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Chap05-Solution1

# Chap05-Solution1 - Chap.5 HW1 Questions 4 At time t = 0 a...

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1 Chap.5 HW1 Questions 4 . At time t = 0, a single force F of constant magnitude begins to act on a rock moving through deep space in the positive direction of an x axis. The rock continues to move along that axis. (a) For time t > 0, which are possible functions x(t) for the rock's position: (1) x = 4 t – 3, (2) x = –4 t 2 + 6 t – 3, (3) x = 4 t 2 + 6 t – 3? Using dt dx v / = , v is positive for t > 0 for cases (1) and (3) (b) For which function is ur F directed opposite the rock's initial direction of motion? Using dt dx v / = and dt dv a / = (and taking t > 0) For (1) initial v is positive. Also a (and therefore F ) is zero For (2) initial v is positive. Also a (and therefore F ) is negative For (3) initial v is positive. Also a (and therefore F ) is positive So there is no case where the initial (at t = 0) v is opposite F . Problems 4. Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces shown, with F 1 = 32 N, F 2 = 55 N, F 3 = 41 N, 1 θ = 30°, and 3 = 60°. What is the asteroid's acceleration (a) in unit-vector notation Forces exerted by the three astronauts are: () 1 2 3 ˆˆ ˆ ˆ 32 cos 30 i sin 30 27.7i+16 j j ˆ 55 cos 0 i sin 0 55i j ˆ ˆ 41 cos 60 i sin 60 20.5i 35.5 j. j F F F + ° = + ° = =− ° + ° = r r r (unit: N) The acceleration of the asteroid is : m F a / v v = ( ) ( ) 22 ˆ ˆ ˆ 27.7i 16 j 35.5j (0.86m/s )i (0.16m/s )j . 120 a ++ + == r (b) a magnitude and (c) a direction relative to the positive direction of the x axis? Magnitude of r a is 2 2 2 2 2 m/s 88 . 0 16 . 0 86 . 0 = + = + = y x a a a v The angle r a makes with the + x axis o x y a a 5 . 10 186 . 0 / tan = = = 5. There are two forces on the 2.00 kg box in the overhead view of Figure 5-32, but only one is shown. For F 1 = 20.0 N, a = 12.0 m/s 2 , and = 30.0°, find the second force (a) in unit-vector notation and as (b) a magnitude and (c) an angle relative to the positive direction of the x axis.

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Chap05-Solution1 - Chap.5 HW1 Questions 4 At time t = 0 a...

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