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EX7.2-50lb Slider

# EX7.2-50lb Slider - lbs 2 Sketch FBD Substitute into U 1-2...

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3/144 The 50 lb slider in the position shown has an initial velocity v 1 of 2 ft/sec. Slides under influence of gravity and friction. μ k = 0.5. Find the velocity of the slider as it passes a position for which the spring is compressed x= 4 inches. The spring is a hardened spring – see figure and equation below. T 1 + U 1-2 = T 2 T 2 = 0.5 mv 2 2 = 0.5*[50/32.2] v 2 2 - + - = = f x spring dx x F mg N 0 2 - 1 2 - 1 )} ( sin { U d U θ μ 2 1 r r r F Write out equations for each term The friction term is negative because it acts in the opposite direction to the displacement– same for the spring . What is the distance x, the normal force N, and the equation for F spring (x)? F spring = 100 x + 9 x 2 lbs Substitute into Work Energy and solve for v
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Unformatted text preview: lbs 2 Sketch - FBD Substitute into U 1-2 equation? EX7.2 50-lb Slider What is your first step? Solution: Problem Type: Find: Given: W=50 lbs, v 1 =2 ft/s, μ k =0.5, x=4 in, diagram V 2 : Velocity when spring is compressed to x Has displacement, springs and velocity, probably should us Work-Energy Write out the Work-Energy Relationship ft x x 33 . 3 12 4 3 = ⇒ + = ( 29 lbs N N F y 25 60 cos 50 = = °-⇒ = ∑ ( 29 ( 29 lbs ft U dx x x U • = +-° +-=--∫ . 20 9 100 12 1 33 . 3 60 sin 50 25 * 5 . 2 1 4 2 2 1 T 1 = 0.5 mv 1 2 = 0.5*[50/32.2] 2 2 =3.10 ft lbs v 2 =5.46 ft/sec...
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