Answer:
Approximately [tex]8.4 \times 10^{2}\; \rm N[/tex], assuming that [tex]g = 9.8\; \rm m \cdot s^{-2}[/tex].
Explanation:
Let [tex]m[/tex] and [tex]a[/tex] denote the mass and acceleration of Spiderman, respectively.
There are two forces on Spiderman:
The directions of these two forces are exactly opposite of one another. Besides, because Spiderman is accelerating upwards, the magnitude of [tex]F(\text{tension})[/tex] (which points upwards) should be greater than that of [tex]W[/tex] (which points downwards towards the ground.)
Subtract the smaller force from the larger one to find the net force on Spiderman:
[tex](\text{Net Force}) = F(\text{tension}) - W[/tex].
On the other hand, apply Newton's Second Law of motion to find the value of the net force on Spiderman:
[tex](\text{Net Force}) = m \cdot a[/tex].
Combine these two equations to get:
[tex]m \cdot a = (\text{Net Force}) = F(\text{tension}) - W[/tex].
Therefore:
[tex]\begin{aligned}& F(\text{tension})\\ &= m \cdot a + W \\ &= m \cdot (a + g)\\ &= 76\; \rm kg \times \left(1.3\; \rm m \cdot s^{-2} + 9.8\; \rm m \cdot s^{-2}\right)\\ &\approx 8.4\times 10^{2}\; \rm N\end{aligned}[/tex].
By Newton's Third Law of motion, Spiderman would exert a force of the same size on the strand of web. Hence, the size of the force in the strand of the web should be approximately [tex]8.4\times 10^{2}\; \rm N[/tex] (downwards.)
