Solve Spring Mass Change Problem: Find Distance for 4kg Mass

In summary, when the 4 kg is attached to the spring, the equilibrium position is 12 cm from the top. When it's dropped, the equilibrium position will be stretched to 18 cm.
  • #1
Jamboree
2
0
I feel like I must be missing something here. I think I'm following the right steps, yet my answer doesn't match one of the choices.

Homework Statement



A Mass of 3.0kg is hung from a spring, causing it to stretch 12 cm at equilibrium. The 3.0kg mass is then replaced by a 4.0kg mass and the new block is released from the unstretched position. How far will the 4.0kg mass block fall before its direction is reversed?

a) 9 cm
b) 18 cm
c) 24 cm
d) 32 cm
e) 48 cm

Homework Equations


Spring Constant-
k= F/x

The Attempt at a Solution


First, I found the force of the 3kg block.
F= 3 * 9.8 = 29.4N
Next, I found the spring constant K
K= F/x[distance] = 29.4/.12m= 245

I Worked backwards to find the distance traveled by the 4kg block, like this.
K=F/x
245= (4*9.8)/x
x=.16m = 16 cm
Which is not one of the options. Where have I gone wrong?

Thanks for any help, it is much appreciated.
 
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  • #2
Welcome to PF.

When you replace the weight and release it, the potential energy of the weight, will become kinetic energy and will also start adding potential energy into the spring. The maximum distance it falls will be when all the gravitational energy becomes potential energy in the spring and kinetic energy becomes momentarily 0.

m*g*h = 1/2*k*h2
 
  • #3
Jamboree said:
I feel like I must be missing something here. I think I'm following the right steps, yet my answer doesn't match one of the choices.

Homework Statement



A Mass of 3.0kg is hung from a spring, causing it to stretch 12 cm at equilibrium. The 3.0kg mass is then replaced by a 4.0kg mass and the new block is released from the unstretched position. How far will the 4.0kg mass block fall before its direction is reversed?

a) 9 cm
b) 18 cm
c) 24 cm
d) 32 cm
e) 48 cm

Homework Equations


Spring Constant-
k= F/x

The Attempt at a Solution


First, I found the force of the 3kg block.
F= 3 * 9.8 = 29.4N
Next, I found the spring constant K
K= F/x[distance] = 29.4/.12m= 245

I Worked backwards to find the distance traveled by the 4kg block, like this.
K=F/x
245= (4*9.8)/x
x=.16m = 16 cm
Which is not one of the options. Where have I gone wrong?

Thanks for any help, it is much appreciated.


You are finding the new equilibrium position when the 4 kg is attached.
But they ask what happens when the 4kg is dropped. Then the srping will stretch way beyond the new equilibrium position. What you must use is conservation of energy in the form mgh = 1/2kx^2
 
  • #4
Wow, I'm amazed I managed to completely ignore that. It always seems so obvious in retrospect...I'm going to go ahead and blame the late hour and lack of sleep.

Thank you both for the help, I've got it now.
 

Related to Solve Spring Mass Change Problem: Find Distance for 4kg Mass

What is the formula for solving a spring mass change problem?

The formula for solving a spring mass change problem is F = -kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

How do you find the distance for a 4kg mass in a spring mass change problem?

To find the distance for a 4kg mass in a spring mass change problem, you will need to use the formula F = -kx and solve for x. Plug in the values for F (the force applied to the spring) and k (the spring constant) and solve for x, which will give you the distance the spring will stretch or compress with a 4kg mass.

What is the unit of measurement for the spring constant?

The unit of measurement for the spring constant is N/m (newtons per meter).

How does the mass of the object affect the spring's displacement?

The mass of the object affects the spring's displacement because it determines the amount of force applied to the spring. The heavier the object, the greater the force, and therefore, the greater the displacement of the spring.

Can the spring constant change in a spring mass change problem?

Yes, the spring constant can change in a spring mass change problem. It depends on the type of spring being used and other factors such as temperature and material composition. However, in a simple spring mass change problem, the spring constant is typically assumed to be constant.

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