a 2kg stone is dropped from the top of a 20 buliding (a) at what height does its potential energy energy equal to its kinetic energy?
To determine the height at which the potential energy equals the kinetic energy, we need to understand the concept of potential energy and kinetic energy.
Potential energy (PE) is the energy stored in an object due to its position, relative to other objects. In this case, we are dealing with gravitational potential energy, which depends on the height of the object and the force of gravity. The formula for gravitational potential energy is:
PE = m * g * h
Where:
PE represents the potential energy
m is the mass of the object (2kg in this case)
g is the acceleration due to gravity (approximated as 9.8 m/s^2 on Earth)
h is the height above the reference point (in this case, the top of the building)
Since we want to find the height at which potential energy matches kinetic energy, we can equate PE to kinetic energy (KE):
PE = KE
Now, the kinetic energy of an object is given by the formula:
KE = 0.5 * m * v^2
Where:
KE represents the kinetic energy
m is the mass (2kg in this case)
v is the velocity of the object
At any given time during free-fall, the potential energy of the object is converted entirely into kinetic energy, neglecting any other forms of energy loss (such as air resistance). To find the velocity at which the potential energy equals the kinetic energy, we equate PE to KE:
m * g * h = 0.5 * m * v^2
Simplifying the equation by canceling out the mass (m) on both sides, we get:
g * h = 0.5 * v^2
Since the initial velocity is zero when the object is dropped, we can simplify further:
g * h = 0.5 * (0) = 0
Therefore, we find that the height at which the potential energy equals the kinetic energy is at ground level (h = 0).