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**1. Homework Statement**

A box slides down an inclined plane (angle = 37*). The mass of the block is 35 kg, the coefficient of kinetic friction between the box and the ramp is 0.3, and the length of the ramp is 8 m. If it starts from rest at the top of the ramp, with what speed does it reach the bottom? Use energy equations.

**2. Homework Equations**

[itex]Work = \Delta K [/itex]

[itex]Work = \Delta E [/itex]

[itex]Work = \Delta K + \Delta U_g + \Delta E_t{}_h[/itex]

**3. The Attempt at a Solution**

I understand how to do this with motion equations:

V

_{F}

^{2}= V

_{i}

^{2}+2ad

V

_{F}

^{2}= 2ad

a = gsin(θ)-(F

_{FR}/m)

a = gsin(37) - (350cos(37)*0.3/35)

a = 6-2.4

V

_{F}

^{2}= 2 * 3.6 * 8

V

_{F}

^{2}= 57.6

V

_{F}= 7.6

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But I am at lost with energy equations

I calculated the Net Work of the system by calculating the Work of each Force and adding them together and I got 1020 J.

I want to plug this into either one of these equations:

[itex]Work = \Delta K [/itex]

1020 = (1/2)mv

^{2}

[itex]Work = \Delta K + \Delta U_g + \Delta E_t{}_h[/itex]

1020 = (1/2)mv

^{2}+ mgy + F

_{FR}* d

But what I don't understand is how the first equation can be equal to the second equation. Wouldn't I get a different answer? Why is the change in kinetic energy alone enough to demonstrate the change in all of the energies?

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