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sol3 - HW Solutions 3 8.01 MIT Prof Kowalski Topics...

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HW Solutions 3 - 8.01 MIT - Prof. Kowalski Topics: circular and relative motion and Newton’s first two laws. 1) 4.4 Please refer to figure 4.26 p.148. This is just a vector algebra problem and the problem is not inter- ested in dynamics. The vector here is the force! a) F x = F cos θ where θ is the angle that the rope makes with the ramp ( θ = 30 o in this problem),so F = | −→ F | = F x cos θ = 60 cos 30 = 69 . 3 N. b) F y = F sin θ = F x tan θ = 34 . 6 N. c) The problem in part a and b is not interested in the force along or perpendicular to the ground. So, as long as we don’t change the angle with respect to the ramp the answer to part a and b would not change. d) F makes an angle 50 o with respect to ground so the F gx and F gy is derived from: F gx = F cos θ g = 69 . 3 × cos 50 o = 53 . 1 N. F gy = F sin θ g = 69 . 3 × sin 50 o = 44 . 5 N. 1
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2) 4.30 a) v ave between two points , e.g. f and i, for a constant acceleration is v ave = v f + v i 2 . Here v f = 0 v ave = v 0 2 The stoping time is t s = x v ave = 2 0 . 130 350 = 7 . 43 × 10 4 s.
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