Work and Kinetic Energy Theorem

[holmeskaei]

Homework Statement

A 4.5 kg box slides down a 5.1m high frictionless hill, starting from rest, across a 2.4m wide horizontal surface, then hits a horizontal spring with spring constant 540 N/m. The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 2.4m long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.26.

A. What is the speed of the box just before reaching the rough surface?
B. What is the speed of the box just before hitting the spring?
C. How far is the spring compressed?
D. Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?

Homework Equations

W=(delta)K
K=1/2mv^2
Wnet=sum of all work
Fk=uk(n)(delta)(x)

The Attempt at a Solution

A. I did 1/2mv^2=mg(delta)(x) and I got 1/2(4.5)v=(4.5)(5.1) v=9.10m/s and it is incorrect.
Since I did this incorrectly and don't know why, I couldn't begin to attempt the rest of the problem. Any help is appreciated, thanks!

 

[LowlyPion]

A. I did 1/2mv^2=mg(delta)(x) and I got 1/2(4.5)v=(4.5)(5.1) v=9.10m/s and it is incorrect.
Since I did this incorrectly and don't know why, I couldn't begin to attempt the rest of the problem. Any help is appreciated, thanks!

I'd redo your calculation. I get a different number for the values using g = 9.8.

1/2*m*v² = m*g*h

v² = 2*g*h = 2*9.8*5.1