P SUPPLEMENTARY work (energy) ANSWERS

P SUPPLEMENTARY - SUPPLEMENTARY WORK SOLUTIONS 1 → → a W = F ∆ d ⇒ W = 1 0 1 0 ⇒ W = 1 0 0 J b Observe that since the rope is making an

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Unformatted text preview: SUPPLEMENTARY WORK SOLUTIONS 1) → → a) W = F ∆ d ⇒ W = ( 1 0 ) ( 1 0 ) ⇒ W = 1 0 0 J . b) Observe that since the rope is making an angle relative to the front of the cart, this angle is relative to the vertical (and not the horizontal). Hence, relative to the ground, the angle is 60° (this angle is needed since our displacement is along the ground. Thus, W = F ∆ d c o s θ ⇒ W = (1 0 )(1 0 ) c o s 6 0 → → ⇒ W = 50 J . 5 3 c) If 6 0 = ( 1 0 ) ( 1 0 ) c o s θ , then c o s θ = ⇒ θ ≈ 5 3 . 1 . 2) a) The force exerted by the spring is a maximum (of 15 N) when the displacement is between 0 m and 2m as well when the displacement is 18 m. b) The force exerted by the spring at displacements 6 m and 16 m is 0 N. c) The work done by the spring during the first six meters of its displacement is the area under the graph. Hence, W = 1 (1 5 )( 2 + 6 ) ⇒ W = 6 0 J . 2 d) W = 1 1 ( − 1 5 )(4 ) + ( − 1 5 )(6 + 4 ) ⇒ W = − 1 0 5 J . 2 2 e) Since the work done is negative, then the force and displacement are in opposite directions. You could think of it as the spring is being compressed while it is moving in the forward direction. The energy is now being stored in the compression cycle of the spring. 1 (1 5 )( 2 ) ⇒ W = 1 5 J . 2 f) W = g) The overall work done by the spring is the sum of the individual works. Hence, W to ta l = 6 0 − 1 0 5 + 1 5 = −3 0 J . h) W = ( 9 . 3 7 5 ) ( 8 ) c o s 0 ⇒ W = 7 5 J . i) j) W = ( − 1 0 .5 ) ( 1 0 ) c o s 0 ⇒ W = − 1 0 5 J W to ta l = 7 5 − 1 0 5 = −3 0 J k) The answers to part g) and j) are equivalent. Instead of having a piecewise linear graph as given, we could have just drawn two horizontal lines, one at a force of 9.375 N for 0 m to 8m and then another horizontal line at a force of –10.5 N from 8 m to 18 m. ...
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This note was uploaded on 07/27/2010 for the course MATH MATH 1025 taught by Professor Tanny during the Spring '09 term at York University.

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