Answer:
a) Ep = 5886[J]; b) v = 14[m/s]; c) W = 5886[J]; d) F = 1763.4[N]
Explanation:
a)
The potential energy can be found using the following expression, we will take the ground level as the reference point where the potential energy is equal to zero.
[tex]E_{p} =m*g*h\\where:\\m = mass = 60[kg]\\g = gravity = 9.81[m/s^2]\\h = elevation = 10 [m]\\E_{p}=60*9.81*10\\E_{p}=5886[J][/tex]
b)
Since energy is conserved, that is, potential energy is transformed into kinetic energy, the moment the harpsichord touches water, all potential energy is transformed into kinetic energy.
[tex]E_{p} = E_{k} \\5886 =0.5*m*v^{2} \\v = \sqrt{\frac{5886}{0.5*60} }\\v = 14[m/s][/tex]
c)
The work is equal to
W = 5886 [J]
d)
We need to use the following equation and find the deceleration of the diver at the moment when he stops his velocity is zero.
[tex]v_{f} ^{2}= v_{o} ^{2}-2*a*d\\where:\\d = 2.5[m]\\v_{f}=0\\v_{o} =14[m/s]\\Therefore\\a = \frac{14^{2} }{2*2.5} \\a = 39.2[m/s^2][/tex]
By performing a sum of forces equal to the product of mass by acceleration (newton's second law), we can find the force that acts to reduce the speed of the diver to zero.
m*g - F = m*a
F = m*a - m*g
F = (60*39.2) - (60*9.81)
F = 1763.4 [N]
The gravitational potential energy of the diver is 6000 J.
The gravitational potential energy = mgh
m = mass of the diver = 60 kg
g = acceleration due to gravity = 10 ms-2
h = height = 10 m
gravitational potential energy = 60 kg × 10 ms-2 × 10 m = 6000 J
Recall that the potential energy of the diver = kinetic energy does the diver have as he strikes the water. Hence, kinetic energy does the diver have as he strikes the water is 6000J.
The work done by the water= gravitational potential energy.
Hence, the work done by the water on the diver to stop his momentum = 6000 J.
Recall that; work done = Force × distance
Force = work done/distance
Force = 6000J/2.5 m
Force = 2400 N
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