91影视

Distance between buildings$\left(\text{D}\right)=4.0\text{鈥�}m$

$\text{h}=0.490\text{鈥�}m$

At$\text{x}=0,{\text{F}}_{\text{h}}=20\text{鈥�}kN\left(\frac{{10}^3\text{鈥塏}}{1\text{鈥塳狈}}\right)=2.0脳{10}^4\text{鈥塏}$

At$\text{x}=4.0,{\text{F}}_{\text{h}}=25\text{鈥�}kN\left(\frac{{10}^3\text{鈥塏}}{1\text{鈥塳狈}}\right)=2.5脳{10}^4\text{鈥塏}$

We find the length of the ramp first, using trigonometry (Pythagoras theorem). After finding the length, we take the value for the horizontal force at the displacement of the man on the ramp. Using those conditions, we find the mass of the man and the ramp.

Formula:

${鈭�}_{}^{}{\text{M}}_{\text{anypointonthebeam}}=0$

$Weight=mg$

Length of the ramp from Pythagoras theorem,

$\begin{array}{c}L=\sqrt{D^2+h^2}\\ =\sqrt{{\left(4.0\text{鈥�}m\right)}^2+{\left(0.49\text{鈥�}m\right)}^2}\\ =\sqrt{16.24\text{鈥�}{m}^2}\\ =4.03\text{鈥�}m\end{array}$

$\begin{array}{l}tan胃=\frac{h}{D}\\ 胃=\left(\frac{0.49}{4.0}\right)\\ 胃=6.98掳\end{array}$

Taking moment at the hinge point and assuming$\text{x}=0$,

${鈭�}_{}^{}{\text{M}}_{\text{x=0}}=0$

$\begin{array}{c}(Weightoframp脳\frac{L}{2}脳cos6.98掳)-({\text{F}}_{\text{h}}脳0.490\text{鈥�}m)=0\\ (Weightoframp脳\frac{\text{L}}{\text{2}}\text{脳肠辞蝉6.98}掳)=({\text{F}}_{\text{h}}脳0.490\text{鈥�}m)\\ Weightoframp=\frac{\left({\text{2脳贵}}_{\text{h}}\text{脳0.490鈥尘}\right)}{\text{L脳肠辞蝉6.98掳}}\\ m_{ramp}g=\frac{\left({\text{2脳贵}}_{\text{h}}\text{脳0.490鈥尘}\right)}{\text{L脳肠辞蝉6.98掳}}\end{array}$

$\begin{array}{c}{m}_{ramp}=\frac{\left({\text{2脳贵}}_{\text{h}}\text{脳0.490鈥尘}\right)}{\text{g脳L脳肠辞蝉6.98掳}}\\ =\frac{(2脳2.0\text{鈥�}脳{10}^4\text{鈥�}N脳0.490\text{鈥�}m)}{9.8\text{鈥�}m/s^2脳4.0\text{鈥�}m脳cos6.98掳}\\ =500\text{鈥�}kg\end{array}$

Mass of the ramp is $500\text{鈥�}kg$.

Taking moment at the hinge point and assuming x = 2 m,

From the graph, we can say that
$\text{At}\text{鈥墄}=2,{\text{F}}_{\text{h}}=2.25脳{10}^4\text{鈥�}N$

${鈭�}_{}^{}蟿=0$

$((weightoframp+weightofman)脳2\text{鈥尘})鈭�({\text{F}}_{\text{h}}脳0.490\text{鈥尘})=0$

$\begin{array}{c}((500\text{鈥�}kg脳9.8\text{鈥�}m/s^2)+(m_{man}脳9.8\text{鈥�}m/s^2))脳2\text{鈥�}m=(2.25脳{10}^4\text{鈥�}N脳0.490\text{鈥�}m)\\ 4900\text{鈥�}N+m_{man}脳9.8\text{鈥�}m/s^2=5512\text{鈥�}N\\ m_{man}脳9.8\text{鈥�}m/s^2=612\text{鈥�}N\\ m_{man}=\frac{612\text{鈥�}N}{9.8\text{鈥�}m/s^2}\\ m_{man}=62.5\text{鈥�}kg\end{array}$

Mass of the man is $62.5\text{鈥�}kg$.