Work and kinetic energy of stretched spring

[silentsaber]

Homework Statement

1.)A mass is on a frictionless horizontal surface and attached to a horizontal spring of
spring constant 200 N/m. If the mass is released from rest when the spring is
compressed by 10 cm, what will its kinetic energy be when the spring is stretched by
7 cm?

2)A child on a sled starts at the top of a 1.6 m high hill and slides along a straight
incline to the bottom at a constant velocity. If the mass of the child and sled is 40 kg,
what is the work done by friction during his slide down the hill?

Homework Equations

1.) 1/2mv^2=1/2KX^2
2.) W=1/2mvf^2-1/2mvi^2 or W=FD

The Attempt at a Solution

for the first one i tried plugging in the numbers to 1/2mv^2=1/2Kx^2 and tried to ifnd the kinetic energy that way but it didnt work what went wrong?

The second one i tired using the work energy theorem but but it said constant velocity so that woould cuase the both the final velocity and initil velocity to be the same and since the mass is the same wouldn't the W be 0? i also tried listing the forces out but then since it doens have an angle i got stuck... what did i do wrong i am confused

 

[lanedance]

Hi silentsaber

for a) are you comparing the difference in energy in the spring at 10cm compressed and 7cm stretched with the kinetic energy?

for b) try drawing the slope and forces for an arbitrary angle, to be constant velocity, the frictional drag must equal the gravtational force, so there is no net acceleration... see how the fits with your W = F.d equation

 

[Feldoh]

For number one why do you think all of the energy will be kinetic at the position is asks you to evaluate?

For number two you're only considering the effects of kinetic energy, which is constant throughout the problem -- What can be said about the other types of energy?