How Do You Calculate Stopping Distance Using Conservation of Mechanical Energy?

[pmfinnegan2]

If anyone could help me with my homework I would GREATLY appreciate it. I am totally lost. There are 2 questions. If you could tell me what/how to do it, I'd be happy to do it. I just need to know how. Thanks so much

Here is part 1:

A .102 kg block sliding on a frictionless surface with initial velocity of .70 m/s slams into a spring at a horizontal coordinate Xo = 0. The spring brings the block to a stop (v=0) at some coordinate X. Use the conservation of mechanical energy to find the stopping distance.

note: since the spring resists with force F=kx the potential energy is Ep=Fx x=kx^2 where k is called the force constant we'll use k = 4.45 N/m

Given:
m=.102 kg
Vo=.70 m/s
Xo=0
k=4.45 N/m
v=0

 

[Pyrrhus]

The block will start with only kinetic energy and then it will end up only with spring potential energy.

 

[CaptainQuaser]

as you should know

Kinetic Ek = 1/2 mv^2
Spring Es = 1/2 kx^2 i think, or is it kx^2

either way, it should be in your book, look it up

 

[Curious3141]

The spring's potential energy upon compression by X is given by $\frac{1}{2}kX^2$

Equate the block's initial Kinetic Energy to the final potential energy stored in the spring to solve for X.

 

[pmfinnegan2]

I am still lost. Can anyone explain it on a more elementary level? I've been at this for about 10 hours and my brain is fried. I checked the book but it isn't telling me much.

 

[Curious3141]

What is the law of conservation of energy ? What is Kinetic Energy (KE), and what is Potential Energy (PE) ? What happens to the block's KE when it encounters the spring's resistance. When the spring gets compressed, what happens to its PE ? When the block has slowed to a complete standstill, its KE is zero, so where has that energy gone ? What can you say about the PE stored in the spring ?

Start by answering those questions, then put the equations in.