How Do You Calculate Spring Constants and Bullet Speeds in Physics Problems?

[94sonoma]

1.) A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0J of work is required to compress the spring by .16m. If the mass is released from rest with the spring compressed, it experiences a maximum acceleration of 10 m/s^2.

Find the value of the spring constant.

i did:

W=Fd
F=W/d
F= 18.75N

then i used:
k=F/x
k=18.75N / .16m
k=117.1875N/m

and its not right... i also tried diving the 18.75 by .32m and it still isn't right



problem 2.)
A 30.0g bullet strikes a .607 kg block attached to a fixed horizontal spring whose spring constant is 6.7E3 N/m and sets it into vibration with an amplitude of 21.3cm. What was the speed of the bullet before impact if the two objects move together after impact?

I went on to use:
1/2(mass of bullet)v^2 = 1/2kA^2
solved for v

v=sq.rt.(((6.7E3N/m)(.213m)^2)/.03kg)
v= 100.659
and it isn't right..dont know where to go from here


problem 3.)
A bunjee jumper with mass 69.0kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 34.9s. He finally comes to rest 22.0m below the level of the bridge. Calculate the spring constant of the bungee cord. Calculate the unstretched length of the bungee cord.

I started out by find the persons force downward but now have no clue where to go from here. I can't even fathom how to set it up...my guess is that i need to do something with dividing the time out into 8 pieces...i have no clue...


any help would be awesome - thanks. also, this is an algebra based physics course so no calculus ;)

 

[vincentchan]

1.energy stored in the spring is 1/2 kx^2, it is irrelevant to the accelaration, ring the bell?
2.this one is a little bit tricky... use conservation of momentum find the velocity of the block+bullet... then apply your 1/2mv^2 = 1/2kA^2
3.I'll assume the gravity turns off after the man reaches the 22.0m below the bridge... (otherwise the calculation will be a little bit more complicated and I don't think you could able to follow)
what is the period of the oscillation?
how does the oscillation period related to the spring constant and the mass?

 

[HallsofIvy]

The very first formula you use: W=Fd
is true only for a constant force. With a spring the force is not constant.

You have to use 1/2 kx^2 that vincentchan gave you.