Answer:
First, the total energy of an object is E, and this is conserved if we do not interact with the object.
We can write:
E = U + K
Where U is the potential energy. For an object of mass M that is lifted a height H from the ground, the potential energy is:
U = M*g*H
where g is the gravitational acceleration. g = 9.8m/s^2
And K is the kinetic energy, written as:
K = (M/2)*v^2
where v is the velocity of the object.
a) We have an object with mass M = 80kg, lifted at a height H = 10m.
The gravitational potential energy is then:
U = 80kg*9.8m/s^2*10m = 7,804 J
And because the object is not moving, the velocity is equal to zero, then at this point the kinetic energy is equal to zero, which will mean that the total energy E is equal to the potential energy.
b) At the instant before hitting the ground the height of the object is near zero, then at this point the potential energy is almost zero, which means that all the potential energy has transformed into kinetic energy. Then the kinetic energy at this point should be:
K = 7,804 J
c) Work is defined as a force doing a motion.
W = F*d
F = force.
d = distance.
In this case, the force is the weight of the object.
Weight = 80kg*9.8m/s^2 = 784N
And the distance that the object moves is 10 meters, then the work done is:
W = 784N*10m = 7,840 J
d) The final velocity v can be obtained from the kinetic energy.
We know that K = (80kg/2)*v^2 = 7,840 J
v^2 = 7,840 J/40kg
v = √( 7,840 J/40kg) = 14m/s