The top end of a spring is held fixed. A block is hung on the bottom end as in Figure OQ15.13a, and the frequency f of the oscillation of the system is measured. The block, a second identical block, and the spring are carried up in a space shuttle to Earth orbit. The two blocks are attached to the ends of the spring. The spring is compressed without making adjacent coils touch (Fig. OQ15.13b), and the system is released to oscillate while floating within the shuttle cabin (Fig. OQ15.13c). What is the frequency of oscillation for this system in terms of f? (a) (b)(c) f (d) (e) 2f
Option (d) is correct answer for this question, since we got
Frequency of oscillation for a particle is given by:
Frequency of oscillation
Mass of object
Galileo thought about whether acceleration should be defined as the rate of change of velocity over time or as the rate of change in velocity over distance. He chose the former, so let's use the name "vroomosity" for the rate of change of velocity over distance. For motion of a particle on a straight line with constant acceleration, the equation gives its velocity v as a function of time. Similarly, for a particle's linear motion with constant vroomosity k , the equation gives the velocity v as a function of the position x if the particle's speed is at x = 0 . (a) Find the law describing the total force acting on this object of mass m. (b) Describe an example of such a motion or explain why it is unrealistic. Consider (c) the possibility of k positive and (d) the possibility of k negative.
A glider of mass m is free to slide along a horizontal air track. It is pushed against a launcher at one end of the track. Model the launcher as a light spring of force constant k compressed by a distance x. The glider is released from rest.
(a) Show that the glider attains a speed of .
(b) Show that the magnitude of the impulse imparted to the glider is given by the expression.
(c) Is more work done on a cart with a large or a small mass?
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