Answered: Spring Constant Data Suspended Mass:…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Steps-Part a
Step 1) In order to calculate the spring constant, the spring is positioned vertically, and a small mass is attached to its lower hook.
Step 2) Visit the site:
https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html
Step 3) Select the Lab icon.
Step 4) Make sure the damping is set to none. Using the ruler, measure the displacement of the spring and calculate the spring constant.
Step 5) The mass is removed and securely attached to an inelastic cord. On other end of the cord is attached to the spring. Another segment of cord is attached to the other side of the spring. The opposite end of this cord is left free. This is the end in which the system will be rotated. The setup is shown in Fig. 1. The ball is rotated in a horizontal circle.
Step 6) The radius of the system is measured before the spring is displaced.
Step 7) The system is now spun around until uniform circular motion is achieved and the spring displacement is measured.

Steps-Part b
Step 1) On a circle, sketch the components of the total acceleration from Eq. (4)
Step 2) Sketch the components of the total centripetal force acting on the ball from Eq. (5).

Spring Constant Data
Suspended Mass: 0.100 kg
Spring Displacement
m
Spring constant
N/m
Uniform Circular Mation Data
Mass of Ball: 10.0 g
Unstretched Spring Length: 10.0 cm
Total Cord Length: 0.5 m
Stretched Spring Length: 30.0 cm
Radius of Circle Before Displacement
m
Radius of Circle After Displacement
m
Centripetal Acceleration
m/s
Tangential Velocity
m's
Centripetal Force
N
Tension in the Cord
N
43
When the velocity of the ball is no longer constant, the circular motion is no longer uniform. The total
acceleration on the ball is now the sum of the tangential component and the radial component,
a = a, +a,
(4)
The total centripetal force acting on the ball is,
EF = F, + F,
(5)
Steps-Part b
Step 1) On a circle, sketch the components of the total acceleration from Eq. (4)
Step 2) Sketch the components of the total centripetal force acting on the ball from Eq. (5).

Introduction
In this laburatory unifum circular uotiuu (UCM) will be studicd and Newton's Sccund Law fo
centripetal acceleration and centripetal force will be verified. A plastic ball will be attached to a spring
and a cord and rotated in UCM. Since the spring constant and displacement of the spring can casily be
determined, the centripetal force can be calculated. From this, the tension in the cord can be determined.
When an object rotates in a circle with constant velocity, this type of motion is called uniform
circular motion. Consider a ball, which can be approximated as a particle, on a string rotating in a circle.
Newton's Second Law of motion still holds; however, the acceleration of the ball is given by the
expression as shown in Eq. 1. Where v, is the tangential velocity of the ball and r is the radius of the
circle. Substituting this back into Newton's Second Law gives us Eq. 2. Since direct measurements of
the tension of the string would be difficult a spring can be used to detemine the centripetal force acting
on the string. Hooke's law is given by Eq. 3.
From Eq. 3, k is the spring constant and x is the displacement of the spring. This is the amount
the spring has stretched from its equilibrium position. The negative sign is the restoring force of the
spring. Note that if the spring is displaced in the y-direction, just replace x with y.
a. =
(1)
EF = ma. =
(2)
E= -ki
(3)
A plastic ball will be attached to a spring and a cord and rotated in UCM, as shown in Fig. 1. The
spring constant of the spring is not known but can be detemined by measuring the displacement of the
spring and applying Hooke's law.
Cord
Cord
ww
wwiwi
Ax
Figure 1. Diagram for the ball-spring system indicating the displacement of the spring.

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