How Do You Calculate Spring Compression and Cart Speed After Collision?

[x86]

Homework Statement

A 1.2 kg dynamics cart is rolling to the right along a horizontal lab desk at 3.6 m/s, when it collides head on with a spring bumper that has a spring constant of 2.00 * 10^2 N/m.

a) Determine the maximum compression of the spring
b) Determine the speed of the cart at the moment that the spring was compressed by 0.10 m.

Homework Equations

E mechanical = E potential + E kinetic
E kinetic = 1/2 m v^2
E elastic = 1/2 k x^2
E gravitational = mgh

The Attempt at a Solution

a) I got 0.28 m, and the book agrees.

b) The answer should be 1.3 m/s. Here's what I get:

Eg is constant, because the height doesn't change. Equal is:

Et = Ee + Ek

In the previous solution, i set Ee2 + 0 = Ek1 + 0 since before there is no elastic energy and afterwards there is no kinetic energy

So Et = 1/2 * 2 * 10 ^2 N/m * 0.28 ^ 2 m ^2 = 7.84 joules

Et - Ee = Ek

7.84 J - 1/2 * 2 * 10^2 N/m * 0.10^2 m^2 = Ek = 6.84 J

1/2 * 1.2 kg * v^2 = 6.84 J

sqrt(6.84 / 1.2 kg / 0.5) = v^2 = 11.4 m^2 / s^2

Square rooted I get 3.4 m/s

The book says I'm doing b wrong, but I don't understand what I did wrong, or if the book is wrong.

 

[Sunil Simha]

I'm getting the same answer as you.

 

[sankalpmittal]

Square rooted I get 3.4 m/s

The book says I'm doing b wrong, but I don't understand what I did wrong, or if the book is wrong.

Hello !

Do not worry. You are correct and if book does not concur with you, its wrong.

I get 3.36 m/s which is approximately same as your answer.

 

[haruspex]

Fwiw, you can get the book answer by making the mistake of setting the KE equal to the PE when the spring is compressed .1 m.