Question

A spring that can be assumed to be ideal hangs from a stand, as shown.

 

a. You wish to determine experimentally the spring constant k of the spring. 

i. What additional, commonly available equipment would you need? 

ii. What measurements would you make? 

iii. How would k be determined from these measurements? 

b. Assume that the spring constant is determined to be 500 N/m. A 2.0-kg mass is attached to the lower end of the spring and released from rest. Determine the frequency of oscillation of the mass. 

c. Suppose that the spring is now used in a spring scale that is limited to a maximum value of 25 N, but you would like to weigh an object of mass M that weighs more than 25 N. You must use commonly available equipment and the spring scale to determine the weight of the object without breaking the scale. 

i. Draw a clear diagram that shows one way that the equipment you choose could be used with the spring scale to determine the weight of the object, 

ii. Explain how you would make the determination. 

Answer 1

(a) Use a ruler and known mass. Hang the known mass on the spring and measure the stretch distance ∆x. The force pulling the spring F_sp is equal to the weight (mg). Plug into F_sp = k ∆x and solve for k

(c) Put the spring and mass on an incline and tilt it until it slips and measure the angle. Use this to find the coefficient of static friction on the incline us = tan θ. Then put the spring and mass on a horizontal surface and pull it until it slips. Based on F_net = 0, we have F_spring – μ_s mg, Giving mg = F_spring / μ. Since μ is most commonly less than 1 this will allow an mg value to be registered larger than the spring force. A simpler solution would be to put the block and spring in water. The upwards buoyant force will allow for a weight to be larger than the spring force. This will be covered in the fluid mechanics unit.