A 1 kg object requires 10 N of force to lift it 5 m from the bottom of a well. (use g = 10 m/s2). The object is then dropped. What is the total energy when the object has fallen halfway down the well (2.5m)?
That depends upon where you define the level of zero potential energy to be. If it is the bottom of the well, the object has 50 J of potential energy when lifted 5 meters from the bottom.
While it falls, it retains that total energy. Half of it will be kinetic energy halfway down.
To determine the total energy when the object has fallen halfway down the well, we need to consider the potential energy and kinetic energy of the object at that point.
1. Determine the potential energy:
The potential energy (PE) is given by the formula: PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance above a reference point.
Given:
Mass of the object (m) = 1 kg
Acceleration due to gravity (g) = 10 m/s^2
Height (h) = 2.5 m (halfway down the well)
Using the formula, we can calculate the potential energy:
PE = 1 kg * 10 m/s^2 * 2.5 m
2. Determine the kinetic energy:
When the object has fallen halfway down the well, it will have converted some of its potential energy into kinetic energy.
The kinetic energy (KE) is given by the formula: KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity.
Given:
Mass of the object (m) = 1 kg
To find the velocity (v), we can use the concept of conservation of energy. The object will have converted all of its potential energy into kinetic energy halfway down, so:
Potential energy at the top = Kinetic energy halfway down
m * g * h = 0.5 * m * v^2
Solving for v:
v^2 = 2 * g * h
v = √(2 * 10 m/s^2 * 2.5 m)
3. Calculate the kinetic energy:
KE = 0.5 * m * v^2
Now that we have the velocity (v), we can compute the kinetic energy at this point.
4. Calculate the total energy:
The total energy (TE) is the sum of potential energy and kinetic energy.
TE = PE + KE
Substitute the values we calculated to find the total energy when the object has fallen halfway down the well.