Putty dropped on a frame suspended from a spring.

[jax988]

Homework Statement

A 0.150 kg frame, when suspended from a coil spring, stretches the spring 0.050 m. A 0.200 kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm

The collision between the two is perfectly inelastic.

Find the maximum distance the frame moves downward from its initial position.

Homework Equations

$$\Delta{K} + \Delta{U} + \Delta{U_o} = 0$$

The Attempt at a Solution

I plugged in the energies into the above equations, and it didn't bring me closer to an answer. I'm not sure how I can relate momentum to energy in this, with a completely inelastic collision.

Any help is appreciated. Thank you.

 

[supratim1]

hello Jax988! welcome to PF!

remember that momentum is conserved. so find the common velocity of putty ad frame.

then with this velocity as 'v', and m = mass of putty + frame, find kinetic energy (initial)

then equate it with 1/2.k.x^2 + mgx
k = spring constant.

x is the required distance.

 

[ashishsinghal]

I plugged in the energies into the above equations, and it didn't bring me closer to an answer. I'm not sure how I can relate momentum to energy in this, with a completely inelastic collision.

In inelastic collision mechanical energy is not conserved. So you cannot directly use energy conservation. But there is no harm in using it when collision is completed.

 

[jax988]

I guess my problem is the quadratic as well. If I carry out the energy equation after the collision, I have the distance x included. However, it takes the form of a quadratic equation.

When using the equation given.

$$\frac{1}{2}Mv_0^2 - Mgd + \frac{1}{2}kd^2 - \frac{1}{2}kx_f^2 = 0$$

Where $$M$$ is the combined mass of the frame and putty, $$x_f$$ is the initial stretch of the spring due to the weight of the frame, $$d$$ is the max distance due to collision the spring stretches, and $$v_0$$ is the initial velocity.

So now $$d$$ is the variable of a quadratic equation, and when I try to solve using the quadratic formula, I get imaginary numbers.

Edit: Attempted again with freshly made calculations. The results after plugging the numbers into the equation and attempting to solve with the quadratic formula resulted in real numbers, albeit negative.