Physics Fundamentals
Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 7, Problem 36P

(a)

To determine

To Find: The force constant of the spring.

(a)

Expert Solution
Check Mark

Answer to Problem 36P

  14.2N/m

Explanation of Solution

Given:

Mass is 0.250kg .

The mass is dropped from rest at point A, with the spring initially unstretched. As the mass falls, the spring stretches and reaches point B.

Formula Used:

The potential energy of the object is given as

  PE=mgh

Where,

  m= Mass

  g= Acceleration due to gravity

  h= Height

The potential energy of spring is given as

  PESpring=12Kx2

Where,

  K= Spring constant

  x= Distance moved

Calculation:

Using the conservation of energy, energy at point A is equal to energy at point B

  (PE)A=(KE)A+(P E Spring)Amgh=12mv2+(12Kx2)mgh=12mv212Kx2

Spring constant is derived as

  2mgh=mv2+Kx2Kx2=2mghmv2K=2mghmv2x2

Here,

  m=0.250kgg=9.8m/s2v=5.00m/sx=2.00m1.50m=0.50mh=2.00m

Substituting the values in above formula

  K=2( 0.25)( 9.8)(2)( 0.25) ( 5 )2 ( 0.5 )2K=9.86.250.25K=3.550.25K=14.2N/m

Conclusion:

Thus, force constant of the spring is 14.2N/m

(b)

To determine

To Find: The magnitude of the acceleration of the mass at point B

(b)

Expert Solution
Check Mark

Answer to Problem 36P

  18.6m/s2

Explanation of Solution

Given:

Mass is 0.250kg .

The mass is dropped from rest at point A, with the spring initially unstretched. As the mass falls, the spring stretches and reaches point B.

Formula Used:

According to Newton’s second law of motion, force is equal to mass times acceleration

  F=ma

Where,

  m= Mass

  a= Acceleration

Calculation:

Using Newton’s second law

  FNet=ma

Also, FNet=kxmg

Thus, equating the above equations

  kxmg=ma

On solving

  a=kxmgm

Here,

  k=14.2N/mm=0.250kgx=2.00m1.50m=0.50mg=9.8m/s2

Substituting the value in equation

  a=( 14.2)( 0.5)( 0.250)( 9.8)( 0.250)a=7.12.450.25a=4.650.25a=18.6m/s2

Conclusion:

Thus, magnitude of the acceleration of the mass at point B is 18.6m/s2 .

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