a 2.0 kg rock sits on the edge of a cliff 12m above the beach. The rock falls off the cliff. How much kinetic energy will it have just before it hits the beach?
To calculate the kinetic energy of the rock just before it hits the beach, we need to use the equation for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
First, we need to calculate the velocity of the rock just before it hits the beach. To do this, we can use the equation for gravitational potential energy:
Potential Energy = mass * gravitational acceleration * height
Given:
Mass (m) = 2.0 kg
Height (h) = 12 m
Gravitational acceleration (g) = 9.8 m/s^2
Plugging in these values into the equation, we get:
Potential Energy = 2.0 kg * 9.8 m/s^2 * 12 m = 235.2 J
When the rock falls to the ground, all of its potential energy is converted into kinetic energy. Therefore, the kinetic energy just before it hits the beach is equal to the potential energy:
Kinetic Energy = 235.2 J
So, the rock will have 235.2 Joules of kinetic energy just before it hits the beach.
To determine the kinetic energy of the rock just before it hits the beach, we can use the principle of conservation of energy. The potential energy that the rock initially has while sitting on the edge of the cliff will be converted into kinetic energy as it falls.
First, we need to calculate the potential energy of the rock at the edge of the cliff using the formula for potential energy:
Potential energy = mass × acceleration due to gravity × height
Given:
Mass of the rock (m) = 2.0 kg
Height above the beach (h) = 12 m
Acceleration due to gravity (g) = 9.8 m/s²
Potential energy = 2.0 kg × 9.8 m/s² × 12 m
Potential energy = 235.2 Joules
Since the potential energy is converted entirely into kinetic energy as the rock falls, the kinetic energy just before it hits the beach will be equal to the potential energy.
Therefore, the kinetic energy of the rock just before it hits the beach is 235.2 Joules.