Please answer the following parts of the question below and show work for each p
ID: 1788626 • Letter: P
Question
Please answer the following parts of the question below and show work for each part.
2.AU- shaped valley with a frictionless surface contains a block of mass m-2kg at an initial height of = 10 m above the valley floor, and on the other side a vertical spring (k 200 N/ m) with equilibrium position a distance hg-9 m above the valley floor. Lety- Obe the spring's equilibrium point. A y=0 ho h, a)14 pts Briefly describe the long- term motion of the block if it is dropped from rest. b) [6 pts] For what initial downward speed vo of the block will its maximum height on the spring side equal its initial height (i.e. 10 m above the valley floor) c)[10 pts] Suppose the block starts with the initial downward speed vo you found in part c. For what compression of the spring is the block's instantaneous speed equal to vo?Explanation / Answer
A) block will move to spring and compress to it by some distance d, stops momentarily then starts moving donwards and then it will reach to its initial position.
and this will continue.
(b) mvo^2 /2 = k (ho - hs)^2 /2
2 *vo^2 = 200 (10-9)^2
vo = 10 m/s
(C)
m*g*ho + m *vo^2 + 0 = m*g*h + m*vo^2 + k(ho - h)^2 /2
2 * 2 * 9.8 *10 = 2 x 2 x 9.8 x h + 200 (10 - h)^2
392 = 39.2 h + 20000 + 200 h^2 - 4000 h
200 h^2 - 3960.8 h + 19608 = 0
h = 9.8 m
compression = ho - h = 10 - 9.8 = 0.2 m