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Recitation Worksheet G Solutions

Recitation Worksheet G Solutions - Worksheet G Free-body...

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Worksheet G: Free-body diagrams 1. A 30-mg spider hangs from two threads from the ceiling as shown below. a. Find the tension on each thread. 2 1 1 2 : cos30 cos40 0 : sin 40 sin30 0 x T T y T T mg ° − ° = °+ °− = 2 equations with 2 unknowns (T 1 , T 2 ) 2 1 1 1 1 6 2 2 cos40 cos30 cos40 sin 40 sin30 cos30 sin 40 cos40 tan30 (30 10 kg)(9.8 m/s ) 0.27 mN sin 40 cos40 tan30 cos40 (0.27 mN) 0.24 mN cos30 T T T T mg mg T T ° = ° ° °+ ° = ° = °+ ° ° × = = °+ ° ° ° = = ° b. The ceiling happens to be the ceiling of an elevator that starts moving up with an acceleration of 2.5 m/s 2 . Find the new tensions on the threads. The free-body diagram is the same, but now the acceleration in the vertical direction is not zero: 2 1 1 2 : cos30 cos40 0 : sin 40 sin30 x T T y T T mg ma ° − ° = °+ °− = 40 ° 30 ° x y mg T 1 T 2

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(Worksheet G) The algebra is almost the same: ( ) ( ) 2 1 1 1 1 6 2 2 cos40 cos30 cos40 sin 40 sin30 cos30 sin 40 cos40 tan30 (30 10 kg)(12.3 m/s ) 0.34 mN sin 40 cos40 tan30 cos40 (0.34 mN) 0.30 mN cos30 T T T T m g a m g a T T ° = ° ° °+ ° = + ° + = °+ ° ° × = = ° + ° ° ° = = °
(Worksheet G) 2. Two blocks of masses
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