75 kg block is dropped from a height of 6 m. How much kinetic energy does it have when it has fallen halfway?
KE=PE=mgh
450
75*6*9.8
Answer is 4410 J
To calculate the kinetic energy of the block when it has fallen halfway, we need to understand the concept of potential energy and its conversion into kinetic energy.
1. Determine the potential energy at the starting height:
The potential energy (PE) of an object at a certain height is given by the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the height.
Given:
Mass of the block (m) = 75 kg
Height (h) = 6 m
Acceleration due to gravity (g) = 9.8 m/s²
PE = mgh
PE = 75 kg * 9.8 m/s² * 6 m
PE = 4410 J (Joules)
So, at the starting height, the potential energy of the block is 4410 Joules.
2. Determine the potential energy at the halfway point:
Since we want to find the kinetic energy at the halfway point, we first need to determine the potential energy at that point. The halfway point corresponds to a height of half the initial height.
Potential energy at the halfway point (PE_halfway) = mgh_halfway
Given that the height at the halfway point (h_halfway) is half of the initial height (h/2), we can substitute that value into the equation.
PE_halfway = mg(h/2)
PE_halfway = 75 kg * 9.8 m/s² * (6 m / 2)
PE_halfway = 2205 J (Joules)
So, at the halfway point, the potential energy of the block is 2205 Joules.
3. Convert potential energy to kinetic energy:
As the block falls, potential energy is converted to kinetic energy. At the halfway point, all the potential energy has been converted into kinetic energy.
Kinetic energy (KE) = PE_halfway
Therefore, the kinetic energy of the 75 kg block when it has fallen halfway is 2205 Joules.