Homework 17

# Homework 17 - homework 17 BAUTISTA, ALDO Due: Mar 3 2006,...

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1 Version number encoded for clicker entry: V1:1, V2:4, V3:2, V4:4, V5:3. Question 1 Part 1 of 2. 10 points. A particle moving along the x -axis has a potential energy U ( x ), as shown in the ac- companying graph. Scale factors: a = 4 . 6 m, b = 28 J. x(meter) b 2b 3b 4b a 2a 3a 4a 5a 6a U(x) (joules) A B C What is the force exerted on the particle when x = 3 a (point A , the lowest point on the curve)? Correct answer: 0 N (tolerance ± 1 %). Explanation: From the de±nition of Potential Energy, we know F = - d U dx . In other words, the force on a particle at any particular point is given by the negative of the slope of the potential energy function at that point. At x = 3 a , the potential energy has a min- imum; the slope of the function is zero at that point. Therefore there are no forces on a par- ticle at that point. ( x = 3 a is an equilibrium point.) Question 2 Part 2 of 2. 10 points. If the particle has a mass of 8 . 8 kg and is released from rest at x = 5 a , what is the particle’s velocity when it reaches x = a ? Correct answer: 2 . 52262 m / s (tolerance ± 1 %). Explanation: Apply Conservation of Energy: U init + K init = U final + K final U B + 0 = U C + 1 2 m v 2 Solving for v gives v = r 2 m ( U B - U C ) = r 2 m (3 b - 2 b ) = r 2 m b = s 2 (8 . 8 kg) (28 J) = 2 . 52262 m / s . Question 3 Part 1 of 1. 10 points. A 4 kg block moving along the x axis is acted upon by a single horizontal force that varies with the block’s position according to the equation F x = a x 2 + b , where a = 7 N / m 2 , and b = - 2 . 9 N. At 1 . 3 m, the block is moving to the right with a speed of 3 . 4 m / s. Determine the speed of the block at 2 . 4 m. Correct answer: 4 . 85076 m / s (tolerance ± 1 %). Explanation: The change in the potential energy is Δ U = U f - U i = - Z f i F x dx = - Z f i ( a x 2 + b ) d x = ± 1 3 a x 3 i + b x i ² - ± 1 3 a x 3 f + b x f ² = 23 . 9397 J . From the conservation of energy,

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## This note was uploaded on 10/13/2009 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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Homework 17 - homework 17 BAUTISTA, ALDO Due: Mar 3 2006,...

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