Answer:
a. l = 19.7m, b. 18.55m, c. Impact Force = 3889.84 N
Explanation:
The total energy of the system when the person is at top of the bridge is
Potential energy = mgh, Kinetic energy = 0
The total energy of the system when the person reaches just above the surface
Potential energy = 0, Kinetic energy = 0, Spring energy = ½ K X2, where k is the spring constant and X is the deflection
Applying conservation of energy
mgh = 0 + 0 + ½ K X²
80 x 9.81 x 40 = ½ (3600/l) X²
31392 = ½ (3600/l) X²
We can also conclude that
l+ X + 1.75 = 40
l + X = 38.25
a. <u>Substitute the value of x from above into the energy conversion expression</u>
31392 = ½ (3600/l)(38.25 - l)²
31392 x 2/3600 = (38.25 + l² – 2l(38.25))/l
17.44l = l2 – 76.5l + 38.25²
l² – 76.5l – 17.44l +1463.0625 = 0
Solving for l we get
L = 19.7
Hence, length of the rope is 19.7m
b. <u>The deflection is calculated by using the relation between l and X</u>
L + X = 38.25
X = 38.25 – 19.7 = 18.55m
c. <u>The impact force is calculated using the impact force formula which relates the impact force with the deflection</u>
F = KX
F = (3600/l) . X
F = (3600/19.7) . (18.55) = 3889.84 N
Thus, the impact force is 3889.84 N
