Answered: A horizontal spring with force constant…

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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Question

A horizontal spring with force constant

k = 665 N/m

is attached to a wall at one end and to a block of mass

m = 2.35 kg

at the other end that rests on a horizontal surface. The block is released from rest from a position 4.30 cm beyond the spring's equilibrium position.

(a) If the surface is frictionless, what is the speed of the block as it passes through the equilibrium position?
m/s

(b) If the surface is rough and the coefficient of kinetic friction between the box and the surface is

?_k = 0.300,

what is the speed of the block as it passes through the equilibrium position?
m/s

Expert Solution

Step 1

^a)

Apply the energy conservation equation and substitute the required values to calculate the speed of the block.

$\begin{array}{l} K E = S E \\ \frac{1}{2} m v^{2} = \frac{1}{2} k x^{2} \\ m v^{2} = k x^{2} \\ (2.35 kg) v^{2} = (665 N/m) {(4.30 cm \times \frac{1 m}{100 cm})}^{2} \\ v = 0.72 m/s \end{array}$

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