonometric functions, and compare the results.
Leonardo da Vinci and the resolution of forces. Leonardo (1452-1519) asked himself how the weight of a body, supported by two strings of different length, is apportioned between the two strings. Three forces arc acting at the point D: the tensions F → and F → 2 in the strings and the weight W → . Leonardo believed that ‖ F → 1 ‖ ‖ F → 2 ‖ = E A ¯ E B ¯ . Was he right? (Source: Les Manuscrits de Leonard de Vinci, published by Ravaisson-Mollien, Paris, 1890.) Hint: Resolve F → 1 into a horizontal and a vertical component; do the same for F → 2 . Since the system is at rest, the equation F → 1 + F → 2 + W → = 0 → holds. Express the ratios ‖ F → 1 ‖ ‖ F → 2 ‖ and E A ¯ E B ¯ in terms of α and β using trigonometric functions, and compare the results.
Solution Summary: The author analyzes how the weight of a body, supported by two strings of different length, is apportioned between them.
Leonardo da Vinci and the resolution of forces. Leonardo (1452-1519) asked himself how the weight of a body, supported by two strings of different length, is apportioned between the two strings.
Three forces arc acting at the point D: the tensions
F
→
and
F
→
2
in the strings and the weight
W
→
. Leonardo believed that
‖
F
→
1
‖
‖
F
→
2
‖
=
E
A
¯
E
B
¯
.
Was he right? (Source: Les Manuscrits de Leonard de Vinci, published by Ravaisson-Mollien, Paris, 1890.) Hint: Resolve
F
→
1
into a horizontal and a vertical component; do the same for
F
→
2
. Since the system is at rest, the equation
F
→
1
+
F
→
2
+
W
→
=
0
→
holds. Express the ratios
‖
F
→
1
‖
‖
F
→
2
‖
and
E
A
¯
E
B
¯
in terms of
α
and
β
using trigonometric functions, and compare the results.
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