The total energy of a 2.00 kg falling rock is 5000 J. If its potential
energy is 1975 J, the kinetic energy of the rock is ____ J.
The speed of the rock is ___ m/s
To find the kinetic energy of the rock, we need to subtract the potential energy from the total energy.
Kinetic Energy = Total Energy - Potential Energy
Given that the total energy is 5000 J and the potential energy is 1975 J, we can substitute these values into the equation:
Kinetic Energy = 5000 J - 1975 J
Kinetic Energy = 3025 J
Therefore, the kinetic energy of the rock is 3025 J.
To find the speed of the rock, we can use the equation:
Kinetic Energy = (1/2) * mass * velocity^2
Substituting the values we know: kinetic energy = 3025 J and the mass = 2.00 kg, we can solve for the velocity:
3025 J = (1/2) * 2.00 kg * velocity^2
Dividing both sides by (1/2) * 2.00 kg, we get:
velocity^2 = (3025 J) / (1/2) * 2.00 kg
velocity^2 = (3025 J) / (2.00 kg)
velocity^2 = 1512.5 m^2/s^2
Taking the square root of both sides:
velocity = √1512.5 m^2/s^2
Calculating this value gives us:
velocity ≈ 38.94 m/s
Therefore, the speed of the falling rock is approximately 38.94 m/s.