- #1
bob tran
- 17
- 0
Homework Statement
In the figure, a 700-kg crate is on a rough surface inclined at 30°. A constant external force P = 5600 N is applied horizontally to the crate. As the force pushes the crate a distance of 3.00 m up the incline, the speed changes from 1.40 m/s to 2.50 m/s. How much work does gravity do on the crate during this process?
Homework Equations
[itex]
W=KE_f - KE_i\\
W=Fd\cos{\theta}
[/itex]
The Attempt at a Solution
[tex]
W=KE_f - KE_i
W_{total}=\frac{1}{2}mv^2_f - \frac{1}{2}mv^2_i\\
W_{total}=\frac{1}{2}m(v^2_f-v^2_i)\\
W_{total}=\frac{1}{2}(700)(2.5^2-1.4^2)\\
W_{total}=1501.5 \ \texttt{J}\\ \ \\
W=Pd\cos{\theta}\\
W=5600(3)\cos{30}\\
W=14549.2 \ \texttt{J}\\ \ \\
W_{total}=W_g+W\\
W_g=W_{total}-W\\
W_g=1501.5-14549.2\\
W_g=-13047.7 \ \texttt{J}
[/tex]
The correct answer is [itex]-10300 \ \texttt{J}[/itex]. I am not sure how I would incorporate friction (if at all).