7) A mad scicentist wants to design a mechanical to successfully launch such a p

Question

7) A mad scicentist wants to design a mechanical to successfully launch such a payload? [Note that the mass of the Earth is about 6 x 10M kg and its radius is about 6.4 x 10 meters.] spring that has the ability to launch a 4 metric ton payload into deep space. Assuming that the spring's maximum compression is 150 m, what would its stifness have to be Answer Bubmit Al Anmwers 8) If mad scientist invets a new material that is twice as stiff as the material in the previous problem, what speed will the payload have when it is very far away from the Earth, assuming a compression cqual to the one in the previous problem? Answer: Not yet correct, tries 1/35 A Aware Hint: What type of energy will be left over when the payload is very far from the Earth? What is the total initial encrgy of the system before the payload is released? 9) You want to determine the stiffness constant of a spring in the physics lab. You attach one end of the spring to a hook that lets it dangle downward. On the other end of the spring you attach a 300 gram weight. You position. What is the stiffness constant of the spring? Answer: keep holding the weight, but lower it down until the spring reaches a stretch of 3 cm. At this point you focl a slight resistance to stretching the spring any further. When you relcase the weight,it hangs stably in is

Explanation / Answer

7)Given,

m = 4 metric ton = 4000 kg ; x = 150 m

We know that the mass spring system has to be vertical for this problem. For the vertical spring we know that

mg = kx =>k = mg/x

k = 4000 x 9.81/150 = 261.6 N/m

Hence, k = 261.6 N/m

8)from conservation of energy

1/2 k x^2 = 1/2 m v^2

v = x sqrt (k/m)

v = 150 x sqrt (261.6/4000) = 38.36 m/s

Hence, v = 38.36 m/s

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