Question

Mass on a spring

1-By doubling the mass of the objet attached to the spring the period of the oscillations will change by a factor of

	-	4
	-	0.5
-		1.4
-		2

2-According to Hook's Law, the force of a spring is proportional to

		-the change in the length of the spring
		-the length of the spring
		-the mass of the spring
		-the change in the mass of the spring

3-The units for the spring constant are

		-N/m
-		N
		-N/kg
		-m/s2

4- A 0.26kg object is placed at the end of a vertical spring. The unstretched (natural) length of the spring is 0.24m. After adding the mass the final length is 0.38m. What is the spring constant (in N/m)?

5- A 0.39kg object is placed at the end of a vertical spring with a spring constant k=23.43N/m . Assuming the spring is massless, what would be the period of oscillations (in s) ?

6- In the previous problem, what is the theoretical value for the period of oscillations, if the hanging mass is 0.2kg and the spring is massless?

-		2s
	-	1s
	-	0.6s
	-	1.4s

7- In the previous problem what is the theoretical value for the period of the oscillations, if the mass is 0.2 kg and the mass of the spring is 0.15 kg?

-		2.1 s
		-1.2 s-
		- 0.67 s
		- 1.5 s

8- The period of oscillations for a mass spring system would ___ if the experiment was done on the surface of the moon. NOTE: The acceleration due to gravity on the surface of the moon is 1/6th of the acceleration due to gravity on Earth.

-		quadruple
	-	double
		- increase by a factor of 6
	-	stay the same

9- The potential energy of a mass-spring system when the spring is fully compressed and the mass is at rest is 200 J. After releasing the mass, assuming there is no dissipative force, the system will oscillate. At a point during the oscillation the potential energy of the system is 50 J. What is the kinetic energy of the mass at that point, assuming the spring is massless?

-		50 J
-		250 J
-		150 J
	-	200 J

Answer 1

You can skip ahead to the part in red --- where I write ---

Given:

Mass on a spring

1-By doubling the mass of the objet attached to the spring the period of the oscillations will change by a factor of

	-	4
	-	0.5
-		1.4
-		2

2-According to Hook's Law, the force of a spring is proportional to

		-the change in the length of the spring
		-the length of the spring
		-the mass of the spring
		-the change in the mass of the spring

3-The units for the spring constant are

		-N/m
-		N
		-N/kg
		-m/s2

4- A 0.26kg object is placed at the end of a vertical spring. The unstretched (natural) length of the spring is 0.24m. After adding the mass the final length is 0.38m. What is the spring constant (in N/m)?

5- A 0.39kg object is placed at the end of a vertical spring with a spring constant k=23.43N/m . Assuming the spring is massless, what would be the period of oscillations (in s) ?

6- In the previous problem, what is the theoretical value for the period of oscillations, if the hanging mass is 0.2kg and the spring is massless?

-		2s
	-	1s
	-	0.6s
	-	1.4s

7- In the previous problem what is the theoretical value for the period of the oscillations, if the mass is 0.2 kg and the mass of the spring is 0.15 kg?

-		2.1 s
		-1.2 s-
		- 0.67 s
		- 1.5 s

8- The period of oscillations for a mass spring system would ___ if the experiment was done on the surface of the moon. NOTE: The acceleration due to gravity on the surface of the moon is 1/6th of the acceleration due to gravity on Earth.

-		quadruple
	-	double
		- increase by a factor of 6
	-	stay the same

9- The potential energy of a mass-spring system when the spring is fully compressed and the mass is at rest is 200 J. After releasing the mass, assuming there is no dissipative force, the system will oscillate. At a point during the oscillation the potential energy of the system is 50 J. What is the kinetic energy of the mass at that point, assuming the spring is massless?

-		50 J
-		250 J
-		150 J
	-	200 J

The period of oscillation of a mass --- (kg's) on a spring of stiffness ---( ) is :

  --- ( in units of seconds ) .

1. If the mass is doubled --- we go from to   and   stays constant :

  --- SOLUTION .

2. According to Hook's Law (   ) , the force of a spring is proportional to :

     .

3. The units for the spring constant are :

   .

4. A 0.26kg object is placed at the end of a vertical spring. The unstretched (natural) length of the spring is 0.24m. After adding the mass the final length is 0.38m. What is the spring constant (in N/m)?

The mass is --- . The weight of the mass --- stretches the spring from   to   :

===>

--- SOLUTION .

5.  A 0.39kg object is placed at the end of a vertical spring with a spring constant k=23.43N/m . Assuming the spring is massless, what would be the period of oscillations (in s) ?

Tthe mass is   and the spring constant is   ; so , the period of oscillation is assuming that the mass of the spring can be neglected :

  --- SOLUTION .

6.In the previous problem, what is the theoretical value for the period of oscillations, if the hanging mass is 0.2kg and the spring is massless?

We then have instead that the mass is ---   , We then have the period is :

  --- SOLUTION .

7. In the previous problem what is the theoretical value for the period of the oscillations, if the mass is 0.2 kg and the mass of the spring is 0.15 kg? .

The mass is ---    and the spring mass is --- . It can be shown that the total equivalent mass placed at the position of the spring is --- .

We then have the period of the system is :

--- Choose    --- SOLUTION .  

8.  The period of oscillations for a mass spring system would if the experiment was done on the surface of the moon. NOTE: The acceleration due to gravity on the surface of the moon is 1/6th of the acceleration due to gravity on Earth.

  Note that the period of oscillation --- is independent of the local acceleration of gravity --- it only depends on mass and the sring constant ---   . That is why the period would be the same on the moon .

9. The potential energy of a mass-spring system when the spring is fully compressed and the mass is at rest is 200 J. After releasing the mass, assuming there is no dissipative force, the system will oscillate. At a point during the oscillation the potential energy of the system is 50 J. What is the kinetic energy of the mass at that point, assuming the spring is massless?

There are no dissipative forces ; so , the total mechanical energy which is the sum of potential energy and kinetic energy is constant :

total initial potential energy because mass is initially at rest ===>

We thus have when   :

  --- SOLUTION .