Problem 10: The restoring force in a Hooke's Law spring is a conservative force, and hence, the work done by that force is represented by a potential- energy function. Consider a spring with spring constant k. One end of the spring is fixed at the origin of the coordinate system, and the other is attached to an oscillating block with mass m. The diagram below shows the potential energy function for the spring and the total mechanical energy of the system. 14.0 12.0 U 10.0 Etotal 8.0 6.0 4.0+ 2.0 0.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 x(cm) Part (a) What is the equilibrium position, in centimeters, of the block? eq=18 ✓ Correct! Part (b) What is the position, in centimeters, of one of the turning points of the spring-mass system. Xturn = 14 ✔ Correct! Part (c) What is the value, in newtons per meter, of the spring constant? k= N/m TL 7 8 9 HOME sin() cos() cotan() asin() tan() acos() E 1 4 5 6 acotan() sinh() 1 2 3 atan() cosh() cotanh() + END . tanh() ODegrees Radians 0 BACKSPACE VC DEL CLEAR Part (d) What is the maximum speed, in meter per second, of the block if its mass is m = 430 g? Vmax=

Problem 10: The restoring force in a Hooke's Law spring is a conservative force, and hence, the work done by that force is represented by a potential- energy function. Consider a spring with spring constant k. One end of the spring is fixed at the origin of the coordinate system, and the other is attached to an oscillating block with mass m. The diagram below shows the potential energy function for the spring and the total mechanical energy of the system. 14.0 12.0 U 10.0 Etotal 8.0 6.0 4.0+ 2.0 0.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 x(cm) Part (a) What is the equilibrium position, in centimeters, of the block? eq=18 ✓ Correct! Part (b) What is the position, in centimeters, of one of the turning points of the spring-mass system. Xturn = 14 ✔ Correct! Part (c) What is the value, in newtons per meter, of the spring constant? k= N/m TL 7 8 9 HOME sin() cos() cotan() asin() tan() acos() E 1 4 5 6 acotan() sinh() 1 2 3 atan() cosh() cotanh() + END . tanh() ODegrees Radians 0 BACKSPACE VC DEL CLEAR Part (d) What is the maximum speed, in meter per second, of the block if its mass is m = 430 g? Vmax=

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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5.1
7.15 A force of 531 NN keeps a certain spring stretched a distance of 0.600 mm . 1. What is the potential energy of the spring when it is stretched 0.600 mm ? Express your answer with the appropriate units. 2. What is its potential energy when it is compressed 8.00 cmcm ? Express your answer with the appropriate units.
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A box with mass of 150 kg is released from point A, 43 meters above the ground. The box slides without friction and then collides with a massless spring that is initially uncompressed. a) What is the total energy of the system? b) What is the speed of the box right before colliding with the spring? After colliding with the spring, the box gets stuck to the spring and starts oscillating back and forth. c) If the spring constant is 300 N/m, what is the amplitude of oscillation for the box-spring system? d) When the spring is compressed by Δs = 1.5 m, find the speed of the box. e) Find the maximum acceleration experienced by the box. f) What is the period of oscillation?
At which point or points is the total energy at its maximum value? At which point or points is the kinetic energy positive?
A horizontal spring attached to a wall has a force constant of k = 780 N/m. A block of mass m = 1.90 kg is attached to the spring and rests on a horizontal, frictionless surface as in the figure below. www x=0 x = x;/2 m x = x₁ (a) The block is pulled to a position x; = 7.00 cm from equilibrium and released. Find the elastic potential energy stored in the spring when the block is 7.00 cm from equilibrium and when the block passes through equilibrium. x (cm) Elastic Potential Energy (J) 7.00 0 (b) Find the speed of the block as it passes through the equilibrium point. m/s (c) What is the speed of the block when it is at a position x;/2 = 3.5 cm? m/s (d) Why isn't the answer to part (c) half the answer to part (b)?
Below is a conservation of energy problem. The solution to this problem is provided. Assess whether the solution provided is correct or incorrect AND EXPLAIN WHY. 1. A 4.6 kg block is at rest against a horizontal spring that is compressed by 0.40 m. The spring has a spring constant of k₁ = 2750 N/m. After leaving the spring, it travels up a 28° incline to a height of 2.8 m. At the top of the hill is a second spring with a spring constant of k₂ = 350 N/m. The horizontal portions are frictionless, but the hill has a coefficient of kinetic friction equal to uk= 0.16. x₁ = 0.40 m (CO))) N k₁ = 2750- m Simplifies to Mk = 0.16 a. How fast does the block leave the spring on the bottom of the hill? x₁ = 0.40 m h₁ = 0 m Vi= 0 m/s 28⁰ k = 2750 N/m m = 4.6 kg 2 Wnc+mghi +1⁄₂kx² W nc +½ = 0 J ½/2kx; ² = 2 mv; = = h = 2.8 m ½ mvf2 X₁ = 0 m hf = 0 m Vi=? m/s mghƒ+½ kxf² +½ mv₁² vf = √k/m* Xi =√(2750 N/m ÷4.6 kg) * (0.40 m) Vf = 9.78 m/s (XX))) = 350 N m
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A block attached to a horizontal spring that has a spring constant of 20 N/m oscillates between x = - 0.63 m and x = 0.63 m on a frictionless surface as shown. What is the kinetic energy of the block when its position is at x = 0, in Joules? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.
Let's see if you can apply what you learned about conservation of energy information about potential energy, kinetic energy, and total energy of the system. In the figure below, a simple pendulum is represented at various positions of its motion. The pendulum has a mass of 0.82 kg and in figure (a) it is moved to a maximum vertical position of 2.1 m. It is released from that position (starts from rest at the top of its motion, highest position) and is allowed to oscillate back and forth. We assume that there is no air resistance or friction in this example, so the pendulum would continue to oscillate forever unless a force was applied to stop it. We also assume that the acceleration due to gravity is 10 m/s2. Fill in the table below for the potential and kinetic energy of the pendulum mass at the various positions of its motion.Start by calculating the potential energy at the highest position using the fact that PE = mgh. At the highest position, the object is released and thus has no…
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A 388 g mass is hung on the spring assembly shown below. The mass stretches the springs to equilibrium. Each spring has a spring constant of 0.75 N/cm. Use g = 10 N/kg. Determine the work done in Joules on the bottom spring by the mass. Note: All units should be in kg and m.