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bekas [8.4K]
3 years ago
9

"a 10 kg rock is pushed off the edge of a bridge 50 meters above the ground. what was the kinetic energy of the rock at the midw

ay point of its fall?"
Physics
1 answer:
valentinak56 [21]3 years ago
8 0
Let's call h the initial height of the rock (h=50 m, the height of the bridge).

Initially, the rock has only gravitational potential energy, which is given by
U_i=mgh
where m=10 kg is the mass of the rock while g is the gravitational acceleration. So, the total mechanical energy of the rock at this point is
E_i = U_i = mgh=(10 kg)(9.81 m/s^2)(50 m)=4905 J

At midway point of its fall, its height is \frac{h}{2}, so its potential energy is
U_f = mg \frac{h}{2} = (10 kg)(9.81 m/s^2)(25 m)=2452.5 J
But now the rock is also moving by speed v, so it also has kinetic energy:
K_f =  \frac{1}{2}mv^2
So the total energy at the midway point of the fall is
E_f = U_f + K_f (1)

The mechanical energy must be conserved, so E_i = E_f, so we can rewrite (1) and solve it to find the kinetic energy of the rock at midway point of its fall:
E_i = U_f + K_f
K_f = E_i - U_f = 4905 J - 2452.5 J=2452.5 J
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