Please help solve this physics problem. Show all work please 7A 314 g object is attached to a massless spring and executessimple harmonic motion with a period of 0.200 sec. on africtionless horizontal surface. If the total energy of thesystem is 4.67 Joules find the following:the maximum speed of the objectabthe force constant of the springthe amplitude of the motion2

Answered: A 314 g object is attached to a…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 20P: A 200-g block is attached to a horizontal spring and executes simple harmonic motion with a period...

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Please help solve this physics problem. Show all work please

7A 314 g object is attached to a massless spring and executes
simple harmonic motion with a period of 0.200 sec. on a
frictionless horizontal surface. If the total energy of the
system is 4.67 Joules find the following:
the maximum speed of the object
a
b
the force constant of the spring
the amplitude of the motion
2

Expert Solution

Step 1

The total energy of the system is the addition of the spring potential energy and kinetic energy.

In this case, The total energy is converted into kinetic energy.

Let m be the mass, v be the velocity, E is the total energy.

$\begin{array}{rcl} E & = & \frac{1}{2} m v^{2} \\ v^{2} & = & \frac{2 E}{m} \\ = & \sqrt{\frac{2 E}{m}} \\ = & \sqrt{\frac{2 \times 4.67 J}{0.314 k g}} \\ v & = & 5.45 m / s \end{array}$

Therefore, the velocity is 5.45 m/s

Step 2

$ω = \sqrt{\frac{k}{m}} S i n c e, T = \frac{2 π}{ω} T = \frac{2 π}{\sqrt{\frac{k}{m}}} Solve for spring constant 'k'. T^{2} = \frac{4 π^{2}}{\frac{k}{m}} \frac{k}{m} = \frac{4 π^{2}}{T^{2}} k = m \times \frac{4 π^{2}}{T^{2}} Plug the known values. = 0.314 k g \times \frac{4 π^{2}}{{(0.200)}^{2}} k = 310 N / m$

Therefore, the spring constant is 310 N/m

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