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# exam1 - TAM 150/152 Fall 2003 Hour Exam 1 I ircle one 150...

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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 free-body 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} lb-ft [A-B| =[-10J§(i+j)-(4j+ 3k)! lb-ft =10ﬁ(4) 1b-ft= 40x51b-ft B-(CXA)= 0 4 3 i 0 —§lb-ft=01b-ft 5 5 —10«/§ 40% 0 dim(B . (c x A)) = LL ...
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exam1 - TAM 150/152 Fall 2003 Hour Exam 1 I ircle one 150...

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