A block dropped on a spring, distance compressed unknown.

[ramses07]

1.
A block of mass m = 1.6 kg is dropped from height h = 61 cm (height above the spring, not total height) onto a spring of spring constant k = 1820 N/m (Fig. 8-38). Find the maximum distance the spring is compressed.

Homework Equations

K=-U, since all energy is conserved, work would equal zero.

The Attempt at a Solution

basically kinetic energy is zero, since its starts from zero and ends with zero.

so i this means that the potential energy must equate.

mgh (potential energy from block at H) = (kx^2)/2(potential energy from spring)

so basically the height from the spring is disclosed, but the spring compression isnt.

I tried this first

mg(x+h)=1/2kx^2

1.6kg * 9.8 m/s^2(x+.61cm)=910n/m *x^2


but it gives me an awkward quadratic equation, where the number under the square root would be negative.

I also tried to find to find the kinetic energy right before it touches the spring, and then apply it to the conservation of energy, where 1/2mvf^2=1/2kx^2 but that ddidnt work either, any suggestions?

 

[hotvette]

I also tried to find to find the kinetic energy right before it touches the spring, and then apply it to the conservation of energy, where 1/2mvf^2=1/2kx^2 but that ddidnt work either...

Pls elaborate. What didn't work? Be careful with units (i.e. cm vs m).

 

[ramses07]

well basically i found the kinetic energy right as it hits the spring, by using the equation
K=U.

which would be 1/2mvf^2-1/2mvi^2=-mgh

the initial velocity would be zero, so that cancels, and leaves me with

1/2mvf^2=-mgh

so i use the kinetic energy produced by the distance from the spring and plug it into the
conservation of elastic energy equation

-1/2mvi^2(kinetic energy produce by the drop)=1/2kx^2(potential elastic energy)

but this equation didnt produce the correct answer either, and i actually don't know the answer since its an online homework assessment.

 

[hotvette]

Looks good so far. What is your expression for x and why do you think the answer you got is wrong? What answer did you get by the way?

 

[benhou]

1.6kg * 9.8 m/s^2(x+.61cm)=910n/m *x^2

but it gives me an awkward quadratic equation, where the number under the square root would be negative.

Why would it give you a negative number? Did you put the equation to the form of ax^2+bx+c=0 before you start? -4ac is a positive number because a is negative and c is positive.