1996 AP Exam Question: Lab Situation with spring

[rvhockey]

A spring that can be assumed ideal hangs (vertically) from a stand.
a. You wish to determine the spring constant k of the spring.
i. What additional equipment do you need?
ii. What measurements would you make?
iii. How would k be determined from these measurements?
b. Assume the spring constant is 500 N/m. A 2 kg mass is attached to the end of the spring and released from rest. Determine the frequency of the oscillation of the mass.
c. Suppose that the spring is now used in a spring scale that is limited to a maximum value of 25N, but you would like to weigh an object of mass M that weighs more than 25N. You must use commonly available equipment and the spring scale to determine the weight without breaking the scale.
i. Draw a clear diagram that shows one way that the equipment could be used with the spring scale to determine the weight of the object.
ii. Explain how you would make the determination.


F_spring = kx
freq = 1/2pi * sqrt(k/m)



I did a and b easy, so you don't need to explain those to me. I'm lost without a paddle for c though, and the only thing I can think of is if you used a string, put the scale so it is parallel to the ground, put the string around a pulley, and put the mass perpendicular to the ground and use torque to figure of the weight. Other than that I'm stumped

 

[redargon]

Using a pulley system or a lever system and measuring the force from the generated torque is a good way to do it, i think.

Could you use 2 scales in parallel to measure the force/weight? That would be the simplest, I'd think.

 

[lonewolf5999]

I agree. Using two or more springs in parallel would distribute the weight evenly over the springs, so you wouldn't exceed the maximum scale reading allowed on each spring scale.

 

[rvhockey]

"now used in a spring scale that is limited to a maximum value of 25N, but you would like to weigh an object of mass M that weighs more than 25N. You must use commonly available equipment and the spring scale to determine the weight"

one spring scale but I think the torque thing is fine, thanks

 

[rvhockey]

but i am having a little trouble figuring out how i can determine the weight using torque.

Does anyone have any ideas?

 

[timmay]

Imagine a seesaw with one end connected to your unknown mass and the spring attached between the other end and a rigid floor. Now, what happens when you move the fulcrum (or pivot point)? If the maximum force that can be applied by the spring is 25N, how can you relate the position of the fulcrum to the maximum force applied at the other end?