Energy Principle with Springs

mardi 29 octobre 2013

1. The problem statement, all variables and given/known data

So we have a test this Friday over several topics in modern mechanics. Our professor gave us last year's test to use as a study guide, but hasn't posted the solutions yet. I'm not sure I'm doing this one right so I was hoping someone could check my work! I feel like my number is a bit big.

A spring whose stiffness is 3500 N/m is used to launch a 4 kg block straight up in the classroom. The

spring is initially compressed 0.2 m, and the block is initially at rest when it is released. When the block is 1.3

m above its starting position, what is its speed? Be sure to specify what objects are in your system and what

objects are in the surroundings. Show all your work, starting from fundamental principles and/or definitions

system: block, spring, gravity

surrounding: none

U_s = Potential Energy of Spring

U_g = Potential Energy of Gravity

k_s = spring stiffness

s_i & s_f = stretch

2. Relevant equations

E_f = E_i + W

U_{s_f} + U_{g_f} + K_f = U_{s_i} + U_{g_i} + ~~K_i~~ + W

K_f = U_{s_i} - U_{s_f} + U_{g_i} - U_{g_f}

.5mv_f² = .5k_s(s_i - s_f)² + mg(y_i - y_f)

v_f² = (ks(s_i - s_f)²)/m + 2g(y_i - y_f)

v_f = sqrt((ks(s_i - s_f)²)/m + 2g(y_i - y_f))

3. The attempt at a solution

I might have messed up the stretch, I'm currently looking over it.

I got v_f = 44.038 m/s