Question related to fuzzy dice inertia and force

Question

the image itself cannot be shown because its not letting me so I'll describe it: on the top is a car rearview mirror and a spring perpendicular to it on one end being fuzzy dice. (Essentially imagine fuzzy dice but instead of string its a spring) there are no numbers in the image so don't worry about that.

1) Your friend starts out by hanging is fuzzy dice from a spring. On the surface of the Earth, he finds the length of the spring to be 8.4 cm. With his car drifting in space (as in diagram B, above) he finds the length of the spring to be 3.5 cm. What would be the length of the spring in a situation similar to diagram C above, if the car were accelerating upward at a rate of 9.8 m/s²?

2) What would be the length of the spring in a situation similar to diagram C above if the car were accelerating upward at a rate of 12.4 m/s²?

3) What would be the length of the spring in a situation similar to diagram C above if the car were accelerating upward at a rate of 6.6 m/s²?

NOTE: ANSWER 1-3 since they correspond with each other and make sure to bold them

Answer 1

Hi Nathan R.,

Essentially you are being asked to determine the spring constant, then apply it with various loads. Since the relaxed length of the spring is 3.5 cm and the length under 1g load is 8.4 cm, the spring constant is (8.4 - 3.5 = 4.9) cm/1 g of dice force. Then accelerating upwards at 1 g will put a 2 g load on the spring, hence it will stretch to 4.9 * 2 = 9.6 cm + 3.5 cm = 13.1 cm. The rest of the problemlets are solved similarly. Don't forget to add the inertial (static) gravitational "force" when calculating total loads under various object accelerations!

For convenience I've left off the detailed units on the spring constant; you can figure them in more detail if you want, though you don't need to. You are just ratioing length to force here.

--Cheers, -- Mr. d.