Given parameters:
Initial velocity of Coin = 0m/s
Time taken before coin hits ground = 5.7s
Unknown:
Final velocity of the coin = ?
Velocity is displacement with time. To solve this problem, we have to apply one of the equations of motion.
The fitting one of them here is shown below;
V = U + gt
where;
V is the final velocity
U is the initial velocity
g is the acceleration due to gravity
t is the time taken
Here we use positive value of acceleration due to gravity because the coin is falling with the effect of acceleration and not against it.
Now input the parameters and solve;
V = 0 + 9.81 x 5.7
V = 55.917m/s
Therefore, the final velocity is 55.917m/s.
Answer
given,
D = 50 mm = 0.05 m
d = 10 mm = 0.01 m
Force to compress the spring
![F = \dfrac{d^4G\delta}{8D^3N}](https://tex.z-dn.net/?f=F%20%3D%20%5Cdfrac%7Bd%5E4G%5Cdelta%7D%7B8D%5E3N%7D)
![\dfrac{\delta}{N} = p - d = 14 - 10 = 4 mm](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cdelta%7D%7BN%7D%20%3D%20p%20-%20d%20%3D%2014%20-%2010%20%3D%204%20mm)
![F = \dfrac{d^4G}{8D^3}\times 0.004](https://tex.z-dn.net/?f=F%20%3D%20%5Cdfrac%7Bd%5E4G%7D%7B8D%5E3%7D%5Ctimes%200.004)
![F = \dfrac{0.1^4\times 79\times 10^9}{8\times 0.05^3}\times 0.004](https://tex.z-dn.net/?f=F%20%3D%20%5Cdfrac%7B0.1%5E4%5Ctimes%2079%5Ctimes%2010%5E9%7D%7B8%5Ctimes%200.05%5E3%7D%5Ctimes%200.004)
F = 3160 N
stress correction factor from stress correction curve is equal to 1.1
now, calculation of corrected stress
![\tau = \dfrac{8FDk_s}{\pi d^3}](https://tex.z-dn.net/?f=%5Ctau%20%3D%20%5Cdfrac%7B8FDk_s%7D%7B%5Cpi%20d%5E3%7D)
![\tau = \dfrac{8\times 3160 \times 0.05 \times 1.1}{\pi \times 0.01^3}](https://tex.z-dn.net/?f=%5Ctau%20%3D%20%5Cdfrac%7B8%5Ctimes%203160%20%5Ctimes%200.05%20%5Ctimes%201.1%7D%7B%5Cpi%20%5Ctimes%200.01%5E3%7D)
= 442.6 Mpa
The tensile strength of the steel material of ASTM A229 is equal to 1300 Mpa
now,
![\tau_s \leq 0.45 S_u](https://tex.z-dn.net/?f=%5Ctau_s%20%5Cleq%200.45%20S_u)
![\tau_s \leq 0.45 \times 1300](https://tex.z-dn.net/?f=%5Ctau_s%20%5Cleq%200.45%20%5Ctimes%201300)
![\tau_s \leq 585\ Mpa](https://tex.z-dn.net/?f=%5Ctau_s%20%5Cleq%20585%5C%20Mpa)
since corrected stress is less than the
hence, spring will return to its original shape.
Answer:
B) 10^-2 cm/s
in term of meter. it is 10^-4 m/s
Explanation: