Problem 10We compress the spring in the above system by 0.5 meters. Assume that the spring constant, k = 1,000 N/mand the mass is 0.4 kg. After the mass is released it travels through a rough patch of uk = 0.6 for 4.0 meters.%3D(a) What is the initial spring potential energy of the system? (125 J)(b) If we let go of the spring, how fast will the mass be moving right after it leaves contact with the spring?(25 m/s)(c) How fast is the mass moving right after the rough patch? (24 m/s)(d) How high up will the mass be launched? (29.5 m)

Answered: We compress the spring in the above…

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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Problem 10
We compress the spring in the above system by 0.5 meters. Assume that the spring constant, k = 1,000 N/m
and the mass is 0.4 kg. After the mass is released it travels through a rough patch of uk = 0.6 for 4.0 meters.
%3D
(a) What is the initial spring potential energy of the system? (125 J)
(b) If we let go of the spring, how fast will the mass be moving right after it leaves contact with the spring?
(25 m/s)
(c) How fast is the mass moving right after the rough patch? (24 m/s)
(d) How high up will the mass be launched? (29.5 m)

Expert Solution

Step 1

(a)

Express the relation for the initial potential energy stored in the spring.

$\begin{array}{rcl} P E_{i} & = & \frac{1}{2} k x^{2} \\ = & \frac{1}{2} \times 1000 N / m \times {(0.5 m)}^{2} \\ = & 125 N \cdot m \times \frac{1 J}{1 N \cdot m} \\ = & 125 J \end{array}$

Here, PE_iis the initial spring potential energy, k is spring constant and x is the distance through which the spring is compressed.

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