A spring stores potential energy U0 when it is compressed a distance x0 from its uncompressed length.

a] In terms of U0, how much energy does it store when it is compressed twice as much? Uel/U0 =?

b] In terms of U0, how much energy does it store when it is compressed half as much? Uel/U0 = ?

c] In terms of x0, how much must it be compressed from its uncompressed length to store twice as much energy? x/x0 = ?

d] In terms of x0, how much must it be compressed from its uncompressed length to store half as much energy? x/x0 = ?

Initially, a particle is moving at 5.33 m/s at an angle of 37.9° above the horizontal. two seconds later, its velocity is 6.11 m/s at an angle of 54.2° below the horizontal. what was the particle's average acceleration during these 2.00 seconds in the x-direction (enter first) and the y-direction?

Part f - example: finding two forces (part i) two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force. the block in (figure 1) has a mass m=10kg and is being pulled by a force f on a table with coefficient of static friction îľs=0.3. four forces act on it: the applied force f (directed î¸=30â above the horizontal). the force of gravity fg=mg (directly down, where g=9.8m/s2). the normal force n (directly up). the force of static friction fs (directly left, opposing any potential motion). if we want to find the size of the force necessary to just barely overcome static friction (in which case fs=îľsn), we use the condition that the sum of the forces in both directions must be 0. using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as: fcosî¸â’îľsn=0 fsinî¸+nâ’mg=0 in order to find the magnitude of force f, we have to solve a system of two equations with both f and the normal force n unknown. use the methods we have learned to find an expression for f in terms of m, g, î¸, and îľs (no n).

Based on this activity, is kinetic energy always transformed into potential energy?