Q. 437. Static Equilibrium involving forces and moments

Question 437.
The forces and couple moments which are exerted on the toe and heel plates of a snow ski are given by
F_t, M_t and F_h, M_h respectively. Replace this system by an equivalent force and couple moment acting at point P. Express the results in Cartesian vector form.
Given:  a= 120 mm,   b= 800 mm,  
           Ft = -50i + 80j - 158k N,   Mt = -6i + 4j + 2k Nm  and
           Fh = -20i + 60j -250k N,   Mh = -20i + 8j + 3k Nm.

Answer 437.
Moment due to F_h
= (b, 0, 0) x (-20, 60, -250)
= (0.8, 0, 0) x (-20, 60, -250)
= (0, 200, 48) Nm

Moment due to F_t
= (a + b, 0, 0) x (-50, 80, -158)
= (0.92, 0, 0) x (-50, 80, - 158)
= (0, 145.36, 73.6) Nm

Sum of moments due to F_h and F_t
M = (0, 345.36, 121.6)
Adding Mt and Mh
total moment
= (0 - 6 - 20, 4 + 8 + 345.36, 2 + 3 + 121.6)
= (-26, 357.36, 126.6)
≈ 0- 26i + 357j + 127k Nm.

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