A spring is hung from the ceiling. A 0.450kg block is then attached to the free

Question

A spring is hung from the ceiling. A 0.450kg block is then attached to the free end of the spring. Whenreleased from rest, the block drops 0.150m before momentarily coming to rest. (a) What is the spring constant of thespring?
Enter anumber. 1 N/m

(b) Find the angular frequency of the block's vibrations.
Enter anumber. 2 rad/s A spiral staircase winds up to the top of atower in an old castle. To measure the height of the tower, a ropeis attached to the top of the tower and hung down the center of thestaircase. However, nothing is available with which to measure thelength of the rope. Therefore, at the bottom of the rope a smallobject is attached so as to form a simple pendulum that just clearsthe floor. The period of the pendulum is measured to be8.7 s. What is the height of thetower?
Enter anumber. 1 m (a) What is the spring constant of thespring?
Enter anumber. 1 N/m

(b) Find the angular frequency of the block's vibrations.
Enter anumber. 2 rad/s Enter anumber. Enter anumber. A spiral staircase winds up to the top of atower in an old castle. To measure the height of the tower, a ropeis attached to the top of the tower and hung down the center of thestaircase. However, nothing is available with which to measure thelength of the rope. Therefore, at the bottom of the rope a smallobject is attached so as to form a simple pendulum that just clearsthe floor. The period of the pendulum is measured to be8.7 s. What is the height of thetower?
Enter anumber. 1 m Enter anumber.

Explanation / Answer

Given that the mass of block is m = 0.45 kg extension in the length is x = 0.15 m --------------------------------------------- If the mass hanging '                   mg = kx                      k = mg /x                         = --------- N/m The angular frequency is = (k/m)                                          =------------ rad/s From the given data the time period o f simple pendulum, Time period of simple pendulum is T = (2)( L / g)           solve for L = --------- m               where acceleration due to gravity g = 9.8 m/s2

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