Inclined plane

1. How much work W we have to do to pull a body weighing 200 kg along an inclined plane with a length of 4 m to a total height of 1.5 m.
2. Find the force we need to exert to do this if we neglect frictional resistance.
3. Find the force we would need if we did not use an inclined plane and the body wanted to lift the body directly.
4. Compare the two forces.

Correct result:

W =  2943 J
F₁ =  735.75 N
F₂ =  1962 N

Solution:

$$\begin{gathered} m=200\text{ kg } \\ l=4\text{ m } \\ h=1.5\text{ m } \\ g=9.81{\text{m/s}}^2 \\ {F}_0=m\cdot g=200\cdot 9.81=1962\text{ N } \\ W=F_0\cdot h=1962\cdot 1.5=2943\text{ J} \end{gathered}$$

$$\begin{gathered} x=\sqrt{l^2-h^2}=\sqrt{4^2-1.5^2}\doteq 3.7081\text{ m } \\ {F}_1=F_0\cdot {\displaystyle \frac{h}{l}}=1962\cdot {\displaystyle \frac{1.5}{4}}={\displaystyle \frac{2943}{4}}={\displaystyle \frac{2943}{4}}\text{ N}=735.75\text{ N} \end{gathered}$$

$$\begin{gathered} F_2=F_0=1962=1962\text{ N } \\ {F}_2>F_1 \end{gathered}$$

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