Answer
Verified
402.6k+ views
Hint: Here the mass of the man is given and he drops to a concrete patio, so, his initial velocity is zero. The height is 0.5m and after striking the patio it takes 2 cm more to stop. So, the patio exerts a force on the man because man also exerts a force on the patio following Newton’s third law.
Complete step by step answer:
Mass, m= 80 kg
Initial velocity, u= 0
Height, h= 0.5 m
Using third equation of motion to find the velocity of the man striking the patio,
\[\begin{align}
&\Rightarrow {{v}^{2}}-{{u}^{2}}=2as \\
&\Rightarrow {{v}^{2}}-0=2\times 9.8\times 0.5 \\
&\Rightarrow {{v}^{2}}=9.8 \\
&\therefore v=3.13m/s \\
\end{align}\]
So, when the man strikes the ground his velocity is 3.13 m/s. Now he moves 2 cm more that is 0.02 m and finally comes to rest. Using
\[\begin{align}
&\Rightarrow {{v}^{2}}-{{u}^{2}}=2as \\
&\Rightarrow 0-{{3.13}^{2}}=2\times a\times 0.02 \\
&\therefore a=-\frac{9.8}{0.04}=-245m/{{s}^{2}} \\
\end{align}\]
Acceleration is negative because the man comes to rest.
So, the average acceleration from when his feet first touch the patio to when he stops is 245 \[m/{{s}^{2}}\].
(b) Now in order to find force using Newton’s second law
\[\begin{align}
&\Rightarrow F=ma+mg \\
&\Rightarrow F =m(g+a) \\
&\Rightarrow F =80(9.8+245) \\
&\Rightarrow F =80\times 254.8 \\
&\therefore F =20384N \\
\end{align}\]
So, the value of average force exerted is 20384 N.
Note: Here in part (B) while finding out the magnitude of average force being exerted, we have taken both the forces into account one is due to motion and the other is due to gravity. Newton’s law should be applied carefully by taking into account the directions.
Complete step by step answer:
Mass, m= 80 kg
Initial velocity, u= 0
Height, h= 0.5 m
Using third equation of motion to find the velocity of the man striking the patio,
\[\begin{align}
&\Rightarrow {{v}^{2}}-{{u}^{2}}=2as \\
&\Rightarrow {{v}^{2}}-0=2\times 9.8\times 0.5 \\
&\Rightarrow {{v}^{2}}=9.8 \\
&\therefore v=3.13m/s \\
\end{align}\]
So, when the man strikes the ground his velocity is 3.13 m/s. Now he moves 2 cm more that is 0.02 m and finally comes to rest. Using
\[\begin{align}
&\Rightarrow {{v}^{2}}-{{u}^{2}}=2as \\
&\Rightarrow 0-{{3.13}^{2}}=2\times a\times 0.02 \\
&\therefore a=-\frac{9.8}{0.04}=-245m/{{s}^{2}} \\
\end{align}\]
Acceleration is negative because the man comes to rest.
So, the average acceleration from when his feet first touch the patio to when he stops is 245 \[m/{{s}^{2}}\].
(b) Now in order to find force using Newton’s second law
\[\begin{align}
&\Rightarrow F=ma+mg \\
&\Rightarrow F =m(g+a) \\
&\Rightarrow F =80(9.8+245) \\
&\Rightarrow F =80\times 254.8 \\
&\therefore F =20384N \\
\end{align}\]
So, the value of average force exerted is 20384 N.
Note: Here in part (B) while finding out the magnitude of average force being exerted, we have taken both the forces into account one is due to motion and the other is due to gravity. Newton’s law should be applied carefully by taking into account the directions.
Recently Updated Pages
Draw a labelled diagram of DC motor class 10 physics CBSE
A rod flies with constant velocity past a mark which class 10 physics CBSE
Why are spaceships provided with heat shields class 10 physics CBSE
What is reflection Write the laws of reflection class 10 physics CBSE
What is the magnetic energy density in terms of standard class 10 physics CBSE
Write any two differences between a binocular and a class 10 physics CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Name 10 Living and Non living things class 9 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE
Select the word that is correctly spelled a Twelveth class 10 english CBSE
Fill the blanks with proper collective nouns 1 A of class 10 english CBSE