Help: Solve Kinetic Energy of Pushing Piano up an Incline

[buffgilville]

A mover is pushing a piano whose mass is 328.4 kg up a plane that is inclined 9.1 degrees to the horzontal. The force of 722.1 Newtons is applied parallel to the incline, whose length is 7.4 meters. Assuming that all contacts are smooth, find the kinetic energy of the piano at the end (in Joules).

F=ma
722.1cos9.1 x + 722.1sin9.1 y = 328.4a x
a = 2.17

vsquared = initial vsquared +2ax
v = 5.67 m/s

K=(1/2)mvsquared
K= 5278.85 joules

but the correct answer is 1574.97 joules. Can someone please tell me what I did wrong?

 

[thermodynamicaldude]

Try to draw a free body diagram. In one direction, you have 722.1 Newtons acting on the piano. In the opposing direction, you have the force of gravity.

F = ma

Mover's force - force of gravity (sin 9.1 * mg) = Net Force

Acceleration = Net Force/Mass

...with this acceleration, just use the same method you had above to find Kinetic Energy.

 

[buffgilville]

thermodynamicaldude, I tried your method, but I got 1573.07 joules. The answer is 1574.97 joules.

722.1 - 509.52 = 212.58
212.58/328.4 = 0.647
v = 9.5756
k = 1573.07

 

[Parth Dave]

The process seems right. The error may just be because of rounding.

 

[buffgilville]

no, it can't be because of rounding because I calculated it straight through without rounding.

 

[Parth Dave]

So did I, but I got a slightly different answer. Which wasn't the same as yours or what it should be.