a body of mass 2kg is released from a point 100m above the ground.
Calculate its kinetic energy 80m from the point of release.?
how long does it take to fall 80m? 4.9t^2 = 80
using that t, get v = 9.8t
using that v, get KE = 1/2 mv^2
If you massage things a bit, you can do it in one formula, but it's often best just to stick to the basic equations of motion.
V^2 = Vo^2 + 2g*(100-80) = 0 + 19.6*20 = 392,
V = 19.8 m/s @ 80 m above gnd.
KE = 0.5*M*V^2 = 0.5*2*392 = Joules.
To calculate the kinetic energy of the body 80m from the point of release, we need to find its velocity at that point.
We can use the law of conservation of energy, which states that the total mechanical energy of the body, which is the sum of its potential energy and kinetic energy, is constant throughout the motion.
Initially, the body has only gravitational potential energy because it is at rest. The potential energy is given by:
Potential Energy (PE) = mass × gravity × height
PE = m × g × h
PE = 2kg × 9.8m/s² × 100m
PE = 1960 Joules
As the body falls freely, its potential energy is converted into kinetic energy. Therefore, at any point during the fall, the potential energy will equal the kinetic energy.
So at the 80m point, the kinetic energy is:
Kinetic Energy (KE) = Potential Energy (PE)
KE = 1960 Joules
Therefore, the kinetic energy of the body at the 80m point is 1960 Joules.
To calculate the kinetic energy of the body 80m from the point of release, we need to know the velocity of the body at that point. In order to determine the velocity, we can use the principle of conservation of energy.
The body initially has gravitational potential energy due to its height above the ground, which is converted into kinetic energy as it falls. According to the conservation of energy, the sum of the initial potential energy and the initial kinetic energy is equal to the sum of the final potential energy and the final kinetic energy.
Using this principle, we can calculate the velocity of the body at a particular height using the formula for potential energy:
Potential Energy = m * g * h
where m is the mass of the body (2kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (100m).
So, the initial potential energy is:
Initial Potential Energy = 2 kg * 9.8 m/s^2 * 100 m
Once the body reaches the height of 80m, all the initial potential energy will be converted into kinetic energy. So, the final potential energy is:
Final Potential Energy = 2 kg * 9.8 m/s^2 * 80 m
Since energy is conserved, we can equate the initial and final potential energies to find the velocity at the height of 80m:
Initial Potential Energy = Final Potential Energy
2 kg * 9.8 m/s^2 * 100 m = 2 kg * 9.8 m/s^2 * 80 m
Simplifying the equation:
980 J = 784 J
So, there is a discrepancy in the calculation. It's likely that an error has been made along the way. I apologize for the mistake and will attempt to recalculate the kinetic energy using the correct values.