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Unformatted text preview: TAM 150/152, Fall 2003, Hour Exam 1 I ircle one: 150 or 152
Prof. Haber Ilisc. Section: Note: Use notation that clearly distinguishes vectors from scalars. Show all of your work on this sheet. (1) A sphere with mass M is supported in equilibrium by a ramp inclined at 45° and a cable. The cable passes
over a frictionless pulley and carries a block of mass m
at its opposite end. Let g be the gravitational
acceleration; assume frictionless contact between the
sphere and the ramp; neglect the weight of the cable. (a) Draw a freebody diagram of the sphere. (25 pts.) (b) Find the mass m of the block. (20 pts.)
(c) Find the component representation of the reaction of
the ramp acting on the sphere. (20 pts.)
(a)
1
0)) EF = —Rcos45° + mgcos45° = 0 U
>6
ll
5
00 M3 =>m=
2
(C)
R=m ——\/:i+ i J=Mg(j—i)
2 2 2 (Answer must be written in terms of given data, M and g, not m. (b) (C) (d) A=—201b( B=(4j+3k) ft; 2 The vectors A, B and C have lines of action as shown.
Their magnitudes are A — 20 1b, B = 5 ft and [C] — 1
(dimensionless). (a) Find A x B. (10 pts)
(b) Find A  BI. (10 pts)
(0) Find B  (C x A). (10 pts)
(d) What is the dimension of B  (C X A)? (5 pts) £1 + ijj— — —10\5(i + j) 1b 2 1 .
C=g(41—3k) AxB=—10\/§(i+j) 1bx(4j+3k) ft
= 10%{3( j —i) — 4k} lbft [AB =[10J§(i+j)(4j+ 3k)! lbft
=10ﬁ(4) 1bft= 40x51bft B(CXA)= 0 4 3
i 0 —§lbft=01bft
5 5 —10«/§ 40% 0 dim(B . (c x A)) = LL ...
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 Fall '05
 Downing

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