Cracking the SAT Physics Subject Test

account for the stretched

distance.

The net force on the block is

F = k(d + y) − mg

but this equation becomes F = ky because kd = mg (as we saw above).

Since the resulting force on the block, F = ky, has the form of Hooke’s law, we
know that the vertical simple harmonic oscillations of the block have the same
characteristics as do horizontal oscillations, with the equilibrium position, y = 0,
not at the spring’s natural length, but at the point where the hanging block is in
equilibrium.

Questions 9-12

A block of mass m = 1.5 kg is attached to the end of a vertical

spring of force constant k = 300 N/m. After the block comes to

rest, it is pulled down a distance of 2.0 cm and released.

9. How far does the weight of the block cause the spring to stretch
   initially?


10. What are the minimum and maximum amounts of stretch of the
    spring during the oscillations of the block?


11. At what point(s) will the speed of the block be zero?


12. At what point(s) will the acceleration of the block be zero?

Here’s How to Crack It

9. The weight of the block initially stretches the spring by a distance of