What Is the Distance the Block Travels Through the Air?

[rocapp]

Homework Statement

The spring in the figure has a spring constant of 1400N/m . It is compressed 16.0cm , then launches a 200g block. The horizontal surface is frictionless, but the block's coefficient of kinetic friction on the incline is 0.210.

FIGURE ATTACHED

What distance d does the block sail through the air?


Correct answer: 13.4 m

Homework Equations

F(spring)=-kx
F(friction)=μ_f*F_N
Work=Fdcos(θ)
Work=(0.5mv₂²)-(0.5mv₁²)

The Attempt at a Solution

F(spring)=(-1400 N/m)(0.16 m)= 224 N

F(friction)=(0.210)(cos(45))(0.2)(9.8)= 0.29 N

224-0.29= 223.71

Work=223.71d
Work=(0.5)(0.2)(?)-(0.5)(0.2)(?)


I think that I should be finding the work and then find distance by dividing by the force. However, I'm not sure how to find the two velocities.

 

[tiny-tim]

hi rocapp!

I think that I should be finding the work and then find distance by dividing by the force. However, I'm not sure how to find the two velocities.

you can't find d from work or energy, you'll need the usual projectile equations

to find the initial speed (just before d), use the work-energy method that you have been using (with the block starting with zero speed), but use gravity also